domain: sde sdv

text:
Kristina Likhacheva

Vincent Bretagnolle

Isabelle Arpin

An exploration of the influence of problem wickedness on project pluralism in sustainability science

Keywords: wicked problems, methodological pluralism, collaborative pluralism, transdisciplinary research, research stances and methods, LTSER

come

Introduction

In the 1960s and 1970s, urban planners identified a new type of problem, which they described as particularly complex, open-ended, and intractable [START_REF] Churchman | Guest editorial: Wicked problems[END_REF][START_REF] Rittel | Dilemmas in a general theory of planning[END_REF]. They termed these problems 'wicked' as there was no consensus on the definitions of and solutions to these problems [START_REF] Roberts | Wicked problems and network approaches to resolution[END_REF] and attempts to solve them often tended to have irreversible consequences and negatively impact the overall situation [START_REF] Xiang | Working with wicked problems in socio-ecological systems: Awareness, acceptance, and adaptation[END_REF]. The term 'wicked problems' has become increasingly popular, especially in environmental studies, and has been used to the point of losing some of its meaning [START_REF] Alford | Wicked and less wicked problems: a typology and a contingency framework[END_REF][START_REF] Peters | What is so wicked about wicked problems? A conceptual analysis and a research program[END_REF]). As a result, degrees of wickedness have been introduced [START_REF] Head | Wicked problems: Implications for public policy and management[END_REF][START_REF] Termeer | A critical assessment of the wicked problem concept: Relevance and usefulness for policy science and practice[END_REF]. In particular, [START_REF] Alford | Wicked and less wicked problems: a typology and a contingency framework[END_REF] have proposed a typology of wickedness based on the level of the intractability of the problem and the distribution of problem knowledge, interests, and power among affected actors.

Another idea gained ground in the 1990s: ecological and social systems are deeply intertwined, and scholars should focus on their interrelationship [START_REF] Berkes | Linking social and ecological systems: management practices and social mechanisms for building resilience[END_REF][START_REF] Collins | An integrated conceptual framework for long-term social-ecological research[END_REF]. This argument gave birth to the concept of social-ecological systems, now defined as complex adaptive systems formed by interacting social and ecological systems [START_REF] Preiser | Social-ecological systems as complex adaptive systems[END_REF]). Social-ecological systems have been found to teem with wicked problems [START_REF] Xiang | Working with wicked problems in socio-ecological systems: Awareness, acceptance, and adaptation[END_REF][START_REF] Head | Why is an APT approach to wicked problems important?[END_REF], with climate change, biodiversity loss, and waste used as classic examples [START_REF] Russell | A philosophical framework for an open and critical transdisciplinary inquiry[END_REF][START_REF] Chan | The ethics of working with wicked urban waste problems: The case of Singapore's Semakau Landfill[END_REF]. In fact, wicked problems and social-ecological systems share common characteristics such as scale sensitivity, path dependence, context dependence, and non-linear relationships [START_REF] Akamani | Managing wicked environmental problems as complex social-ecological systems: The promise of adaptive governance[END_REF]. They may be seen as two faces of the same coin and have become core concepts of an emerging scientific discipline: sustainability science.

Sustainability science has been defined in various ways (see [START_REF] Komiyama | Sustainability science: Building a new discipline[END_REF][START_REF] Kates | What kind of a science is sustainability science[END_REF][START_REF] Spangenberg | Sustainability science: A review, an analysis and some empirical lessons[END_REF][START_REF] Shahadu | Towards an umbrella science of sustainability[END_REF][START_REF] Fang | What kind of a science is sustainability science?' An evidence-based reexamination[END_REF][START_REF] Mino | Framing in sustainability science: Theoretical and practical approaches[END_REF]. We retain the definition by Fang et al. (2018: 12), based on an extensive literature analysis: 'Sustainability science is a use-inspired basic science of sustainable development, which focuses on understanding human-environment interactions and linking the understanding to actions by promoting a place-based, multi-scale, and transdisciplinary approach'. Beyond minor differences, all definitions emphasise that sustainability science is problem-driven and aims to tackle 'real-world' problems, especially wicked ones.

However, the literature on the influence of problem wickedness on the practice of sustainability science is curiously sparse. Regarding its influence on the participation of nonacademic actors, Bieluch et al. (2017) found that the preferences of local government officers for different participation strategies were significantly impacted by problem wickedness, except for environmental problems (as opposed to economic and policy problems). [START_REF] Schneider | Promising degrees of stakeholder interaction in research for sustainable development[END_REF] identified the level of contestation of a problem as one of six criteria impacting stakeholder interaction processes. As for the influence of problem wickedness on the methods used, to our knowledge, it has not been investigated so far. Here we intend to help fill this gap by investigating the relationship between the wickedness level of the problems addressed and how scientists handle these problems in practice.

More specifically, we address the following question: what is the relationship between the wickedness of the problems and the research stances and methods adopted to address these problems? We explored this relationship by analysing a sample of research projects from a national network designed to foster long-term and place-based inter-and transdisciplinary environmental research in France. In brief, we expected a positive relationship between the wickedness of the problems, the variety of research methods, and the plurality of nonacademic partners in the research project (see the rationale for these expectations below).

First, we review the literature about research stances and methods in sustainability science. Then, we explain how we constructed our sample, and how we investigated and compared the wickedness of the problems addressed and the research stances and methods adopted. After presenting our results, we offer interpretations for the more limited than expected correspondence we found between them.

Research stances and methods in sustainability science

Here we understand a research stance as a strategy used to deal with a given wicked problem. A classical research stance is reductionism, which consists of simplifying the complexity of a problem as much as necessary to be able to solve it [START_REF] Hazard | A tool for reflecting on research stances to support sustainability transitions[END_REF]. Reductionism often entails bringing a real-world problem into a place (typically, a laboratory or a model) where the scientists can reduce its complexity and then export the solution to the real world. It is thus based on a series of displacements between the real world and a 'truth-spot' [START_REF] Gieryn | Three truth-spots[END_REF][START_REF] Gieryn | City as truth-spot: Laboratories and field-sites in urban studies[END_REF], as shown by numerous social studies of science in recent decades (e.g. [START_REF] Latour | Give me a laboratory and I will raise the world[END_REF]). This reductionist stance has resulted in the gradual distancing of scientists from the rest of society and the emergence of a growing number of disciplines.

In contrast, sustainability scientists working on social-ecological systems seek precisely to account for their complexity. They consider reductionism to be ill-suited to the characteristics of wicked problems and doomed to failure when attempting to tackle them [START_REF] Pahl-Wostl | Transition towards a new global change science: Requirements for methodologies, methods, data and knowledge[END_REF]Head and Xiang 2016b;[START_REF] Preiser | Complexitybased social-ecological systems research: Philosophical foundations and practical implications[END_REF]. Wicked problems cannot be detached from the real world and integrating their complexity, rather than reducing it, is seen as crucial to addressing them in a more appropriate manner [START_REF] Klenk | Climate change and transdisciplinary science: Problematizing the integration imperative[END_REF]. Furthermore, sustainability scientists propose bringing together research actors with various disciplinary backgrounds and societal actors to conduct inter-and transdisciplinary research on wicked problems [START_REF] Lang | Transdisciplinary research in sustainability science: Practice, principles, and challenges[END_REF][START_REF] Jahn | Transdisciplinarity: Between mainstreaming and marginalization[END_REF][START_REF] Brandt | A review of transdisciplinary research in sustainability science[END_REF]. Defined as 'iterative and collaborative processes involving diverse types of expertise, knowledge and actors to produce context-specific knowledge and pathways towards a sustainable future' (Norström et al. 2020: 183), knowledge co-production is considered crucial for integration and transdisciplinary research as they are understood in sustainability science [START_REF] Holzer | A methodology for evaluating transdisciplinary research on coupled socio-ecological systems[END_REF][START_REF] Wyborn | Co-producing sustainability: Reordering the governance of science, policy, and practice[END_REF][START_REF] Norström | Principles for knowledge co-production in sustainability research[END_REF].

Such calls for renewed research stances have pushed for a re-thinking of research methods. We define a research method as a 'codified way of producing knowledge of a focus of interest' (de Vos et al. 2019: 2). Research methods are the concrete means by which researchers produce knowledge and are at the very heart of scientific practice and innovation [START_REF] Koppman | Who moves to the methodological edge? Factors that encourage scientists to use unconventional methods[END_REF]. As their design and implementation usually require specific skills and entail risks and rewards, research methods are crucial for defining who can engage in the research process and who is left out. They also strongly influence the results and outcomes of research. The research strategies promoted to address wicked problems in socialecological systems are expected to entail major changes in classical research methods1 , if not their complete overhaul [START_REF] Preiser | Social-ecological systems as complex adaptive systems[END_REF].

In fact, there has been a recent burst of publications on the methodological issues and challenges of sustainability science [START_REF] Poteete | Working Together: Collective Action, the Commons, and Multiple Methods in Practice[END_REF][START_REF] Spangenberg | Sustainability science: A review, an analysis and some empirical lessons[END_REF][START_REF] Caniglia | Experiments and evidence in sustainability science: A typology[END_REF][START_REF] Wehrden | Methodological challenges in sustainability science: A call for method plurality, procedural rigor and longitudinal research[END_REF][START_REF] Preiser | Social-ecological systems as complex adaptive systems[END_REF]Caniglia et al. 2020;[START_REF] Jerneck | Theoretical and methodological pluralism in sustainability science[END_REF][START_REF] Biggs | The Routledge handbook of research methods for social-ecological systems[END_REF]. Researchers have emphasised the wealth of methods that may be useful in tackling wicked problems and stressed the value of methodological pluralism, i.e. 'the use of different methods with the aim of investigating a common phenomenon but from different perspectives' (Biggs et al. 2022: 52). Over the last decade, various lists and typologies of methods targeted at newcomers to the field (e.g. [START_REF] Biggs | The Routledge handbook of research methods for social-ecological systems[END_REF] 2 ) have been developed to encourage sustainability scientists to broaden their range of research methods and help them select methods appropriate to the specific problems they seek to address. For example, [START_REF] Vos | Methods for understanding social-ecological systems: A review of place-based studies[END_REF] identified more than 300 methods that they grouped into 28 categories [START_REF] Biggs | The Routledge handbook of research methods for social-ecological systems[END_REF].

Collaborative pluralism and methodological pluralism are, therefore, two cornerstones of sustainability science. Our goal here was not to provide sustainability scientists with an additional toolkit on how to achieve this dual pluralism but to study the level of pluralism scientists adopt when dealing with diversely wicked sustainability problems in socialecological systems. To do so, we interviewed all the leaders of a distributed national network of research infrastructures designed to promote inter-and transdisciplinary environmental research. We asked them to describe at least one ongoing (or recently completed) research project in this field. Drawing a sample of projects from a single national research network had two important advantages: first, the commonality of language facilitated the collection of information on the projects; second, the fact that the projects took place in the same context, or at least very similar, scientific and administrative contexts, made it easier to explore the relationship between the complexity of the problems and the research positions and methods adopted.

For each project, we then investigated three core aspects. First, we analysed the wickedness level of the problem addressed by decomposing wickedness into two dimensions, as suggested by [START_REF] Alford | Wicked and less wicked problems: a typology and a contingency framework[END_REF]: i) the difficulty of defining both the problem and its solution(s) (cognitive complexity); ii) the heterogeneity of the actors affected by this problem and the level of conflict among these actors (political complexity of the problem). We expected a positive relationship between these two dimensions, i.e. that the difficulty in defining the problem and its solution(s) would increase alongside the heterogeneity of the actors affected and the level of conflict over the problem (or vice versa). Second, we also decomposed project pluralism into two dimensions: the diversity of the research partners (collaborative pluralism of the project) and the diversity of methods used (methodological pluralism of the project). We again expected a positive relationship, i.e. that the diversity of methods would increase with the diversity of partners. Finally, we analysed the relationship between problem wickedness and project pluralism.

We expected that i) the diversity of research partners involved in the projects (collaborative pluralism of the project) would reflect the diversity of actors affected by the problem addressed (political complexity of the problem); ii) the diversity of methods used (methodological pluralism of the project) would reflect the cognitive complexity of the problem. Our overarching hypothesis was, therefore, that researchers addressing more wicked problems would consider it necessary to resort to a wider range of methods and partners than researchers addressing less wicked problems.

Methods

The French network of 'Zones Ateliers' as a case study

Zones Ateliers (ZAs) are the French version of long-term social-ecological research (LTSER) sites at the international level [START_REF] Haberl | From LTER to LTSER: Conceptualizing the socio-economic dimension of long-term socioecological research[END_REF][START_REF] Angelstam | LTSER platforms as a place-based transdisciplinary research infrastructure: learning landscape approach through evaluation[END_REF]. They are placebased research infrastructures that were initiated by the French National Centre for Scientific Research (CNRS) in the early 2000s to promote long-term inter-and transdisciplinary research at the interface between nature and society [START_REF] Lévêque | Les zones ateliers, des dispositifs pour la recherche sur l'environnement et les anthroposystèmes: Une action du programme 'Environnement, vie et sociétés du CNRS[END_REF]. The 14 current ZAs address a broad array of sustainability problems, including the impacts of industrial agriculture on biodiversity and human health, of large-scale facilities on the functioning of rivers, or of climate change on farming practices3 . They have recently placed socialecological systems at the core of their common conceptual framework [START_REF] Bretagnolle | Action-orientated research and framework: Insights from the French long-term social-ecological research network[END_REF]. As they cover a wide range of social-ecological systems across the country, they provided us with a diversity of research projects aimed at tackling diversely wicked sustainability problems.

Selecting a sample of research projects from the LTSER network

Following others (e.g. [START_REF] Bammer | Enhancing research collaborations: Three key management challenges[END_REF]Hirsch Hadorn et al. 2008;[START_REF] Wiek | From complex systems analysis to transformational change: A comparative appraisal of sustainability science projects[END_REF][START_REF] Newig | Linking modes of research to their scientific and societal outcomes: Evidence from 81 sustainability-oriented research projects[END_REF], we analysed research projects as the basic unit for conducting our investigation. Indeed, research projects, i.e. 'temporally, financially and staff-wise limited units of activities in relation to one or more related research goals' (Newig et al. 2019: 149), are relatively easy to identify and constitute meaningful entities for research actors and their partners.

In spring 2020, we conducted remote interviews with the ZA leaders to identify at least one transdisciplinary research project underway or recently completed. The selected research projects had to tackle a complex environmental issue (we deliberately did not use the term 'wicked problem'). We asked our informants to specify the objectives and stage of development of these projects and the partners involved. We defined research partners as individuals or institutions formally engaged in the projects through their participation, e.g. in the design of research questions and methods, the collection and analysis of data, or the dissemination of results. We also relied on project websites and available documents (responses to research calls, reports, and published papers) and, where necessary, email exchanges and interviews with project leaders to complete the project information. We selected all projects for which we had sufficient information on the problem addressed, the project members and partners, and the methods used. The sample of 17 projects we obtained included at least one project from each ZA. We asked the project leaders to validate a synoptic presentation of their project (see table 1).

Project classification and positioning

Based on the material collected, we analysed for each project i) the cognitive complexity of the problem addressed; ii) its political complexity; iii) the methodological pluralism of the project; iv) its collaborative pluralism. We developed two analysis grids, one with the two dimensions corresponding to the wickedness of the problems addressed (grid 1) and the other with the two dimensions corresponding to the pluralism of the projects (grid 2). We then proceeded in two steps.

First, we developed a coarse-grained classification of the 17 projects and corresponding problems by implementing a three-level gradation (low, medium and high) for each dimension in the two grids, resulting in nine boxes in each grid (three boxes per dimension). We placed all projects and corresponding problems in the appropriate box of the two grids. Two of the authors proceeded separately and compared their results, seeking agreement with the third author in the few cases where they had assigned different boxes to a project or a problem. We then presented our preliminary results to the project leaders through email and in an online meeting, asking them to check that we had positioned their project and the problem it addressed in the correct box of each grid according to their knowledge and understanding of our work. The project leaders validated our positioning of the vast majority of projects and corresponding problems (86% agreement, n=34). Discussions based on additional information on the projects led us to move them to a neighbouring box in one case (#17) for grid 1 and four cases (#2, 4, 5, 16) for grid 2.

Then, we refined this preliminary classification by positioning each problem (grid 1) or project (grid 2) in relation to its neighbours within a cell. Each project or problem was thus assigned not only a specific cell but also a specific position within that cell. This allowed us to assign coordinates to each project (problem) on the x-and y-axes of grid 1 (2). We did not ask the project leaders to validate this second step, as it required comparative knowledge of the different projects. Below we detail the criteria we used to assign the level of complexity of the problems and the pluralism of the projects.

Grid 1: Problem wickedness

The cognitive and political complexity of the problems addressed appear on the y-and xaxes, respectively, of grid 1. We adapted the criterion proposed by [START_REF] Alford | Wicked and less wicked problems: a typology and a contingency framework[END_REF] to evaluate the cognitive complexity of the problem addressed in each project (see table 2). Indeed, we found it challenging to evaluate the clarity of the problem and the clarity of the solution(s) separately, as suggested by these authors. Instead, we considered the cognitive complexity low when both the problem and its solution(s) appeared to be clear, intermediate when they were moderately clear, and high when they were unclear. In turn, we used the criterion they proposed to evaluate the political complexity of the problem. We considered the political complexity to be low when access to relevant knowledge about the problem was relatively easy, and conflict over the problem was limited; intermediate when access to relevant knowledge was difficult but the level of conflict was limited; and high when access to knowledge was difficult, and the level of conflict was high.

Grid 2: Project pluralism

The methodological and collaborative pluralism of the projects are represented on the y-and x-axes, respectively, of grid 2. To evaluate methodological pluralism, we considered the number of methods used and the number of research approaches to which they relate. Biggs et al. (2022) distinguished between three types of research approaches: analytical/objective approaches, which are grounded in empirical measurements that are quantified and aim to generate objective descriptions of the phenomena studied; interpretive/subjective approaches, which focus on the meanings, experiences, feelings, and interpretations that people attach to phenomena; and collaborative approaches, which aim to co-produce knowledge and elicit or integrate different types of knowledge. Considering not only the number of research methods but also the number of research approaches to which they relate is crucial because it encompasses the epistemological distance among them. Using two methods associated with distinct approaches might entail a similar or even higher level of methodological pluralism than using more methods associated with a unique research approach.

We considered the diversity of methods to be low if the methods used in a project related to a single research approach, regardless of the number of methods used; intermediate if two research approaches were used, with one or two methods for each research approach; and high when two research approaches were used with more than two methods for each research approach, or when all three research approaches were used, regardless of the number of methods used. Regarding collaborative pluralism, we split project partners following the OECD typology of non-academic actors that distinguishes among four categories: the private sector (i.e. business and industry), the public sector (i.e. government and civil service), the civic sector (i.e. civil society and non-governmental organisations), and citizens/communities (OECD, 2020). We considered the diversity of project partners to be low when only academics were involved in the project, intermediate when at most two categories of nonacademic actors were also involved, and high when this was the case for at least three categories. We tested the correlations between the political complexity (x-coordinate on grid 1) and the cognitive complexity (y-coordinate on grid 1) of the problems, and between the collaborative pluralism (x-coordinate on grid 2) and the methodological pluralism of the corresponding projects (y-coordinate on grid 2). We also compared the respective positions of the political complexity of the problem (x-coordinate on grid 1) and the collaborative pluralism of the project (x-coordinate on grid 2), as well as the respective positions of the cognitive complexity of the problem (y-coordinated on grid 1) and the methodological pluralism of the project (y-coordinated on grid 2). Finally, we projected each of the 17 problems (projects) onto the diagonal (y=x) of grid 1 (2). This gave us new coordinates (projectGrid1 and projectGrid2), which represent the wickedness of the problem and the pluralism of the project. We then tested the correlation between these coordinates. Given the small sample size, all correlations were tested using non-parametric Spearman tests. All statistical tests were performed using RStudio.

Results

Problem wickedness

In line with our expectations, there was an overall slightly positive (r=0.21) albeit nonsignificant (p=0.4, n=17) trend within our sample of projects regarding the cognitive and political complexity of the problems addressed (see Grid 1 in Fig. 1). In other words, the problems addressed and their solutions were more difficult to define as the range of actors affected grew. Indeed, no projects that addressed a very unclear problem affected a narrow range of actors, nor, symmetrically, did a problem affect a wide range of actors and address a clear problem with clear solutions. However, there were many exceptions, as underlined by the non-significant relationship, since several projects were not aligned on the diagonal, with a majority of them positioned below it (Fig. 1). This finding reveals that the political complexity of the problem addressed in these projects contributed more to the overall problem wickedness than its cognitive complexity. The opposite was true for only three projects (#2, 9, 15). It can also be noted that a large majority of projects in our sample addressed moderately wicked problems, two of them (#5, 6) very wicked problems, and one a weakly wicked problem (#14).

Project pluralism

Again as expected, we found an overall positiveand weakly significant (r=0.49, p=0.04, n=17; Fig. 2)relationship between methodological pluralism and collaborative pluralism within our sample of projects. In other words, the diversity of methods increased with the diversity of research partners. There were no projects with low heterogeneity of research partners and intermediate or high diversity of research methods, nor with a high diversity of research partners and low diversity of research methods. Five projects (#1, 3, 6, 9, 15) were very well aligned on the diagonal, which means that their collaborative and methodological pluralism contributed equally to their overall pluralism. Four projects (#2, 8, 11, 12) were almost aligned on the diagonal. Six projects (#4, 5, 7, 10, 13, 16) were substantially below the diagonal, which means that their collaborative pluralism contributed more to their overall pluralism than their methodological pluralism. The opposite was true for two projects (#14, 17).

Correspondence between problem wickedness and project pluralism

Only four pairs of project and associated problem (#4, 6, 7, 11) occupied the same box (out of nine possibilities) in both grids (Figs. 1, 2), i.e. contrary to our initial expectations, the correspondence between problem wickedness and project pluralism was actually limited. As said, we refined these results by testing the correlation between the coordinates of the projects and their associated problems projected onto the diagonals of the two grids (Fig. 3a) We found an overall tendency toward positive correlation, which was marginally significant (r=0.41; p=0.08, n=17; see Fig. 3a), indicating that the relative positions of the projects in the two grids along the diagonals were more or less conserved. However, this held particularly true for the right part of the graph, i.e. the most wicked projects, while the level of correspondence between problem wickedness and project pluralism was more dispersed around the diagonal when problem wickedness was low (Fig. 3a). In weakly wicked projects, project pluralism was either slightly higher (#15), much higher (#1, 14), slightly lower (#9), or much lower (#8) than expected given the wickedness of the problem at hand. On the contrary, projects addressing highly wicked problems tended to have a level of pluralism that did not deviate much from the wickedness level of the problem addressed. Six projects (#4, 6, 7, 11, 12, 15) were almost perfectly aligned on the diagonal. Their levels of problem wickedness and project pluralism contrasted, ranging from low (e.g. #15) to high (e.g. #6). Main outliers (detected from their distance to the diagonal, in reference to Fig. 3) were #1, 2, 14, and 17 above the diagonal, and #8, 9, and 13 below the diagonal (and to a lesser extent, #3, 5, 10, and 16). Conversely, by using the residual distance of each project from the corresponding diagonals, we found no relationships between the residuals in grid 1 versus grid 2 (Fig. 3b).

We designated the situations where the methodological (collaborative) pluralism was close to expected given the cognitive (political) complexity of the problem addressed as methodological (collaborative) correspondence, as methodological (collaborative) reductionism when it was lower, and as methodological (collaborative) integrationism when it was higher. We found that most projects presented at least one type of correspondence but that reductionism and integrationism were also well represented in our sample (Table 4). We found no project with methodological integrationism and collaborative reductionism or vice versa.

Discussion

Sustainability science has been presented as 'a different kind of science' (Kates 2011: 19450; see also [START_REF] Clark | Sustainability science: the emerging research program[END_REF]. This claim is associated with its central objective, which is to tackle the wicked problems facing contemporary societies. Here we investigated the influence of problem wickedness on how scientists address wicked problems in practice. We analysed the relationship between the level of problem wickedness and project pluralism by documenting the research stances and methods adopted to address diversely wicked environmental problems in 17 research projects. We refined the approach by distinguishing between the political and cognitive complexity of the problem on the one hand and between the collaborative pluralism and methodological pluralism of the project on the other. We found overall positive correlations between cognitive complexity and political complexity, methodological pluralism and collaborative pluralism, and problem wickedness and project pluralism, but the levels of correlation were always, at best, weakly significant. We identified three research stances in our sample: correspondence, when there was a rather close match between collaborative (methodological) pluralism and political (cognitive) complexity; reductionism, when methodological or collaborative pluralism was lower than expected; and integrationism, in the opposite case. Below we discuss the influence of problem wickedness on these strategies.

Problem wickedness

The dispersion of the level of correspondence between problem wickedness and project pluralism (Fig. 3a) suggests that projects addressing highly wicked problems have less leeway regarding the level of pluralism than projects addressing weakly wicked problems. On the one hand, it is understandably difficult to involve more actors than those interested in or affected by a highly wicked problem or to use more methods and approaches than the cognitive complexity of the problem suggests. Strong integrationism, then, is a poor option when addressing a highly wicked problem. On the other hand, involving far fewer actors or using a limited number of methods and approaches can threaten project legitimacy and relevance, making strong reductionism equally difficult.

We found a tendency toward reductionism in projects addressing moderately wicked problems (see Fig 3a), which may have several explanations. Although strongly advocated in sustainability science [START_REF] Poteete | Working Together: Collective Action, the Commons, and Multiple Methods in Practice[END_REF][START_REF] Biggs | The Routledge handbook of research methods for social-ecological systems[END_REF], methodological pluralism faces practical obstacles that can be 'formidable' [START_REF] Poteete | Working Together: Collective Action, the Commons, and Multiple Methods in Practice[END_REF]). These include the need for the research team to master the specific skills required by each research method, which demands time and money; for some incumbent team members to acquire additional skills; or for new members with these skills to join the team. In addition, combining research methods from different approaches may cause misunderstandings and tensions between project participants, e.g. using qualitative methods when trained in quantitative methods. Research based on a mix of scientific approaches may also be more difficult to publish and valorise in research careers [START_REF] Poteete | Working Together: Collective Action, the Commons, and Multiple Methods in Practice[END_REF].

Similarly, the literature on participation in sustainability science (e.g. [START_REF] Bammer | Enhancing research collaborations: Three key management challenges[END_REF][START_REF] Lang | Transdisciplinary research in sustainability science: Practice, principles, and challenges[END_REF]) has highlighted the many obstacles that can hinder actor involvement in a project. These include, on the actors' side, a lack of interest in the project, a lack of confidence in its capacity to improve their or the overall situation, and a lack of energy to invest in timeconsuming participatory processes; on the researchers' side, impediments include a lack of facilitation and mediation skills. Finally, while the level of problem wickedness is likely to increase actors' interest in the project, its influence on their confidence in the project's capacity to improve the situation is more difficult to predict. This would require an in-depth analysis of how the various actors envisage the potential benefits and costs of (not) participating in the project.

While the obstacles to methodological and collaborative pluralism may explain the reductionist strategy, the integrationist strategy appears more counterintuitive. We found that projects characterised by methodological integrationism (#1, 14, 17) and collaborative integrationism (#1, 2, 14, 15) tended to address weakly to moderately wicked problems (Table 4). These strategies seem to be related to specific circumstances of the projects rather than generic factors. For example, project #1 focused on a moderately wicked problem (i.e. the adaptation of mountain pastures and associated grazing systems to climate change) that brought together all the actors interested in mountain pastures. According to the project leader, this would have been impossible with a more controversial issue such as wolf predation, a highly wicked problem in the French Alps [START_REF] Mounet | Les territoires de l'imprévisible. Conflits, controverses et 'vivre ensemble' autour de la gestion de la faune sauvage[END_REF][START_REF] Doré | Des loups dans la cité : Éléments d'écologie pragmatiste[END_REF]. The project aimed to develop a 'space for dialogue' [START_REF] Nettier | Adaptation au changement climatique sur les alpages. Modéliser le système alpage-exploitations pour renouveler les cadres d'analyse de la gestion des alpages par les systèmes pastoraux[END_REF], and the wickedness level of mountain pastures' adaptation to climate change lent itself perfectly to this process. Each participant then developed their own methods and approaches, and additional methods were used to foster their interactions, leading to high methodological pluralism. Project #15 focused on the presence of exotic invasive species of turtles in urban parks, which most visitors have not considered a problem [START_REF] Glatron | Réinterroger ce qu'est la nature en ville avec les tortues exotiques des parcs publics de Strasbourg[END_REF]. Interviewing these actors enabled the project leaders to open up a debate about the place of invasive exotic species in urban contexts and the possibility of adopting a more 'benevolent' attitude toward them [START_REF] Glatron | Réinterroger ce qu'est la nature en ville avec les tortues exotiques des parcs publics de Strasbourg[END_REF]. In this case, collaborative integrationism could be seen as a strategy to counteract the dominant ecological perspective (i.e. invasive exotic species are problematic and should be eradicated).

Project duration and leadership

Project duration and leadership are two other factors that are well known to interfere with transdisciplinarity [START_REF] Poteete | Working Together: Collective Action, the Commons, and Multiple Methods in Practice[END_REF][START_REF] Lang | Transdisciplinary research in sustainability science: Practice, principles, and challenges[END_REF][START_REF] Hitziger | EVOLvINC: EValuating knOwLedge INtegration Capacity in multistakeholder governance[END_REF]. A short project duration seems to foster methodological reductionism, which is congruent with previous studies [START_REF] Poteete | Working Together: Collective Action, the Commons, and Multiple Methods in Practice[END_REF]). Notably, it takes time to master the skills associated with various methods, especially if they pertain to different scientific approaches. We sought to explore the impact of these two factors on project pluralism despite our small sample size, which precludes multivariate analyses and statistical testing. Out of the six projects characterised by methodological reductionism (#5, 8, 9, 10, 13, 16), four (#5, 8, 10, 16) had a short duration, one (#9) had an intermediate duration, and one (#13) was a long-term project. Therefore, the tendency is less clear than for problem wickedness. The pattern was even less clear for collaborative reductionism, with two long-term projects (#3, 13) out of five characterised by collaborative reductionism.

Interestingly, project #13, characterised by both methodological and collaborative reductionism, was a long-term citizen science project addressing the poor quality of river water and recurring algal blooms in western Brittany. It was based on the weekly monitoring of water samples collected by scientists and essentially one type of citizen (high school students). Methodological and collaborative reductionism may be a common strategy in longterm monitoring projects, as it facilitates the standardisation of data production protocols.

An equal number of short-term and long-term projects showed methodological or collaborative integrationism, whereas we expected the number of long-term projects meeting this criterion would be higher. One potential explanation is that short-term projects actually benefit from the long-term dimension of ZAs. Two-or three-year projects can build on a much longer history that has given the participants time to master a diversity of methods and to establish and maintain relationships with a broad range of actors. For example, its inclusion in a long tradition of collaboration between researchers with various disciplinary backgrounds and local actors enabled project #14 to involve a wide range of actors and use various methods around the radioactivity of natural springs despite its short duration.

Finally, we found that projects characterised by reductionism were mostly led by male scientists trained in ecology or hydroecology, whereas projects characterised by integrationism were mostly led by women with more diverse disciplinary backgrounds (ecology, sustainability science, and human geography). [START_REF] Koppman | Who moves to the methodological edge? Factors that encourage scientists to use unconventional methods[END_REF] found that scholars with high status (i.e. men affiliated with a more prestigious discipline) were more likely to adopt high-risk, high-reward strategies and, in particular, unconventional methods, provided these were not too unconventional. Methodological and collaborative pluralism can be considered unconventional methods [START_REF] Biggs | The Routledge handbook of research methods for social-ecological systems[END_REF], and they may be too unconventional to be adopted by high-status researchers, although there are exceptions in our sample. For example, projects #2 and 6 (addressing a highly wicked problem and characterised by methodological and collaborative correspondence) were led by two latecareer male researchers, the former in human geography and the latter in ecology.

Limitations

Our results are exploratory and need to be confirmed and refined. The first limitation regards the positioning of the cases in the two grids, especially in grid 1 (problem wickedness). Assessing the wickedness of a problem is certainly not straightforward [START_REF] Peters | Are wicked problems really so wicked? Perceptions of policy problems[END_REF].While we found really helpful to decompose problem wickedness into two dimensions, assessing the problems' cognitive complexity proved to be particularly challenging. Indeed, we could not strictly follow Alford and Head's (2017) proposal, i.e. distinguish between the level of clarity of the problem and the level of clarity of its solution(s). We found it more feasible to identify three levels of clarity of the problem and its solution(s), as explained in the method section. Despite this adaptation, we acknowledge that there is some subjectivity when positioning a problem's cognitive complexity. Positioning the political complexity of the problem was also problematic in some cases. For example, we discussed the extent to which the rapid melting of sea ice in polar ecosystems (project #9) is a politically complex problem (and eventually decided it directly affected a few actors and generated little conflict). As for the positioning in grid 2 (project pluralism), it could be biased by the heterogeneous level of information available for each project and our personal knowledge of some projects. We limited this bias as much as possible through discussion among ourselves and with the project leaders.

We are therefore confident that the positioning of the problems and projects is not arbitrary, although some slight changes could probably be considered (and would affect the statistical tests). Furthermore, we could have chosen the typology of methods proposed by von Wehrden4 rather than that proposed by [START_REF] Biggs | The Routledge handbook of research methods for social-ecological systems[END_REF]. However, there is significant overlap between the two typologies, and the three categories of research approaches we have used are broad enough to be robust. Consequently, we believe that using another typology would not have changed our results, at least qualitatively.

The sample size is the second limitation of our study. On the one hand, we could not obtain statistically robust results with only 17 projects. A larger and more diversified sample would be necessary to further our understanding of the influence of problem wickedness on project pluralism and to test factors that we only started to explore here, such as project duration and leadership, or that we did not consider, such as financial resources. On the other hand, there were too many projects to give us in-depth knowledge of each of them. Therefore, we could not evaluate the influence of qualitative factors such as intensity of interactions or trust among project partners, which has often been underlined as an important factor for collaborative pluralism (e.g. [START_REF] Harris | Transdisciplinary environmental research: Building trust across professional cultures[END_REF][START_REF] Cundill | Nurturing communities of practice for transdisciplinary research[END_REF].

Conclusion

Contemporary societies are faced with a growing number of diversely wicked environmental problems, including highly wicked or super wicked ones. Sustainability science has developed specific research stances and methods to tackle these problems. The textbooks about methods and participation in sustainability science that have recently flourished are undeniably useful in helping newcomers to the field choose methods and participation strategies that are appropriate to the problems they seek to address. However, we believe that there is also a need to clarify the factors that influence the research stances and methods adopted in projects addressing wicked environmental problems. Therefore, we adopted a pragmatic rather than prescriptive approach to exploring these factors, with particular attention to the level of problem wickedness. An original feature of our study is that we considered participation and methods as two types of project pluralism, whereas the literature tends to focus on one or the other.

We found that project pluralism tended to increase with problem wickedness. Moreover, projects addressing highly wicked problems have little room for manoeuvre and are more likely to have a level of methodological and collaborative pluralism that matches the wickedness of the problem at hand. Addressing such problems is therefore especially constraining. In contrast, projects addressing weakly to moderately wicked problems have more flexibility when choosing between the three strategies we have identified: correspondence, reductionism, and integrationism.

Beyond problem wickedness, our study enabled us to discern the influence of other factors such as project duration and leadership. Because the results presented here are preliminary and need to be strengthened, we hope that our paper will pave the way for studies based on larger and more diverse project samples. Such projects will contribute to a better understanding of the implications of addressing highly wicked problems for research stances and methods and, more generally, the factors influencing how sustainability science is concretely enacted.

These include collecting naturalist data through field inventories or sociological data through interviews, carrying out ecological experiments in the field or in the lab, and modelling the past or future evolution of social or ecological systems.

See also td-net toolbox: https://naturalsciences.ch/co-producing-knowledge-explained/methods/td-net_toolbox, and the sustainability methods wiki: https://sustainabilitymethods.org/index.php/Main_Page

For a synthetic description of ZAs, see[START_REF] Bretagnolle | Action-orientated research and framework: Insights from the French long-term social-ecological research network[END_REF], table 1.

See https://sustainabilitymethods.org/index.php/Methods

Acknowledgements

We would like to thank the project leaders and directors of all French LTSER sites for sharing their knowledge of the projects and insights about research stances and methods.

Funding

This work was supported by the COLLAB² project funded by the French National Research Agency ((ANR-19-CE03-19-0002) and by the COLZA project of the Labex ITTEM.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


domain: chim sde

text:
Wei Liao

Emilie Dumas

Abdelhamid Elaissari

Adem Gharsallaoui
email: adem.gharsallaoui@univ-lyon1.fr

A study of the formation mechanism of multilayer emulsions by isothermal titration calorimetry and dynamic light scattering

Keywords: Multilayer emulsions, Isothermal titration calorimetry, Dynamic light scattering, Electrostatic interactions, Bridging flocculation

The formation of multilayered interfaces around oil droplets in oil-in-water (O/W) systems has great advantages in delivering lipid-soluble active compounds. Until now, few thermodynamic analyses have been performed on the preparation process of multi-layer emulsions. In this study, isothermal titration calorimetry (ITC) and dynamic light scattering (DLS) were used to investigate the binding properties and physical properties of low methoxyl pectin (LMP) and sodium caseinate (CAS) based multilayer emulsions during the formation process. ITC titration confirmed LMP does bind CAS-coated droplets through the electrostatic forces and it was a spontaneous exothermic process (ΔG < 0, ΔH < 0). Furthermore, stable multilayer emulsions can be only formulated by titrating the primary emulsion into LMP instead of back-titrating. Finally, the effects of different mixing methods on the stability of multilayer emulsions were evaluated. The DLS results suggest that titration rather than mixing directly can lead to more uniform and smaller-sized droplets, which can be attributed to the fact that slow titration can effectively avoid droplet aggregation.

Introduction

Oil in water (O/W) emulsion systems, produced by homogenizing oil and aqueous phases together in the presence of one or more emulsifiers, have been extensively applied in foods such as soft drinks, milk, mayonnaise, and vinaigrette, etc. [START_REF] Guzey | Formation, stability and properties of multilayer emulsions for application in the food industry[END_REF]. Along with the food safety concerns, there is a growing interest trend in the food field to replace commercial synthetic emulsifiers with natural "label-friendly" ones [START_REF] Dammak | Nanoemulsions: Using emulsifiers from natural sources replacing synthetic ones-A review[END_REF]. In this regard, several food protein-based emulsifiers, from different sources like milk, whey, eggs, legume, oilseed, and so on, have been extensively investigated as natural emulsifiers in recent years due to their amphiphilic character, polymeric structure, and electrical charge characteristics [START_REF] Kim | Dairy and plant proteins as natural food emulsifiers[END_REF]. Despite their favorable properties, protein-stabilized emulsions have been reported to be highly sensitive to environmental stresses such as pH, ionic strength, temperature, and oxygen [START_REF] Bouyer | Proteins, polysaccharides, and their complexes used as stabilizers for emulsions: Alternatives to synthetic surfactants in the pharmaceutical field[END_REF]. This instability of protein-based emulsions under these conditions will limit their further application in certain commercial products. In fact, the quality and stability of emulsions can be improved by combining protein emulsifiers with other natural polymers to form multilayered interfaces [START_REF] Surh | Influence of pH and pectin type on properties and stability of sodium-caseinate stabilized oil-in-water emulsions[END_REF]. For example, protein-coated droplets are either negatively or positively charged when the pH is below or above their isoelectric point (pI) [START_REF] Wang | Low Methoxyl pectin / sodium caseinate complexing behavior studied by isothermal titration calorimetry[END_REF], and then they could attract the oppositely charged polysaccharides present in the continuous phase, thereby forming a thicker layer at O/W interface. [START_REF] Zhang | Mixed plant-based emulsifiers inhibit the oxidation of proteins and lipids in walnut oil-in-water emulsions: Almond protein isolate-camellia saponin[END_REF] developed multilayer emulsions by addition of camellia saponin (CS) into almond protein isolate (API) based primary emulsions at pH 3. Compared with primary emulsions, droplets with multi-layered interfaces have the ability to significantly inhibit lipid and protein oxidation during storage. Compare with emulsions with single-layer interfaces, emulsions with multilayered interfaces were also found to have better stability against environmental stresses, such as pH extremes, high ionic strengths, thermal processing, and freezing [START_REF] Ogawa | Production and characterization of O/W emulsions containing cationic droplets stabilized by lecithin-chitosan membranes[END_REF][START_REF] Ogawa | Production and characterization of o/w emulsions containing droplets stabilized by lecithinchitosan-pectin mutilayered membranes[END_REF].

The basic mechanism for the preparation of multilayer interfaces is by adding oppositely charged polymers to a "primary" emulsion prepared by conventional homogenization techniques [START_REF] Ogawa | Production and characterization of O/W emulsions containing cationic droplets stabilized by lecithin-chitosan membranes[END_REF]. As a result, a "secondary" emulsion with a two-layer interface could be formulated due to electrostatic attraction. This process can be repeated several times to produce three or more-layer emulsions with desired functional properties. Previous studies [START_REF] Guzey | Formation, stability and properties of multilayer emulsions for application in the food industry[END_REF][START_REF] Mcclements | Advances in fabrication of emulsions with enhanced functionality using structural design principles[END_REF] demonstrated that adsorption layers can be deposited around droplets in two different ways: a one-step or two-step mixing procedure, depending on the charge-pH properties of the used biopolymer. In the one-step mixing method, a solution containing oppositely charged biopolymers is directly mixed with a primary emulsion containing charged droplets. This approach tends to promote the tendency of droplets to flocculate or coalesce during the process, and the aggregation is generally irreversible [START_REF] Guzey | Formation, stability and properties of multilayer emulsions for application in the food industry[END_REF][START_REF] Surh | Influence of pH and pectin type on properties and stability of sodium-caseinate stabilized oil-in-water emulsions[END_REF]. In the two-step method, the solution containing the charged biopolymer is mixed with the primary emulsion at a pH where there is no strong electrostatic attraction between them. The pH of the mixture is then adjusted to a pH where the droplets and the unabsorbed polymer have opposite charges, so that the polymer can be adsorbed to the droplet surface. This method is usually preferred for the production of multilayered interfaces at laboratory scale, since the second layer of biopolymer is more uniformly distributed throughout the aqueous phase prior to adsorption [START_REF] Liu | Study on the interaction between succinylated soy protein isolate and chitosan and its utilization in the development of oil-in-water bilayer emulsions[END_REF][START_REF] Mundo | Enhancing emulsion functionality using multilayer technology: Coating lipid droplets with saponin-polypeptide-polysaccharide layers by electrostatic deposition[END_REF][START_REF] Shi | Influence of molecular weight of an anionic marine polysaccharide (sulfated fucan) on the stability and digestibility of multilayer emulsions: Establishment of structure-function relationships[END_REF]. Nonetheless, the two-step approach has several drawbacks: (i) Irreversible aggregation occurs when the pH is adjusted to pass the pI of the protein emulsifier; (ii) not suitable for the preparation of emulsions with more than two layers; (iii) relatively complex process is not suitable for industrial mass production. For this reason, the one-step approach was selected in our study and further optimized to avoid droplet aggregation for preparing stable multilayer emulsions.

To minimize droplet aggregation in the one step method, it is necessary to ensure that enough biopolymers for coatings is present in the system to surround the entire surface of the added oil droplets. Otherwise, bridging flocculation may occur, as one polyelectrolyte may adsorb to the surface of multiple droplets, causing them to link together [START_REF] Mcclements | Advances in fabrication of emulsions with enhanced functionality using structural design principles[END_REF]. Even with sufficient free polyelectrolyte concentration in the aqueous phase, droplet aggregation cannot be completely avoided because particle-particle collisions are sometimes faster than the adsorption of biopolymers to the surface of the primary coating droplets. One strategy to avoid the droplet aggregation during the process of forming multilayer emulsions is to control the ratio of mixing by titrating primary emulsions into coating solutions [START_REF] Zeeb | Controlling lipid digestion using enzyme-induced crosslinking of biopolymer interfacial layers in multilayer emulsions[END_REF].

Therefore, the concentration and mixing methods of biopolymers must be carefully designed to avoid extensive droplet aggregation and massive free polyelectrolyte remaining in the aqueous phase after the coating step.

The saturation concentration for a mutilayer system has been mostly characterized by dynamic light scattering (DLS), which provides the saturation condition by identifying the ζ-potential plateau [START_REF] Okubo | Multilayered adsorption of macrocations and macroanions on colloidal spheres as studied by dynamic light scattering measurements[END_REF]. In this study, we used isothermal titration calorimetry (ITC) and conventional DLS to investigate the interaction and thermodynamic characteristics between sodium caseinate (CAS) stabilized emulsion and low methoxyl pectin (LMP) during the preparation of multilayer emulsions. In the first part, the thermodynamic parameters and surface charge during the formation (titration and back-titration) of the multilayer emulsion were evaluated to understand the stabilization mechanism of the multilayer emulsion during the preparation. Meanwhile, the advantages of ITC and DLS in measuring the system are described and compared. In the second part, the multilayer emulsions prepared by titration and direct mixing methods were compared in terms of particle size distribution, zeta potential (ζ-potential), creaming behavior, microstructure, and fluorescence intensity. This research could provide more information for the rational design of multilayer emulsions.

Materials and methods

Materials

The powder of CAS with 93.20% protein content (determined by the Kjeldahl method, N=6.38) was purchased from Fisher Scientific (UK). The powder of LMP (esterification degree from 22% to 28% and acetylation degree from 20% to 23%) with 81.21% carbohydrate content was obtained from Cargill (Baupte, France). A medium chain triacylglycerol oil (MCT) was purchased from Gattefossé (Saint-Priest, France). Imidazole, acetic acid, sodium azide, sodium hydroxide, and hydrochloric acid were purchased from Sigma-Aldrich Chimie (St Quentin Fallavier, France). The water used in all preparations was deionized water.

Sample preparation

Imidazole-acetate buffer solutions (5 mM) containing 0.04 wt.% sodium azide (to avoid microbial growth, (Chang et al., 2016)) was prepared by dispersing weighed amounts of imidazole and acetic acid into deionized water. Biopolymer stock solutions were prepared by slowly dispersing 0.53 wt.% CAS and 0.50 wt.% LMP separately into 5 mM imidazole-acetate buffer and stirring overnight to ensure complete hydration. The pH of both stock solutions was then adjusted to 3.0 by adding HCl (1 M) 24 h prior their use.

Preparation of primary emulsions and multilayer emulsions

Oil-in-water coarse emulsions were prepared by mixing 5.0 g MCT oil and 95 g emulsifier aqueous solution (0.53 wt.% CAS stock solution at pH 3.0) by high-speed homogenization (IKA, Staufen, Germany) under 13,500 rpm for 5 minutes. The resultant pre-emulsions was then passed through a microfluidizer (Microfluidics LM20, Microfluidics Corp., Newton, MA, USA) 5 times at 5 × 10 7 Pa to obtain nanoemulsions [START_REF] Liao | Effect of carrier oil on the properties of sodium caseinate stabilized O/W nanoemulsions containing Trans-cinnamaldehyde[END_REF]. The obtained nanoemulsions (containing 0.5 wt.% CAS) were then adjusted to pH 3.0 and considered as "primary emulsions".

Multilayer emulsions were prepared by titrating the primary emulsions into LMP stock solution (0.5 wt.%) at a rate of 2.5 mL/min by using an automated procedure with the TitroLine 5000 (TitroLine 5000, Xylem Analytics GmbH, Weilheim in Oberbayern, Germany). During the titration, the samples were kept under agitation and different ratios of primary emulsion/LMP were collected for subsequent analysis.

To investigate the effect of LMP on the formulation of multilayer emulsions when the coating material was insufficient, back-titration was also performed on the same ratio of CAS-based emulsion/LMP. Meanwhile, direct mixing was performed by slowly pouring different volumes of primary emulsions in same ratios (w/w) into the LMP stock solution under stirring to compare the effects of different mixing methods on the multilayer emulsions.

Isothermal titration calorimetry (ITC)

The energetics of the interactions between primary emulsions and LMP was measured using an isothermal titration calorimeter (VP-ITC) from MicroCal (Malvern Instruments, Northampton, MA) in a reaction cell volume of 1.4214 mL. LMP and CAS-based emulsions were diluted to the desired concentration (0.05 or 0.50 wt.%) with the same buffer (5 mM imidazole-acetate buffer, pH 3.0). All solutions were degassed under stirring for 5-10 min before being loaded. The pH of each solution was checked again before measuring to ensure the same values in the cell and in the syringe. The calorimetric cell was filled with LMP solution (0.5 wt.%) and the electric injector was filled with CAS-based emulsion (0.05 wt.%), equilibrated at 25 °C. The titration was performed by adding an initial 2 μL injection and 28 consecutive 10 μL injections while continuously stirring the mixture at 307 rpm. Each injection lasted 20 s with a 200 s interval between consecutive injections. Back-titration was also performed by placing the CAS-based emulsion (0.5 wt.%) into the cell and the LMP solution (0.05 wt.%) into the syringe, separately. Controlled titrations were performed by injecting the primary emulsion or LMP solution into imidazole-acetate buffer to obtain the heat of dilution, so corrected data were obtained by subtracting the heat of dilution data from the raw data. Data analysis was carried out by Origin 7.0 software.

The Gibbs free energy is calculated by the equation ΔG=ΔH -TΔS. Measurements were performed in triplicate and results are reported as mean and standard deviation.

Intrinsic fluorescence

Intrinsic fluorescence intensity of multilayer emulsions with different ratios of CAS-based emulsion/LMP was carried out at room temperature by a multimode microplate reader equipped with a temperature-controlled 96-wells microplate (Thermo Scientific™ Varioskan). The excitation wavelength was set at 280 nm and the emission spectrum was recorded in the wavelength range of 298-550 nm with an excitation and emission slit width of 5 nm. The multilayer emulsions formulated by titration in different ratios was diluted with 5 mM imidazole acetate buffer (pH 3.0) to a final concentration of 0.05 wt.% CAS. The diluted samples were then evenly transferred to 96-well plates for analysis, with 6 measurements per sample. The fluorescence intensity of acetate-imidazole buffer and pure LMP solution were used as a blank and a control, separately.

Zeta potential (ζ potential)

The ζ potential was performed by electrophoretic mobility (Malvern Instruments, Worcestershire, UK) under room temperature. To avoid multiple scattering effects, each sample was diluted to a concentration of around 0.05 wt.% with the same buffer (5 mM imidazole-acetate buffer, pH 3). Diluted samples were transferred to disposable cells for electrophoretic mobility measurement. All measurements were performed three times and the ζ-potential values were calculated by the software as the average of three individual measurements.

Mean particle size

Mean particle size (nm), polydispersity index (PdI) and size distribution were determined by dynamic light scattering using a Ζetasizer Nano-ZS90 (Malvern Instruments, Worcestershire, UK) under room temperature. To eliminate multiple scattering effects, each sample was diluted to a droplet concentration around 0.1 wt.% with corresponding pH buffers. After 90 s of equilibrium, each sample was analyzed three times.

Microscopic image

Before analysis, each sample should be gently stirred in glass tubes to ensure they were homogeneous. A drop of the emulsion was placed on a microscope slide and covered with a coverslip. The microstructure of samples was then visualized at room temperature using an Evos bright-field microscope (EVOS M5000, Thermo-Invitrogen, USA).

Statistical analysis

All experiments were carried out at least three times with freshly prepared samples. Data are reported as means ± standard deviations.

Results and discussions

Formation mechanism of multilayer emulsions

Zeta potential analysis

The appropriate concentration of the biopolymer coating around the primary emulsion can usually be assessed by measuring the zeta potential [START_REF] Okubo | Multilayered adsorption of macrocations and macroanions on colloidal spheres as studied by dynamic light scattering measurements[END_REF]. It has been reported that the ζ-potential of colloidal systems varies with the continuous addition of adsorbable polymers, and the plateau of the ζ-potential as function of ratio is related to the surface saturation of the polymer coating (Chang et al., 2016). LMP solution (Fig. 1A) at pH 3.0 is negative (-17.0 mV) which is attributed to the ionization of its carboxyl groups. When the ratio of CAS-based emulsion/LMP is increased, the ζ-potential initially remain stable until the ratio reached 0.5, then became increasingly less negative, with a point of zero charge in the ratio range around 1.25 -1.50, and finally reached a plateau for higher ratio (3.0) (ζ-potential close to that of primary emulsion). This is the fact that the primary emulsion exhibited positive charge at pH 3.0 because the protonation of the basic side chain (NH 3 + ) of the casein molecule. As a result, LMP molecules can be adsorbed on the droplet surface by electrostatic force, and then the overall negative charge of the system gradually increases until there are not enough LMPs in the system to cover the newly dropped droplet. As shown in Fig. 1B, the ζ-potential of the primary emulsion is positive (+32.6 mV) and this value could be considered enough to ensure high intermolecular repulsions [START_REF] Lieberman | Pharmaceutical dosage forms: Disperse systems[END_REF]. When the LMP concentration was increased, the ζ-potential initially remains stable until the ratio reaches 0.3, then becomes increasingly less positive, with a point of zero charge in the ratio range around 0.6 -0.8, and finally reached a plateau at a ratio of 1.5 (Fig. 1B). According to previous reports (Chang et al., 2016;[START_REF] Liu | Formation, characterization, and application of chitosan/pectin-stabilized multilayer emulsions as astaxanthin delivery systems[END_REF], the plateau of ζ-potential indicates that the lipid droplet surface is saturated with coating polysaccharides at this level. It should be mentioned that during the experiment, the titration of the primary emulsion into the LMP solution resulted in a stable multilayer emulsion, while titration in the opposite direction (LMP solution into the primary emulsion) showed obvious flocs and these flocs did not disappear with the continuous addition of LMP (Data not shown). Based on our results, the forward titration reached a plateau at a ratio 3.0 (Fig. 1A), which corresponds exactly to a ratio of 0.3 (Fig. 1B) for titration of the primary emulsion into the LMP solution. After the ratio 0.3, the absolute value of the zeta potential begins to decrease, indicating that the droplet saturation potentials corresponding to the titrated and back-titrated samples are consistent. Therefore, this

finding suggests that the zeta potential can represent the overall distribution of particles in solution but cannot reflect whether the multilayer emulsion formulation is stable during preparation (the occurrence of particle aggregation).

Meanwhile, to find the exact concentration of coating polymer at which the multilayer emulsions reach the plateau, a large number of samples in different ratios should be prepared to measure for ζ-potential measurements, which are considered very complex and time-consuming processes. In this regard, we employed ITC to measure thermodynamic parameters to gain a deeper understanding of the stoichiometry of layer-by-layer interactions and to analyze the energetics of multilayered interfaces processes.

ITC analysis

ITC have been widely used to investigate molecular interactions in biological systems [START_REF] Jafari | Production of sub-micron emulsions by ultrasound and microfluidization techniques[END_REF][START_REF] Wang | Low Methoxyl pectin / sodium caseinate complexing behavior studied by isothermal titration calorimetry[END_REF], but there are few reports on the interaction between droplets and molecules [START_REF] Fotticchia | Thermodynamic Signature of Secondary Nano-emulsion Formation by Isothermal Titration Calorimetry[END_REF]. Hence, ITC was used to obtain more information about the evolution of deposition around the primary emulsion, such as the equilibrium adsorption constant, enthalpy of adsorption, and adsorption stoichiometry. CAS-based emulsions and LMP solutions at pH 3.0 were chosen to perform ITC tests at 25 °C because CAS-coated droplets showed positive charge and LMP molecules showed negative charges at pH 3.0 [START_REF] Wang | Low Methoxyl pectin / sodium caseinate complexing behavior studied by isothermal titration calorimetry[END_REF]. In this study, heat flow versus time curves (the upper of Fig. 2) were obtained by gradually injecting 0.5 wt.% primary emulsion or 0.5 wt.% LMP solution into a reaction cell containing 0.05 g/L LMP solution or 0.05 wt.% primary emulsion at 25 °C. The enthalpy changes (the lower of Fig. 2) as function of mass ratio were obtained by the software. The mass unit was used to replace the molecular unit in this study, because both CAS and LMP are high molecular weight polymers.

The ITC measurements (Fig. 2A) showed that the titrating process was exothermic with a stepwise change in the exothermic value for each injection. When the ratio of primary emulsion/LMP is lower than 1.0, the values of heat released per injection are very close, which indicates that the injected CAS-coated droplets have a more stable interaction with the LMP molecules in the reaction cell at this stage. This phase also corresponds to that when the absolute value potential of zeta (Fig. 1A) gradually approaching the "0" point from larger values (-17.0 mV to -8.42 mV), implying that multiple emulsions may go from stable to relatively unstable from this point (Ratio 1.0). This was probably attributed to the fact that, at the initial stage, excess negative LMP molecules in the cell can quickly adsorb on the surface of the positively charged emulsion droplets due to electrostatic interactions. Our previous study [START_REF] Wang | Low Methoxyl pectin / sodium caseinate complexing behavior studied by isothermal titration calorimetry[END_REF] reported the interaction between CAS and LMP when used at the same contents in this study. Interestingly, the heat released by the interaction between CAS and LMP decreases with regularity from the beginning. This difference may stem from differences in binding between molecules and between molecules and droplets. The CAS-encapsulated droplets prepared in this study have nanoscale diameters with an average particle size of about 300 nm, so the CAS molecules adsorbed on the surface of the oil droplets have a more ordered structure in the system than free casein molecules in the aqueous phase. As a result, each casein-coated droplet entering the cell has enough LMP molecules to cover the droplet surface through electrostatic attraction rather than disordered droplet aggregation, thereby releasing a relatively stable heat per injection at the initial stage. For ITC measurements between CAS and LMP solutions, complexes were formed during each injection and these complexes were confirmed to be insoluble at pH 3.0 [START_REF] Wang | Low Methoxyl pectin / sodium caseinate complexing behavior studied by isothermal titration calorimetry[END_REF]. Therefore, it can be hypothesized that the casein molecules may rapidly form disordered network fibers after entering the reaction cell, and the degree of network structure is more extensive, and the heat released is higher. When the ratio was above 1.0, the heat released per injection stated to decrease regularly (Fig. 2A). This may be attributed to the gradual depletion of LMP chains in the reaction cell. Above the ratio of 1.4, the enthalpy becomes slightly positive and remains stable, indicating that none of the LMP molecules in the cell can interact with the newly added droplet. However, the result of zeta potential (Fig. 1 A) showed that the plateau was obtained when the ratio of CAS-based emulsion/LMP was around 3.0, which was not consist with ITC results. It was reported that the ζ-potential is highly sensitive to the environmental conditions, and slight differences in the ion concentration can affect measurements [START_REF] Fotticchia | Thermodynamic Signature of Secondary Nano-emulsion Formation by Isothermal Titration Calorimetry[END_REF]. For instance, sample should be diluted before measurements the ζ-potential and the dilution may also influence the authenticity of the system. Fotticchia et al.

(2014) showed similar results by titration chitosan or poly-l-lysine into egg lecithin based emulsions and they demonstrated that ITC could provide more accurate information than DLS.

Fig. 2A showed that the enthalpy change (ΔH) in the titration was -0.534.40 kcal/mg. The Gibbs free energy (ΔG) was also negative (-8.96 kcal/mg) by fitting the curve of " one set of sites ", indicating that the interaction between the primary emulsion and LMP was a spontaneous reaction. Similar exothermic sequences were also found in ovalbumin/chitosan [START_REF] Xiong | Ovalbumin-chitosan complex coacervation: Phase behavior, thermodynamic and rheological properties[END_REF] and soy proteins/gum Arabic [START_REF] Dong | Mutual titration of soy proteins and gum arabic and the complexing behavior studied by isothermal titration calorimetry, turbidity and ternary phase boundaries[END_REF]. This result supports the generally accepted view that adsorption is primarily driven by electrostatic interactions [START_REF] Burgos-Díaz | Multilayer emulsions stabilized by vegetable proteins and polysaccharides[END_REF][START_REF] Fotticchia | Thermodynamic Signature of Secondary Nano-emulsion Formation by Isothermal Titration Calorimetry[END_REF]. Indeed, the interaction in the preparation of the multilayer emulsion is a more complex interaction than just an electrostatic mechanism. It may also include hydrophobic interactions, van-der-Waals forces, and hydrogen bonding. However, we cannot say whether these forces are present, because ITC measures the sum of all events that occur in the reaction cell. Furthermore, comparing the ΔG value (-8.13 kcal/mg) obtained from the interaction between CAS and LMP [START_REF] Wang | Low Methoxyl pectin / sodium caseinate complexing behavior studied by isothermal titration calorimetry[END_REF], it was found that the absolute value of ΔG is higher in this study. This could be attributed to the fact that the adsorbed casein (+32.6 mV) exhibited stronger surface charge than free casein molecules (+20 mV) in the continuous phase at pH 3.0 [START_REF] Wang | Influence of low methoxyl pectin on the physicochemical properties of sodium caseinate-stabilized emulsions[END_REF].

ITC measurements by titrating LMP solution into primary emulsions were also performed to understand the heat flow (Fig. 2B) in the presence of insufficient polysaccharides. Instead of decreasing regularly, the heat released of each injection increased in the initial phase and the maximum heating was obtained at ratio 0.3.

Several possibilities may explain this behavior: (i) insoluble flocs were clearly observed by titration of LMP into the primary emulsion at the initial stage, and these flocs did not disappear with the continuous addition of LMP (Data not shown). This can be attributed to the bridging flocculation caused by negatively charged pectin molecules and positively charged droplets. The bridging flocculation process may be accompanied by more complex reactions than electrostatic adsorption, such as some endothermic effects (unfavorable conformational changes, hydrophobic interactions, etc. (Bou-Abdallah & Terpstra, 2012)) and, (ii) when the pH of stock solution was adjusted to 3.0 by HCl, some ions remained in the solution may inhibit binding interactions [START_REF] Xiong | Complex coacervation of ovalbumin-carboxymethylcellulose assessed by isothermal titration calorimeter and rheology: Effect of ionic strength and charge density of polysaccharide[END_REF] due to the formation of an ionic screen that prevents the interaction between the two biopolymers. Interestingly, the ratio 0.3 also corresponds to the starting decrease of ζ-potential (Fig. 1B), suggesting that the overall droplet surface charge in this system changed. After this ratio, the heat released after each injection started to decrease regularly and reaches the "0" point at ratio 0.7. However, Fig. 1B showed that the ζ-potential reached a plateau until the ratio 1.5, while ITC data indicated that there was no obvious heat changed at ratios higher than 0.7. This finding suggested that the continued decreased in potential caused by the addition of LMP is probably not accompanied by a significant thermal change.

Schematic representation of the formation of multilayer emulsions by titration

Based on the above results, a schematic diagram was established to summarize the main events occurring as function of the ratio in the titration and back-titration systems (Fig. 3). For the primary emulsion titration by LMP solution, stable multilayer emulsions are successfully formed at the initial stage, which were stable to droplet flocculation. This is because each injection contains enough LMP chains to completely cover oil droplets and gives them a negative surface charge, thereby avoiding droplet aggregation due to electrostatic repulsion. Theoretically, as the LMP in the system is gradually depleted, the injected droplets will interact with other LMP-coated droplets, causing large droplets to aggregate. In general, bridging flocculation tends to occur earlier (before the biopolymer in the continuous phase is completely depleted), which are mainly depending on the mixing methods (mixing [START_REF] Liu | Formation, characterization, and application of chitosan/pectin-stabilized multilayer emulsions as astaxanthin delivery systems[END_REF] or titration [START_REF] Zeeb | Controlling lipid digestion using enzyme-induced crosslinking of biopolymer interfacial layers in multilayer emulsions[END_REF]) and biopolymer properties (e.g., charge density, molecular weight, and conformation [START_REF] Gharsallaoui | Utilisation of pectin coating to enhance spray-dry stability of pea protein-stabilised oil-in-water emulsions[END_REF]). For back-titration, bridging flocculation occurs at the initial stage, as the injected negatively charged LMP molecules will adsorb to the surface of multiple droplets and link them together. Although negatively charged pectin continued to be added to the system, making the surface of the entire system negatively charged (Fig. 1B), the flocs that had produced did not disappear. This finding is consistent with some other reports [START_REF] Liu | Formation, characterization, and application of chitosan/pectin-stabilized multilayer emulsions as astaxanthin delivery systems[END_REF][START_REF] Surh | Influence of pH and pectin type on properties and stability of sodium-caseinate stabilized oil-in-water emulsions[END_REF]. Clusters of droplets held together by protein bridges is generally not reversible, which can be disrupted only by strong shear forces (e.g. a second-stage of homogenization) [START_REF] Dickinson | Strategies to control and inhibit the flocculation of protein-stabilized oil-in-water emulsions[END_REF]. For instance, F. [START_REF] Liu | Utilization of interfacial engineering to improve physicochemical stability of β-carotene emulsions: Multilayer coatings formed using protein and protein-polyphenol conjugates[END_REF] mixed primary emulsions and lactoferrin and then used a blender and high pressure homogenizer to redisperse droplets to obtain stable multilayer emulsions. However, [START_REF] Fotticchia | Thermodynamic Signature of Secondary Nano-emulsion Formation by Isothermal Titration Calorimetry[END_REF] indicated that stable multilayer emulsions can be prepared by titrating chitosan or poly-L-lysine into the primary emulsion, although bridging flocculation occurs at the initial stage of titration. [START_REF] Tang | The microstructure and physiochemical stability of Pickering emulsions stabilized by chitosan particles coating with sodium alginate: Influence of the ratio between chitosan and sodium alginate[END_REF] successfully prepared multilayer emulsions by direct mixing relatively high content of sodium alginate with chitosan based picking emulsions. These differences may originate from the properties of different biopolymers (e.g., charge density, molecular weight and conformation), the primary layer thickness of emulsion droplets, as well as solution conditions (e.g., pH, ionic strength, temperature, and stirring) [START_REF] Burgos-Díaz | Multilayer emulsions stabilized by vegetable proteins and polysaccharides[END_REF].

Analysis of fluoresence intensity

Several studies have reported [START_REF] Acharya | Binding of resveratrol with sodium caseinate in aqueous solutions[END_REF][START_REF] Qiu | Influence of protein type on oxidation and digestibility of fish oil-in-water emulsions: Gliadin, caseinate, and whey protein[END_REF] that CAS or CAS-based droplets exhibited an obvious emission band around 330 nm when the extraction band was 280 nm due to the presence of tryptophan. For this reason, measurements of tryptophan fluorescence spectroscopy during the formation of CAS-LMP based multilayer emulsion were used to study CAS conformational changes, owing to the fact that the intrinsic fluorescence of tryptophan residues is highly sensitive to the polarity of microenvironments [START_REF] Li | Preparation and characterization of phytosterol-loaded microcapsules based on the complex coacervation[END_REF].

Fig. 4A shows the fluorescence spectra of multilayer emulsions prepared by titrating the primary emulsion into LMP solution with different ratios and all samples maintained the same CAS content. All samples emulsion showed strong fluorescence emission upon excitation at 280 nm, with a peak near 330 nm. Interestingly, when the ratio ≤ 0.6, there was no obvious shift in the maximum emission wavelength of LMP-CAS based emulsion; however, when the ratio was above 0.6, the wavelength corresponding to the maximum showed a slight red shift compared to the primary emulsion. It has been reported that the red or blue shift in the emission band of CAS was usually related to changes in the tryptophan environment [START_REF] Li | Physicochemical properties of stable multilayer nanoemulsion prepared via the spontaneously-ordered adsorption of short and long chains[END_REF].

Therefore, no shift was observed at ratio ≤ 0.6 which suggest that binding of LMP and CAS-coated droplets in this stage did not change the tryptophan environment.

The quenching of the fluorescence intensity has been reported as an indicator of the interaction of the components in the solution [START_REF] Wang | Physicochemical characterisation of β-carotene emulsion stabilised by covalent complexes of α-lactalbumin with (-)-epigallocatechin gallate or chlorogenic acid[END_REF]. Therefore, the adsorption force of LMP to the surface droplets of the primary emulsion can be deduced from the test results. In this regard, the maximum fluorescence intensities of these emulsions prepared by titration as a function of ratio are plotted in Fig. 4B. In the ratio range of 0 to 0.6, titration-prepared samples showed similar maximum fluorescence intensities; however, when the ratio is greater than 0.6, the maximum intensity of samples decreases obviously with the increase of the ratio until it reaches 1.75. The decrease in entropy intensity indicates that some of the tryptophan residues of CAS adsorbed on the oil droplets were transferred from the polar surface to the hydrophobic interior, which may be due to the interaction of tryptophan located in the hydrophobic region of the protein with pectin through hydrophobic bonds. The decrease in intensity suggests that some of the tryptophan residues of CAS adsorbed on the oil droplet are transferred from the polar surface to the hydrophobic interior, which was probably attributed to the droplet aggregation. Similar behavior was reported for aggregation of soybean protein isolate/pectin complexes [START_REF] Li | Preparation and characterization of phytosterol-loaded microcapsules based on the complex coacervation[END_REF].

This result also indicates that formation mechanism of multilayer emulsions by LMP and CAS coated droplet is not only electrostatic but also accompanied by a certain degree of hydrophobic interactions (especially when the droplets are extensively aggregated), which was supported by the data of ITC results. At the same time, the maximum fluorescence intensity of these samples increased as the ratio increased from 1.75 to 2.5. This can be attributed to the presence of some individual CAS-coated droplets in the system due to the relatively high CAS-based emulsion/LMP ratio.

Effect of titration or mixing on the properties of multilayer emulsions: analysis of droplet size and flocculation

It should be noted that many papers demonstrated the successful preparation of multilayer emulsions by adding primary emulsions to other coating materials [START_REF] Burgos-Díaz | Multilayer emulsions stabilized by vegetable proteins and polysaccharides[END_REF][START_REF] Liu | Formation, characterization, and application of chitosan/pectin-stabilized multilayer emulsions as astaxanthin delivery systems[END_REF][START_REF] Shi | Influence of molecular weight of an anionic marine polysaccharide (sulfated fucan) on the stability and digestibility of multilayer emulsions: Establishment of structure-function relationships[END_REF]. However, there are no details on how to define "add". In fact, there are many ways of addition, such as slow/quick addition, titration or direct pouring, and these different ways of addition seem to have a significant effect on droplet aggregation in the preparation of multilayer emulsions. In this section, the direct mixing and titration under stirring were used to prepare multilayer emulsions in different ratios of CAS-based emulsion/LMP. Then, dynamic light scattering (DLS) (Fig. 5A-D), creaming index (Fig. 6A), and optical microscopy (Fig. 6 B) will be presented to evaluate the surface charge, mean particle size and droplet aggregation of these emulsions.

Fig. 5A exhibited the zeta potential of emulsions in both preparation methods.

Interestingly, the multilayer emulsions in both methods showed similar trends in surface charge as a function of ratio, although distinct flocs were observed earlier in the emulsions prepared by direct mixing. This might be the limitation of microelectrophoresis mobility method: samples need to be highly diluted and this process may have changed the surface charge of the system [START_REF] Hu | Techniques and methods to study functional characteristics of emulsion systems[END_REF][START_REF] Salvia-Trujillo | Influence of particle size on lipid digestion and β-carotene bioaccessibility in emulsions and nanoemulsions[END_REF]. For example, droplet aggregation in highly concentrated emulsions may be partially redispersed to some extent after dilution and agitation.

Primary emulsions exhibited nanoscale diameter (~300 nm, Fig. 5B) with relatively lower polydispersity index (PdI) values (Fig. 5C). As the ratio increases, all emulsions showed increased droplet size and PdI values, which can be attributed to the fact that negatively charged LMP adsorbed on the surface of CAS-coated droplets or droplet aggregates. A similar result was found in the study of chitosan/pectin-stabilized multilayer emulsions [START_REF] Liu | Formation, characterization, and application of chitosan/pectin-stabilized multilayer emulsions as astaxanthin delivery systems[END_REF]. It is worth noting that the particle size and PdI values of samples prepared by mixing method are higher than those prepared by titration one. Until the ratio reached 0.8, the titration-prepared multilayer emulsions still exhibited nanoscale average droplet diameter (~600 nm) based on DLS analysis; however, when the ratio was higher than 0.5, the size of sample prepared by mixing was outside the measurement range of DLS. This was probably attributed the fact that directly mixing provides more droplets in the same time than titration, and consequently droplet-droplet collisions may occur more rapidly than polyelectrolyte molecules adsorb to the droplet surfaces, thereby caused larger droplets [START_REF] Guzey | Formation, stability and properties of multilayer emulsions for application in the food industry[END_REF]. However, during the titration process, a small number of droplets added each time can be quickly encapsulated by the polyelectrolyte at a lower concentration ratio. As a result, once the surface charge reached a certain value, there will be a strong electrostatic repulsion between the surface and similarly charged polyelectrolytes in the aqueous phase, which limits further adsorption of the polyelectrolyte, thereby reducing the probability of droplet-droplet collision and retarding the occurrence of particle aggregation. This result was also confirmed by the droplet size distribution. The titration-prepared samples did not show distinct peaks in the larger size range until ratio reached 0.5, while even with a ratio of only 0.1 (Fig. 5D), distinct peaks in the larger size range were detected in the sample formed by mixing (Fig. 5E). This result proved that droplet flocculation is readily to occur in the mixing directly methods, indicating that different adding methods have a significant effect on the droplet flocculation during the formulation of multilayer emulsions.

Fig. 6 A showed the visual appearance of multilayer emulsions prepared by directly mixing and titration methods. As expected, those prepared by mixing showed a cream layer when the ratio increased. Even at a ratio of 0.1, a phase separation can be observed where an opaque cream layer at the top and a strongly turbid droplet-depleted layer at the bottom, which was consistent with result of particle size (Fig. 5E). This behavior can be attributed to bridging flocculation promotion leading to an increase in particle size, which facilitates gravitational separation [START_REF] Grundy | Influence of oat components on lipid digestion using an in vitro model: Impact of viscosity and depletion flocculation mechanism[END_REF]. However, when the ratio was increased to 0.5, there was a slight creaming at the bottom of the emulsion prepared by mixing, which may be due to an increase in viscosity (polymer entanglement or viscoelastic network formation) [START_REF] Grundy | Influence of oat components on lipid digestion using an in vitro model: Impact of viscosity and depletion flocculation mechanism[END_REF]. As a result, the increased viscosity restricts the upward movement of the aggregated droplets. Notably, the multilayer emulsion prepared by titration showed much better stable creaming stability than that prepared by mixing, since no obvious phase separation occurred until the ratio reached 1.0. This could be attributed to relatively low PdI value (Fig. 5C) in these emulsions.

For further analysis, the microstructure of the primary emulsion (control) and several selected multilayer emulsions prepared by titration in different ratios (0.5:1; 0.8:1; 1:1; 1.5:1; 2:1) were observed by optic microscopy. These samples represent different states of droplets during the preparation of multilayer emulsions. Compared to the primary emulsion, the multilayer emulsion also exhibits a very homogeneous microstructure in the ratio ≤ 0.5, which supports the results of the size measurements.

As the ratio increased, droplet aggregation was clearly observed at higher chitosan concentrations, especially when the ratio was higher than 1.0. This is because there are not enough LMP molecules in the system to coat the droplets, and then two or more droplets share a polysaccharide chain to form aggregates. Remarkably, both extensive droplet aggregation and significantly increased droplet size (Fig. 5B) occurred around the ratio 1.0, which corresponds to the ratio where the heat released by titration (Fig. 2A) began to decrease. These findings suggest that ITC could provide accurate information on when flocculation occurs, leading to optimal conditions for the preparation of O/W multilayer emulsions.

Conclusion

This study tried to explain the mechanism of the formation of multilayer emulsions by titrating primary emulsions into coating materials. According to the obtained results, ITC measurements by titration of the primary emulsion into the coating material allow the acquisition of thermodynamic characteristics of the studied system, which are fast, accurate and informative compared to the information obtained from zeta potential measurements. ITC titration confirmed that LMP does bind CAS-coated droplets through the electrostatic forces and it was a spontaneous exothermic process (ΔG < 0, ΔH < 0). The binding is also accompanied by hydrophobic forces. Titration of the primary emulsion into the LMP solution resulted in a stable multilayer emulsion, while titration in the opposite direction showed obvious flocs due to bridging flocculation. Meanwhile, more uniform and smaller-sized droplets can be prepared by titrating the primary emulsion into LMP solution rather than mixing them directly, which can be attributed to the fact that slow addition can effectively avoid the aggregation of droplets. Based on emulsion stability and microscopy observations, ITC appears to have the ability to define when flocculation begins, thus providing optimal conditions for the preparation of O/W multilayer emulsions. In this way, the remaining coating materials in the continuous phase of the prepared double-layer emulsion can be reduced, so as to further prepare emulsions with three or four interfaces…, thus providing more possibilities for O/W food emulsion products.

Fig. 1

 1 Fig. 1 showed the ζ-potential of multilayer emulsions prepared by titration and back-titration as function of CAS/LMP or LMP/CAS ratio. The ζ-potential of pure

Fig. 1 .Fig. 2 .Fig. 3 .

 123 Fig. 1. ζ-potential of multilayer emulsions at pH 3.0 as a function of ratio: (A) titrating the primary emulsion into LMP solution or (B) titrating LMP solution into the primary emulsion.

Fig. 6 .

 6 Fig. 6. (A) Visual appearance of multilayer emulsions prepared by titration or mixing as function of ratio and (B) Photomicrographs of multilayer emulsions prepared by titration. The scale bar is 20 μm in length.

ACKNOWLEDGEMENTS

Wei Liao greatly thanks Chinese Scholarship Council for support.

CONFLICTS OF INTEREST

The author declares that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research reported.