Iuri Baptista

Dominique Valentin

Erick Saldaña

Jorge Behrens

Effects of packaging color on expected flavor, texture and liking of chocolate in Brazil and France

Keywords: Consumer perception, Cross-cultural, Visual cues, Packaging, Color, Chocolate

Effects of packaging color on expected flavor, texture and liking of chocolate in Brazil and France Highlights

-Black packaging made consumers expect chocolates to be more bitter.

-Pink and yellow packaging made consumers expect chocolates to be sweeter.

-The effect of a packaging color on expected liking depended on chocolate type.

-Warm and cold classification of colors did not explain the effects of packaging color.

-The effects of packaging color were not significantly different between cultures.

Introduction

Research has shown that not only the color of the product itself, but also the colors of the tableware, packaging, and environment can influence expectations and perception of a food or a drink [START_REF] Spence | Background colour & its impact on food perception & behaviour[END_REF]. According to the predictive coding theory, this happens because when consumers see a product, such as a bar of chocolate, their brains immediately search for cues that match previous experiences and try to anticipate what it is and what are its characteristics [START_REF] Piqueras-Fizsman | Sensory expectations based on product-extrinsic food cues: An interdisciplinary review of the empirical evidence and theoretical accounts[END_REF]. This process creates expectations that have been shown to affect behavioral response, sensory perception, and neural activation [START_REF] Litt | Manipulating basic taste perception to explore how product information affects experience[END_REF][START_REF] Okamoto | Extrinsic information influences taste and flavor perception: A review from psychological and neuroimaging perspectives[END_REF], making the subject fundamental for food industries and food services interested in building a complete experience for their consumers.

It is argued that color is the most distinctive visual cue in a packaging [START_REF] Singh | Impact of color on marketing[END_REF], but its effects depend on many factors such as the level of attention [START_REF] Brignell | Attentional and approach biases for pictorial food cues: Influence of external eating[END_REF], the frequency of consumption of the product [START_REF] Lick | Sensory expectations generated by colours of red wine labels[END_REF], the cultural context [START_REF] Piqueras-Fiszman | Exploring implicit and explicit crossmodal colour-flavour correspondences in product packaging[END_REF], the consumers' sensitivity to design [START_REF] Becker | Tough package, strong taste: The influence of packaging design on taste impressions and product evaluations[END_REF], and the product itself [START_REF] Zellner | The effect of wrapper color on candy flavour expectations and perceptions[END_REF]. A recent review [START_REF] Spence | Packaging colour and its multiple roles[END_REF] summarized the multiple roles of packaging color on consumers' expectation and perception of identity, taste, flavor, fragrance, healthiness, and willingness to pay. After the review, new contributions on the effects of packaging color reported that it may influence the emotions evoked by a burger [START_REF] Merlo | Measuring dynamics of emotions evoked by the packaging colour of hamburgers using Temporal Dominance of Emotions (TDE)[END_REF], its inside color (i.e., the side in contact with the product) may influence the desirability of yogurt [START_REF] Van Esch | The effects of inner packaging color on the desirability of food[END_REF], and the color of the label may influence the expected taste of specialty coffee [START_REF] De Sousa | Colour and shape of design elements of the packaging labels influence consumer expectations and hedonic judgments of specialty coffee[END_REF].

Specifically on the subject of this study, several significant effects of packaging color were reported on expected flavor, somatosensory sensations, and liking of food. Studies commonly associated these effects with the warm and cold classifications of colors. The first group includes colors of long length waves, like red, pink, and yellow; the second includes colors of short length waves, like blue, purple and green [START_REF] Huang | Eat with your eyes: package color influences the expectation of food taste and healthiness moderated by external eating[END_REF]. First, [START_REF] Deliza | Product packaging and branding[END_REF] showed that an orange box made consumers expect passion fruit juice to be sweeter and less sharp, refreshing, and liked than a white box. Then, it was found that a dairy dessert in a yellow packaging was expected to be sweeter, creamier, and more liked than the same dessert in a black packaging [START_REF] Ares | Studying the influence of package shape and colour on consumer expectations of milk desserts using word association and conjoint analysis[END_REF]. [START_REF] Rebollar | Influence of chewing gum packaging design on consumer expectation and willingness to buy: An analysis of functional, sensory and experience attributes[END_REF] reported that chewing gums in warm-colored packaging were expected to be sweeter, fruitier, and sourer than in cold colors or scale of grey; and [START_REF] Huang | Eat with your eyes: package color influences the expectation of food taste and healthiness moderated by external eating[END_REF] reported that cereal, ice cream, iced tea, and yogurt in red packaging were expected to be sweeter than in green or blue. [START_REF] Tijssen | Why a 'light' product package should not be light blue: Effects of package colour on perceived healthiness and attractiveness of sugar-and fat-reduced products[END_REF] found that a dairy drink in a red box was expected sweeter, creamier, more flavorful and liked than in a purple or a blue box; and that a sausage in a red box was expected to be saltier than in a green or blue box. Comparing juice, sorbet, and gums in red and yellow packaging, [START_REF] Matthews | Establishing boundary conditions for multiple design elements congruent with taste expectations[END_REF] showed significant effects on sourness and sweetness expectations. Finally, [START_REF] Rosa | Influences of visual attributes of food packaging on consumer preference and associations with taste and healthiness[END_REF] reported that red-to-yellow, blue-togreen, and greyscale packaging influenced consumers' expectations for cookies tastes and liking in multiple directions.

Thus, besides protecting physically, chemically, and microbiologically a food product, packaging is a communication tool that draws attention, expresses identity, induces appetite, intensifies emotions, and conveys messages about the products' attributes (Velasco & Spence, 2019). Its potential to communicate might be particularly relevant for the 7.3 million tons of chocolate consumed globally [START_REF] Conway | Statistics & facts on chocolate consumption and industry[END_REF], since they are usually eaten straight from the packaging and since there is a wide range of attributes that could be interesting to communicate: aromas (floral, fruity, nutty), tastes (bitterness, sweetness, sourness), oral sensations (snap, melting, silky), types (white, milk, dark), categories (confectionary, compound, bean-to-bar), varietals (forastero, criollo, trinitario), and countries of origin (Colombia, Madagascar, Ivory Coast) (Beckett, 1994).

There are very few studies on the effects of packaging color on the expectations of chocolate taste, flavor, texture, and liking. A master thesis [START_REF] Van Lith | Communicating health through package color and material: The influence of color and material of food packaging on perceived product healthfulness[END_REF] showed that a chocolate in red packaging was expected to be significantly healthier than in yellow packaging and a chocolate in dark brown was expected to be significantly more natural than in yellow or pink, but significant effects were not found regarding attractiveness or tastiness.

Another research [START_REF] Kovač | Consumers' preferences for visual elements on chocolate packaging[END_REF] reported that strawberry-flavored chocolate was significantly more attractive when presented in vivid pink packaging than in a less saturated color. As these two studies did not tackle the effect of packaging color on tastes and texture of chocolate, further research could help pastry chefs, chocolatiers, designers, artisans, and industries to choose colors to their products' background, either it is a plate, a packaging or a shop window.

The purpose of this study was to evaluate the effects of seven different colors of packaging on expected sweetness, bitterness, fruitiness, melting, and liking of milk and dark chocolates. As color and taste associations were shown to vary among cultures [START_REF] Wan | Cross-cultural differences in crossmodal correspondences between basic tastes and visual features[END_REF], the questionnaire was simultaneously answered by a group of Brazilian and a group of French consumers. There are also expressive differences in the chocolate consumption between the two countries, although chocolate is commonly considered the most desired food in all the Western world [START_REF] Richard | Food cravings in everyday life: An EMA study on snack-related thoughts, cravings, and consumption[END_REF]. While the French eat 7.3 kg of chocolate per capita/year, with dark chocolate representing 30% of consumption among adults [START_REF] Cohen | Chocolat : les Français en consomment plus de 7kg par an [Chocolate: the French eat more than 7 kg per year of it[END_REF], Brazilians eat 2.8 kg and only 3% of it is dark chocolate [START_REF] Sebrae | Relatório de inteligência: Produção e consumo de chocolate no Brasil [Intelligence report: production and consumption of chocolate in Brazil[END_REF].

Based on the framework described above, the hypotheses were: H1: the packaging color affects the expectations of sweetness, bitterness, fruitiness, melting, and liking of chocolate; H2: Cold-colored packaging increase the expected bitterness (H2a), warm-colored packaging increase expected sweetness (H2b) and fruitiness (H2c); H3: packaging colors differently affect expectations for milk and dark chocolates; H4: packaging colors differently affect expectations of Brazilian and French consumers.

Methods

Stimuli

The stimuli (Figure 1) were pictures (958 x 958 pixels) of Lindt (Lindt & Sprüngli AG, Kilchberg, Switzerland) milk chocolate (min. 30% cocoa) and dark chocolate (min. 70% cocoa) in black, blue, brown, green, red, pink and yellow packaging. The packaging were folded rectangular (10.5 x 4 cm) pieces of Maldor's 130 g/m² colored paper (Clairefontaine, Etival Clairefontaine, France). The images are photographs, all taken in less than 5 minutes with a Galaxy S7 (Samsung, Manaus, Brazil) in an open space with direct sunlight. They were cropped, resized and had their contrast increased by 30% on Photoshop CS6 (Adobe, San José, CA, USA).

Participants

An email inviting chocolate consumers to participate in the research was sent to students and staff from AgroSup Dijon and the School of Biology, Earth and Environment Sciences of the University of Burgundy in France, and from the University of Campinas' School of Food Engineering and School of Agricultural Engineering in Brazil. They were informed that they were going to "answer a questionnaire about four chocolates" and nothing else on the subject or aim of the study. Together with the invitation, they received a link that directed to an online survey designed and hosted on Compusense Cloud (Compusense, Guelph, Canada). Before starting the questionnaires, respondents read and were given the choice to accept or decline an informed consent form. This study was approved by the University of Campinas' Ethic in Research Committee (protocol 20489019.4.0000.5404).

Using their own devices (i.e., smartphones, tablets or computers), 445 chocolate consumers in France and 245 in Brazil completed the questionnaire during the first two weeks of March 2020. From them, 32 in France and 27 in Brazil were not included in the study for being underage, not being French or Brazilian, or giving an invalid answer to any of the questions. The first 210 valid respondents from Brazilian group were selected. This N was chosen so the maximum of data was used and the number of evaluations for each sample was balanced. Then, French participants were also selected in "first in, first included" criterium to match the Brazilian group in number (210), age range (18-60 y.o.), gender distribution (146 female), and mean age (26.40±8.32 y.o. in France,26.40±6.69 y.o. in Brazil). This screening process was performed to obtain comparable groups across cultures (Ares, 2018).

Data collection

If respondents accepted to participate in the study, one of the samples from Figure 1 was shown without any other information on the purpose of the study or on the sample brand, cocoa content, packaging color etc. Then, participants were asked to rate their expectation of sweetness, bitterness, fruitiness and melting using a 9-point intensity scale (1 = not at all, 9 = extremely) and expected liking using a 9-point hedonic scale (1 = extremely dislike, 9 = extremely like). The questions were "How sweet/bitter/melting/fruity do you think this chocolate is?" and "How much do you think you would like this chocolate?". All communication and questionnaires were in Portuguese in Brazil and in French in France, the translation to French was independently checked by three native speakers familiar with sensory analysis of food, but no equivalency test was performed.

Each participant monadically evaluated two samples of dark chocolate and two of milk chocolate, therefore, four of the14 different samples. The balanced incomplete block was a Williams design provided by Compusense with 98 sets created by modifying a 14 x 14 Latin Square [START_REF] Williams | Experimental designs balanced for the estimation of residual effects of treatments[END_REF]. The presentation of the chocolate types and the order of appearance of the attributes were balanced between participants. After evaluating the samples, they were asked about what type of chocolate they usually eat ("white", "milk", "dark > 60% cacao", and/or "dark < 60%"), with which frequency ("once a month", "2 to 4 times per month", "2 to 6 times per week", or "everyday"), which are their nationality (open answer), gender ("masculine", "feminine", or "other"), and age (open answer).

Statistical analysis

Three-way mixed design analyses of variance (ANOVA) (model GLM, SAS Institute, Cary, USA) at 5% significance level were performed separately for each attribute, so Holm-Bonferroni was used to correct for multiple comparisons. ANOVA was performed on least square (LS) means to compensate for the incomplete block, with block as random factor because of the subjective nature of human behaviour, with country as between-subject fixed factor because each group has a different nationality and it was a controlled factor, and with sample as within-subject fixed factor because participants had different samples and it was also a controlled factor. When the sample effect was significant, Tukey-Kramer's test was used for pairwise comparison, also corrected by Holm-Bonferroni. Further contrast analysis opposing dark and milk chocolate samples was performed using Excel 2010 (Microsoft, Remond, USA). Multiple factor analysis (MFA) was then performed on the samples by attributes by country matrix to provide a synthetic view of the data. MFA was followed by hierarchical cluster analysis (HCA) using the Ward's agglomeration criterion on the first two dimensions of the MFA. Both MFA and HCA were performed using FactoMineR [START_REF] Lê | FactoMineR: An R package for multivariate analysis[END_REF] for R (R Core Team, 2020).

Results

Participants

Type of chocolate consumed and frequency of consumption were both significantly different (χ² = 27.85, df = 3, p < .01 and χ² = 10.48, df = 3, p = .02, respectively) between the two groups. As shown in Table 1, more French participants reported eating dark chocolate (> 60% cocoa) and more Brazilians reported eating white, milk, and dark (< 60% cocoa) chocolates. Also, while French participants are well distributed between all frequencies of consumption (1/month to everyday), most Brazilians eat chocolate on intermediary frequencies (2-4/month and 1-6/week). Furthermore, the French showed more specificity regarding the type of chocolate eaten (1.79 versus 2.05 types of chocolate per person, χ² = 9.67, df = 3, p = .03). The mean ratings given by participants to the milk and dark chocolate samples in different packaging colors are shown in Table 3. Chocolate packaged in pink and yellow were generally expected to be sweeter, less bitter, more melting, and fruitier. On the other hand, black packaging increased bitterness ratings and lowered sweetness, fruitness, and melting ratings. Scores for red, blue, and green samples were rarely significantly different from other samples. Brown packaging had the greatest number of significant differences, being rated as the sweetest, the least bitter, and most melting and liked among dark chocolates, as well as the most bitter and the least sweet among milk chocolates.

Black, blue, and green packaging had the lowest liking ratings among dark and the highest ratings among milk chocolates, while the opposite happened to pink and yellow, that is, they received the lowest ratings among milk and the highest among dark. Regarding fruitiness, the dark chocolate in pink and red packaging received the highest mean rates, they were significantly different from milk chocolate in blue and black packaging. ). In addition to the contrast analysis, the greater standard deviations of the mean ratings (0.62 vs 0.38 in sweetness, 0.65 vs 0.48 in bitterness, 0.45 vs 0.30 in fruitiness, 0.52 vs 0.30 in melting, 0.39 vs 0.17 in liking) and the greater number of significant differences between samples (27 vs 9 in total) indicate that packaging color affected more the expectations for dark chocolate than for milk chocolate.

MFA and HCA

The correlation circle (Figure 2A) indicates small differences between the Brazilian and French groups. The first dimension explains 72.85% of the variance and is negatively correlated to bitterness (-.99 and -.99) and melting (.23 and -.32), while positively correlated to sweetness (.99 and .99), fruitiness (.99 and .99), and liking (.85 and .67) in Brazil and France, respectively. The second dimension is mostly correlated to melting (.93 and .90) and explains 17.43% of the variance so that the first two components of the MFA account for 90.28% of total variance.

The individual factor map (Figure 2B) shows a clear separation between the milk (right) and the dark chocolates (left) on the first dimension. As shown by Table 3, milk chocolates were generally expected to be sweeter (means 6.82±0.38 vs. 3.26±0.62), less bitter (2.73±0.48 vs. 6.76±0.65) and fruity (3.76±0,30 vs. 3.98±0.45), more melting (6.41±0.30 vs.

3.53±0.52) and liked (6.52±0.17 vs. 5.96±0.39) than dark chocolate. The second dimension shows both chocolates packaged in pink, red, yellow, and green (up) in opposition to blue, black, and brown (down). Overall, the projections of each country for a same sample are more distant vertically than horizontally, indicating that melting is an important attribute to discriminate the answers from the Brazilian and French groups.

HCA revealed three clusters, the first with all milk chocolate samples (left), the second with dark chocolate samples in pink, red, yellow and green packaging (right/up), and third with dark chocolate packaged in brown, blue and black (right/down). The first cluster is correlated with sweeter, fruitier, and more liked samples; the two others are correlated with more bitter samples. The difference between the second and the third clusters is on the second dimension, the former being positively correlated to melting and the latter negatively.

Discussion

Color

The first hypothesis (H1) was confirmed, that is, packaging colors significantly affected the expectations of sweetness, bitterness, fruitiness, melting and liking. A review of [START_REF] Spence | On the multiple effects of packaging colour on consumer behaviour and product experience in the 'food and beverage' and 'home and personal care' categories[END_REF] showed significant effects of packaging colors on other food and beverage products, but the only previous research on chocolate [START_REF] Van Lith | Communicating health through package color and material: The influence of color and material of food packaging on perceived product healthfulness[END_REF] with 23 participants in Netherlands reported no significant effect of seven different colors of packaging on tastiness and attractiveness. Reasons why the present study found significant differences in liking, while the previous did not on tastiness and attractiveness, might be: the colors used, a cultural difference, the lack of other information (i.e., logo, label, illustrative picture) and/or just a greater number of participants.

As dark and milk chocolate were shown interleaved to make the aim of the study less obvious to participants, the sample effect accounted for the influence of chocolate type and of packaging color at the same time. All attributes were significantly affected by sample, but sweetness, bitterness and melting were more strongly than fruitiness and liking. On one hand, it is evident that type of chocolate was more relevant for sweetness, bitterness and melting, because all milk chocolate samples were significantly different from all dark chocolate samples in these attributes, regardless of packaging color. On the other hand, color was more relevant for fruitiness than type of chocolate, because none of the samples were rated significantly fruitier than the other type packed in the same color, while there were some significant effects between samples with different colors. On liking, effects of type and packaging color were dependent and can not be separated.

ANOVA revealed that black packaging is correlated to bitterness, while pink and yellow packaging are correlated to sweetness. [START_REF] Spence | On tasty colours and colourful tastes? Assessing, explaining, and utilizing crossmodal correspondences between colours and basic tastes[END_REF] indicated that the associations black-bitter and pink-sweet are commonly reported in different cultures, but not the yellow-sweet association, as this color is generally correlated to sourness. Yet, the yellow-sweet association is somehow coherent with the findings that Uruguayan consumers expected milk dessert in black packaging to be more bitter than in yellow or white [START_REF] Ares | Studying the influence of package shape and colour on consumer expectations of milk desserts using word association and conjoint analysis[END_REF]; that Spanish consumers expected chewing gum in grayscale (black to white) packaging to be less sweet than in warm (red to yellow) or cool (blue and green) colors [START_REF] Rebollar | Influence of chewing gum packaging design on consumer expectation and willingness to buy: An analysis of functional, sensory and experience attributes[END_REF]; and that Brazilians expected and perceived two coffees as sweeter when in a yellow cup [START_REF] Carvalho | Cup colour influences consumers' expectations and experience on tasting specialty coffee[END_REF].

Previous studies [START_REF] Rebollar | Influence of chewing gum packaging design on consumer expectation and willingness to buy: An analysis of functional, sensory and experience attributes[END_REF][START_REF] Spence | On tasty colours and colourful tastes? Assessing, explaining, and utilizing crossmodal correspondences between colours and basic tastes[END_REF][START_REF] Huang | Eat with your eyes: package color influences the expectation of food taste and healthiness moderated by external eating[END_REF][START_REF] Tijssen | Why a 'light' product package should not be light blue: Effects of package colour on perceived healthiness and attractiveness of sugar-and fat-reduced products[END_REF] reported that red packaging consistently increases expectations of sweetness, creaminess, and fruitiness in food products, but both chocolate samples in red packaging in this study received intermediary rates. Red was only significantly different from black on bitterness among dark chocolate and from pink on sweetness among milk chocolate.

The faible effect might be due to the brightness and/or saturation used in this experiment, but van Lith (2015) also did not find significant effects for red packaging. [START_REF] Spence | On the multiple effects of packaging colour on consumer behaviour and product experience in the 'food and beverage' and 'home and personal care' categories[END_REF] argued that it could be due to the Dutch association between red packaging and dark chocolate, the finding of the same result in France and Brazil indicates the lack of effect is more general in Western cultures.

Brightness and/or saturation could also be relevant to understand why samples in green packaging were rated significantly more bitter than in brown, pink, and yellow among dark chocolate, and blue and pink among milk chocolate. Two out of five studies reviewed by [START_REF] Spence | On tasty colours and colourful tastes? Assessing, explaining, and utilizing crossmodal correspondences between colours and basic tastes[END_REF] reported an association between green and bitterness, while four reported association with sourness. This ambivalence is not rarely explained by the prevalence of limes or lemons in the participants' culture [START_REF] Carvalho | Cup colour influences consumers' expectations and experience on tasting specialty coffee[END_REF], but in this study Brazilians distinctly associated green to bitterness. So, it is possible that the use of a brighter or darker shade of green might also play a role in the ambiguity, as a same culture might associate the first with the color of lime and the second with the color of dark green vegetables like broccoli and spinach.

The dark chocolate in brown packaging received the most ambivalent ratings, being the sweetest and the least bitter among dark chocolates, while it got the highest rating for bitterness and the lowest for sweetness among milk chocolate. This might be due to a dual effect of packaging color depending on chocolate type or, more likely, a miscalibration of the lighting by the camera used in this study, as the dark chocolate seems slightly brighter in the brown packaging than the other dark chocolate samples. This unbalanced lighting was unnoticed by the researchers before the conclusion of the data collection. Other samples might also have lighter differences, but these differences varied according to the device used by the participant and are, at least in part, an effect of the contrast with the packaging color.

As the stimuli showed both chocolate and packaging, the samples were combinations of two colors. It has been shown that the combination of two congruent colors can be more strongly associated to a taste than the colors alone, especially when one is dominant and the other is auxiliary (Woods & Spence, 2016;Woods et al., 2016). In the present study, stronger effects of chocolate type indicate that the color of the chocolate was more important than the color of the packaging, suggesting that the former was perceived as foreground and the latter as background. That is understandable, since participants were asked to rate their expectations for the chocolate, not for the packaging. Thus, the results in this study are the effects of the combination of the packaging color with the color of chocolate and they might not be replicable in packaging that do not show the chocolate by transparency or illustration.

Warm and cold colors

The hypothesis that cold colors would increase bitterness ratings (H2a) and warmcolored packaging would increase sweetness (H2b) and fruitiness (H2c) ratings was not confirmed. First, MFA separated almost perfectly between cold and warm colors, except for both samples in green, that are together with pink, red and yellow on the upper part of the individual map (Figure 2B). Then, the milk chocolate in red packaging received much closer ratings to black, blue, green, and brown than to pink and yellow in sweetness and bitterness, being rated significantly more bitter than pink. In the other direction, the milk chocolate in blue packaging, a cold color, was rated the second most sweet and the second less bitter, being expected significantly less bitter than brown and green. Among dark chocolate the distinction was stronger, as all warm colors were rated-although not always significantly-as sweeter and less bitter than all cold colors, except brown, whose results are questionable.

Based on the cold and warm distinction, most studies compare and find significant effects on expectation and perception of food and drinks in red and blue packaging [START_REF] Rebollar | Influence of chewing gum packaging design on consumer expectation and willingness to buy: An analysis of functional, sensory and experience attributes[END_REF][START_REF] Huang | Eat with your eyes: package color influences the expectation of food taste and healthiness moderated by external eating[END_REF][START_REF] Tijssen | Why a 'light' product package should not be light blue: Effects of package colour on perceived healthiness and attractiveness of sugar-and fat-reduced products[END_REF][START_REF] Van Esch | The effects of inner packaging color on the desirability of food[END_REF][START_REF] Rosa | Influences of visual attributes of food packaging on consumer preference and associations with taste and healthiness[END_REF].

This study found no significant difference between these two packaging colors in any attribute of any chocolate type. These unusual results might be particular to chocolate packaging, to Brazilian and French cultures, or to the brightness and saturation used by this experiment, but they resemble the results on single colors reported by Woods & Spence (2016). Thus, researchers, industries, artisans, chefs, baristas, mixologists, packaging designers, food bloggers and photographers might consider contrasting black to pink or yellow, instead of red to blue when willing to influence the consumer's expectations.

Chocolate type

The third hypothesis (H3) was confirmed: packaging colors affected milk and dark chocolate differently. The greater standard deviation of the mean ratings and the greater number of significant differences indicate that packaging color affected more the expectations for dark chocolate than for milk chocolate. HCA also evidences that, as dark chocolate samples were separated in two clusters, while the milk chocolate samples were all grouped in one single cluster. This difference might be a consequence of a stronger and wider flavor and texture profile found in chocolates with higher cocoa content, and/or of the adding effect of shape and color congruency [START_REF] De Sousa | Colour and shape of design elements of the packaging labels influence consumer expectations and hedonic judgments of specialty coffee[END_REF]. As dark chocolate is related to squared-shapes and milk chocolate to round-shapes [START_REF] Ngo | Assessing the shapes and speech sounds that people associate with chocolate samples varying in cocoa content[END_REF], results could be different if the chocolate samples were rounded.

Regarding liking, packaging colors influenced the types of chocolate differently, even in opposite directions. Table 2 shows that while the black packaging made the milk chocolate the most liked of all samples, the same packaging made the dark chocolate the least liked.

The pink packaging had an opposite effect, making the dark chocolate the second most likedonly behind the one packed in brown, whose results are questionable as mentioned on the previous item-and the milk chocolate the second least liked among its type. Other colors, except brown, had similar ambivalent effects, increasing liking in one of the types and decreasing on the other.

If at first it would be intuitive and congruent to use dark packaging colors for dark chocolates and light colors for milk chocolates, this study shows that contrasting the chocolate type and the packaging color might make it more appealing for consumers. This might be an explanation for why some industries in Europe use red packaging for dark chocolate, as mentioned before. Perhaps the incongruity between packaging color and chocolate type increases liking by making the product look more balanced, that is, "sweet colors" make dark chocolate look not too bitter, and "bitter colors" make milk chocolate look not too sweet.

This result does not necessarily mean that consumers individually prefer balanced chocolates, but that the group preference converges on balanced chocolates, something natural if we expect to have individuals with preferences normally distributed through all the spectrum of bitterness to sweetness. Therefore, food industries and services that use visual cues to sell their products to a broad public, such as chocolate bars in a supermarket or a chocolate-based pastry on a shop window, could improve their overall expected liking by using the right packaging or background color to the right type of chocolate. This resource should be used with care, though, since great disconfirmation of expectation may lead to a penalty on post-comsumption liking [START_REF] Cardello | Effects of disconfirmed consumer expectations on food acceptability[END_REF].

Cross-cultural effects

The hypothesis that packaging color would affect Brazilian and French consumers differently (H4) was not confirmed. ANOVA combining the effects of country and sample showed no significant difference between groups, indicating that packaging colors affected ratings in the same general way in both groups. This understanding is also supported by the proximity between groups of the angles on the correlation circle (Figure 2A) and of the projections on the individual map (Figure 2B). For practical applications, it evidences that no change in packaging or context colors might be necessary for exporting chocolate products or offering a chocolate pastry dish in Brazil, France, and possibly many other Western cultures.

It is interesting to add that ANOVA found significant effects of country alone in all attributes except sweetness. These results show that the overall rating of bitterness, fruitiness, melting, and liking was different between groups, but not that packaging colors had different effects. For example, the Brazilian mean rating for bitterness of all samples was significantly higher than the French, probably a consequence of the smaller percentage of Brazilians that reported eating chocolate with more than 60% cocoa. As they are less familiar to bitter chocolates, they rated bitterness higher than the French.

In the other direction, it is unexpected that there was no significant difference for sweetness between countries with such different relationships with sugar, as Brazilian desserts are known for being distinctly sweet and sugar being part of the cultural, economic and political history of the country (Freyre, 2007). But the lack of difference does not necessarily indicate that they perceive sweetness equally, it only shows that both groups had similar expectations of sweetness when seeing images of chocolate samples. What Brazilian consumers would rate as a moderately sweet chocolate when tasted might still be too sweet for French consumers.

Limitations

As recent studies showed that the lightning and chroma may affect emotions more than the hue alone [START_REF] Schloss | Blue hues don't bring the blues: questioning conventional notions of color-emotion associations[END_REF] and, as color-taste effects might occur via emotions correspondences [START_REF] Palmer | Music-color associations are mediated by emotion[END_REF], they were a relevant uncontrolled factor in this study.

Further studies should investigate the effects of colors in more complex and realistic packaging, including more than one hue, brightness and/or saturation. As the aim of this study was to explore the color effect, no other detail was included in the packaging, such as brand, weight, claims, product description or illustration. Participants of both groups were recruited from institutions that teach and research Food, Biology and Agriculture, therefore their background knowledge of scientific methods and/or food likely influenced the results.

This study also did not check participants for color blindness, nor controlled the final resolution and color balance of the pictures since participants used their own devices to answer the questionnaire. To make the goal of the experiment less obvious to participants, this study chose to collect and analyze data on milk and dark chocolate samples together.

This might have led to a smaller number of significant differences, particularly among milk chocolate samples, because the effects of packaging color on dark chocolate were stronger.

Another step forward on the subject would be testing if these effects on expectation affect consumers' actual perception, because that is not always the case [START_REF] Zellner | The effect of wrapper color on candy flavour expectations and perceptions[END_REF].

Conclusion

This study was the first to find significant effects of several packaging colors on expected taste, flavor, texture and liking of chocolate. It was also the first to evaluate that for two types of the same food product with opposing sensory qualities (bitter x sweet) among two different cultures. Another difference was showing both the product (chocolate) and the packaging on the picture. Significant interactions between chocolate type, packaging color and culture showed that effects are co-dependent, making it important to consider and control all these variables together. It is possible to conclude that black packaging induces greater expectation of bitterness and yellow and pink packaging induce greater expectation of sweetness and melting in chocolate. Also, that the effects of a packaging color on expected liking might take opposite directions for milk and dark chocolate. The effects of context color on food must be further investigated to understand how industries, artisans, chefs, baristas, mixologists, packaging designers, food bloggers and photographers may use it to influence the consumers' expectations for its products and services.

Figure 1 .

 1 Figure 1. Dark chocolate (above) and milk chocolate (below) in green, red, pink, yellow, blue, black and brown packaging.

Figure 2 .

 2 Figure 2. Multiple factor analysis: (A) Correlation circle of variables in Brazil and France; (B) Individual factor map with HCA clusters.

Table 1 .

 1 Chocolate consumption profiles of the Brazilian (N = 210) and French (N =210) groups, in percentage.

	Brazil %	France %

The performed analyses of variance (Table

2

) showed that significant main effects of country were found for all attributes but sweetness (means 5.08±1.94 vs. 4.98±1.85, in Brazilian and French groups, respectively). Brazilian participants expected the chocolates to be fruitier (5.20±1.85 vs. 4.73±1.94), more bitter (5.02±1.99 vs. 4.47±2.34), melting (4.07±0.51 vs. 3.65±0.28), and liked (6.45±0.42 vs. 6.04±0.43) than French. ANOVA also revealed significant main effects of sample for all descriptors, but no significant sample by country interaction was found.

Table 2 .

 2 F values and p-values for each dependent variable from the three-way ANOVA with block, country and sample as factors. Significance of 5% after Holm-Bonferroni's correction for multiple comparison is p < .01.

		Sweetness	Bitterness	Fruitiness	Melting	Liking
	Effects F	p	F	p	F	p	F	p	F	p
	Block	1.7 < .01	1.44	< .01	2.6	< .01	1.99 < .01	1.77 < .01
	Country 0.83 .36	22.43 < .01	10.33 < .01	17.98 < .01	12.06 < .01
	Sample 197 < .01	196.42 < .01	4.19 < .01	108 < .01	6.62 < .01
	Sample*
	Country 1.3 .20	1.81	.04	0.74 .73	1.49 .11	.78	.68

Table 3 .

 3 Least square means and standard deviation for sweetness, fruitiness, melting, and liking of dark and milk chocolates in seven packaging colors (1 = not at all, 9 = extremely).

	Values with the same letters in each column were not significantly different according to
	Tukey-Kramer's test at 5% significance corrected by Holm-Bonferroni for multiple
	comparison.
			Sweetness	Bitterness	Fruitiness Melting	Liking
		Black	2.27±1.33 e	7.77±1.49 a 3.49±2.43 bc 2.92±1.70 e 5.45±2.28 c
		Blue	2.94±1.64 de 7.07±1.96 abc 3.59±2.13 bc 3.12±1.64 de 5.68±2.02 bc
		Brown	4.11±1.69 c	5.89±1.85 d 3.53±2.15 bc 4.48±1.87 c 6.54±1.74 a
	Dark	Green	2.88±1.62 de 7.27±1.73 ab 4.05±2.22 abc 3.22±1.76 de 5.63±2.25 bc
		Pink	3.75±1.63 c	6.31±1.95 cd 4.62±2.21 a 3.79±1.15 cd 6.25±1.79 abc
		Red	3.33±1.68 cd 6.73±1.90 bcd 4.40±2.26 ab 3.48±1.77 de 6.08±1.78 abc
		Yellow	3.57±1.64 cd 6.31±1.90 cd 4.19±2.06 abc 3.70±1.89 cde 6.09±1.89 abc
		Black	6.62±1.49 ab 3.06±2.00 efg 3.41±1.92 c 6.32±1.54 ab 6.80±1.45 a
		Blue	7.20±1.44 ab 2.21±1.34 fg 3.44±1.99 c 6.50±1.74 ab 6.53±1.70 a
		Brown	6.43±1.53 b	3.25±1.88 e 3.50±1.97 bc 6.42±1.70 ab 6.62±1.53 a
	Milk	Green	6.43±1.61 b	3.15±1.79 e 4.09±2.17 abc 5.86±1.93 b 6.30±1.71 ab
		Pink	7.14±1.24 ab 2.17±1.39 g 4.08±2.04 abc 6.71±1.73 ab 6.45±1.54 ab
		Red	6.60±1.58 ab 3.00±1.77 ef 3.98±2.20 abc 6.29±1.86 ab 6.60±1.55 a
		Yellow	7.31±1.32 a	2.30±1.36 fg 3.82±2.22 abc 6.74±1.49 a 6.35±1.70 ab


Cassandre Leverrier

Giana Almeida Perré

Gérard Cuvelier

Paul Menut

Giana Almeida

Modelling shear viscosity of soft plant cell suspensions

Keywords:

Introduction

Food products include many examples of soft materials: emulsions (mayonnaise, milk...), foams (chocolate mousse, Chantilly, whipped egg white...), suspensions (spreadable paste, processed fruits and vegetables...) and gels (yoghurt, jelly ...). Most of them are complex multicomponent systems, which explains the rapid expansion of the application of physics and materials science in food science and technology [START_REF] Ubbink | Soft matter approaches to structured foods: from "cook-and-look" to rational food design ? Faraday Discuss[END_REF][START_REF] Vilgis | Soft matter food physics-the physics of food and cooking[END_REF][START_REF] Sman | Soft matter approaches to food structuring[END_REF][START_REF] Boire | Soft-Matter Approaches for Controlling Food Protein Interactions and Assembly[END_REF] Fruit and vegetable purees consist in a suspension of plant cells and are an example of soft material encountered in food. They are obtained by cooking and grinding the flesh of a fruit or a vegetable. Flesh is composed of cells, whose size varies according to the plant, from tens to several hundreds of microns. A plant cell wall, mainly composed of insoluble polymers, delimits the cells. During cooking, soluble polymers (pectins) contained in the middle lamella between the cell walls will solubilize and the fruit flesh disintegrates, releasing cell clusters of heterogeneous size, individual cells and cell fragments. Cooking parameters will have an impact on the particle size distribution and on the rigidity of the walls, an intensive cooking leading to more porous and less rigid cell walls, and less cell clusters in suspension. Fruit or vegetable suspensions are thus composed of a dispersed phase, the plant particles (plant cells without turgor), suspended in an aqueous continuous phase mainly composed of water, polymers (pectins), sugar and ions initially present in the fruit or vegetable.

Plant particles obtained thereby have specific structural and physical properties. They are only made of plant cell walls filled with the continuous phase, thus defining a particle whose volume varies with the concentration of the suspension [START_REF] Lopez-Sanchez | Shear Elastic Deformation and Particle Packing in Plant Cell Dispersions[END_REF][START_REF] Leverrier | Influence of Particle Size and Concentration on Rheological Behaviour of Reconstituted Apple Purees[END_REF] . These particles are porous, deformable and compressible and can be nested in each other. Plant particles are large size non-colloidal objects, which shape and rigidity depend on plant's variety and maturity, but also on mechanical or thermal treatments undergone by the fruits. Shape and rigidity also depend on particle's internal structure: clusters of cells are larger but also more irregular in shape and more rigid than individual cells, due to their internal architecture [START_REF] Leverrier | Influence of Particle Size and Concentration on Rheological Behaviour of Reconstituted Apple Purees[END_REF] .

Suspensions of plant particles strongly resemble soft glassy materials [START_REF] Roversi | Supramolecular assemblies from plant cell polysaccharides: Self-healing and aging behavior[END_REF] , which in rheological terms are defined as "very soft solids, yet flow readily above a critical yield stress" [START_REF] Chen | Rheology of Soft Materials[END_REF] . The category of soft glassy material comprises foams, emulsions and star polymer gels among others. Specifically, the suspensions of plant particles could be part of the soft particle glasses, defined by Seth (2011) as "materials made of deformable particles as diverse as microgels, emulsion droplets, star polymers, micelles and proteins which are jammed at volume fraction where they are in contact and interact via soft elastic repulsions", behaving like "weak elastic solids at rest but flow[ing] very much like liquids above the yield stress".

Understanding the rheological behavior of such suspensions and mastering parameters impacting this behavior is a challenge for the food industry. If the rheology of plant particle suspensions has been extensively studied in order to understand the impact of many parameters such as variety, thermal and mechanical treatments or the continuous phase [START_REF] Day | Dynamic rheological properties of plant cell-wall particle dispersions[END_REF][START_REF] Espinosa-Muñoz | Structural parameters that determine the rheological properties of apple puree[END_REF] no rheological model applicable over a wide range of concentrations has been developed yet to describe the rheological behavior of such suspensions, in flow or at rest. In general, models for the viscosity of granular or colloidal suspensions require the knowledge of the particle volume fraction, which is here difficult to estimate. Literature does not agree on one definition so far and many parameters are still used to evaluate the medium's congestion such as the insoluble solids content [START_REF] Leverrier | Influence of Particle Size and Concentration on Rheological Behaviour of Reconstituted Apple Purees[END_REF] , the water insoluble solids content [START_REF] Schijvens | Effect of processing conditions on the composition and rheological properties of applesauce[END_REF] or the percentage of pulp [START_REF] Moelants | Relation Between Particle Properties and Rheological Characteristics of Carrot-derived Suspensions[END_REF] . Nevertheless, three concentration domains have been highlighted on several kind of plant particle suspensions [START_REF] Lopez-Sanchez | Shear Elastic Deformation and Particle Packing in Plant Cell Dispersions[END_REF][START_REF] Leverrier | Influence of Particle Size and Concentration on Rheological Behaviour of Reconstituted Apple Purees[END_REF][START_REF] Day | Control of Morphological and Rheological Properties of Carrot Cell Wall Particle Dispersions through Processing[END_REF] and discussed in literature. Until now, their modelling have been limited to empirical equations, such as linear, exponential or power law fittings, which range of validity is limited to their own concentration domain.

In this article, we will propose a single model describing the viscosity as a function of the concentration over the full range of concentration investigated, taking into account the compression when the concentration increases. This model will be conceptually based on a model initially proposed by Mendoza [START_REF] Koumakis | Direct comparison of the rheology of model hard and soft particle glasses[END_REF][START_REF] Mendoza | Model for the Shear Viscosity of Suspensions of Star Polymers and Other Soft Particles[END_REF] for soft particles, and initially applied to star polymers. We propose here to adapt this model so that it can describe the viscosity divergence that occurs at a finite, maximum volume fraction above which particles cannot be compressed anymore. The validity of the model will be tested on real apple purees characterized by different particles properties, so that it will be possible to correlate the model parameters with particles properties such as their rigidity, shape and size. We will investigate how the effect of polydispersity, associate with different values of the random close packing volume fraction, affect the quality of the model. Finally, we will use a single suspensions of monodispersed apple particles suspended in several continuous phases to evaluate how the model parameters could also reflect variations in continuous phase lubrication properties.

Material and methods

Plant material and processing conditions

A single batch of mature Golden Delicious (Malus domestica Borkh. cv Golden Delicious) was transformed into puree by a French manufacturer (Conserves France) following an industrial hot break process. From this raw material, two kinds of suspensions were studied: ground purees and model suspensions made of isolated apple cells dispersed in various aqueous media.

Ground purees

Three particle size distributions were obtained using mechanical treatment as described in Leverrier et al. (2016). By using such procedure, and by contrast with thermal treatments cell walls' rigidity is not affected by grinding. The architecture of the particle (either individual cells or clustered) may however have an impact on its global rigidity: clusters are supposed to be more rigid when compared to individual cells [START_REF] Leverrier | Influence of Particle Size and Concentration on Rheological Behaviour of Reconstituted Apple Purees[END_REF] .

Model suspensions

Model suspensions composed of individual cells were also constructed from the same raw material using wet sieving and solvent exchange as described in Leverrier (2017). This protocol is known to maintain an intact cell structure [START_REF] Müller | Material properties of processed fruit and vegetables I . Effect of extraction and thermal treatment on apple parenchyma[END_REF] . Apple particles (isolated dry individual cells) were suspended in three controlled aqueous media (one solution of NaCl at 1%w/w and two solutions of carboxymethylcellulose of 1%w/w and 3.2%w/w, of 1mPa.s, 12.6mPa.s and 108mPa.s respectively) and in the original continuous phase of apple puree obtained by centrifugation (apple serum of 12.8 mPa.s).

Particle size distributions and rheological measurements

The particle size distribution of samples was obtained using a laser diffraction analyser (Mastersizer 2000, Malvern Instruments). Samples were dispersed in distilled water (refractive index: 1.33). The refractive index of vegetable cells is estimated to be 1.52 and the absorption was set at 0.1 [START_REF] Leverrier | Influence of Particle Size and Concentration on Rheological Behaviour of Reconstituted Apple Purees[END_REF][START_REF] Day | Dynamic rheological properties of plant cell-wall particle dispersions[END_REF][START_REF] Leverrier | Design of Model Apple Cells Suspensions: Rheological Properties and Impact of the Continuous Phase[END_REF][START_REF] Espinosa | Effect of processing on rheological, structural and sensory properties of apple puree[END_REF][START_REF] Espinosa | Texture de la purée de pomme : influence de la structure sur les propriétés rhéologiques et la perception sensorielle -effet du traitement mécanique[END_REF] . Measurements were made in triplicate. Microscopic observations were made as described in Leverrier et al. (2016).

The rheological measurements were performed using a stress controlled rheometer (MCR301, Anton Paar) equipped with large gap coaxial cylinders [START_REF] Leverrier | Influence of Particle Size and Concentration on Rheological Behaviour of Reconstituted Apple Purees[END_REF][START_REF] Leverrier | Design of Model Apple Cells Suspensions: Rheological Properties and Impact of the Continuous Phase[END_REF] . Apparent viscosities of the suspensions were taken at 50s -1 .

Results & Discussion

How to access the particles' volume fraction?

Unlike hard spheres, the volume fraction of soft deformable particles is not well defined [START_REF] Shewan | Viscosity of soft spherical micro-hydrogel suspensions[END_REF][START_REF] Boehm | Food Hydrocolloids A method for developing structure-rheology relationships in comminuted plant-based food and non-ideal soft particle suspensions[END_REF] .

For microgel suspensions, the apparent volume fraction is often linearly related to the polymer concentration [START_REF] Fernandez-Nieves | Microgel Suspensions Fundamentals and Applications[END_REF] and based on the particles' volume in diluted conditions [START_REF] Shewan | Viscosity of soft spherical micro-hydrogel suspensions[END_REF] , for which polymer networks are in their most swollen state. The apparent volume fraction of microgels suspensions is thus frequently defined as , where is their specific volume in diluted conditions [START_REF] Shewan | Viscosity of soft spherical micro-hydrogel suspensions[END_REF] , determined from an Einstein-type equation. A comparable approach has been used in 2012 by Espinosa (2012) on apple cells suspended in their own serum. The volume fraction of individual apple cells can be then written as (1) Where is the voluminosity of the cells (volume occupied by unit of mass) and is the insoluble solids content. The parameter being linked to the particle size and shape. By integrating Eq. ( 1) in a second order expression of the kind of Batchelor & Green (1972) such as 1 " " # $, and by analogy with the Huggins equation (defined for dilute polymer solutions as %&' () * " # the following equation was obtained :

-1 " # (2)
The parameter is linked for spherical particles to their deformability, its value is between 1 (for gas bubbles) [START_REF] Taylor | The viscosity of a fluid containing small drops of another fluid[END_REF] This approach provides access to and takes into account the deformability and the rigidity of the particles by setting the parameter . However, it slightly overstates the real volume fraction occupied in intermediate and concentrated domains.

Indeed, considering a linear relationship between the volume fraction and the quantity of cell wall in suspension (insoluble solids content ) implies that the voluminosity of the particles is the same whatever the concentration. This is not the case, as illustrated in Figure 1. Three concentration domains were highlighted in literature [START_REF] Lopez-Sanchez | Shear Elastic Deformation and Particle Packing in Plant Cell Dispersions[END_REF][START_REF] Day | Control of Morphological and Rheological Properties of Carrot Cell Wall Particle Dispersions through Processing[END_REF] . In the diluted domain, particles are able to flow freely and do not interact with each other. In the intermediate domain, described as the building of a stress-bearing network between particles, particles are at rest in contact with each other: elastic properties become measurable. Note that for spherical particles, the onset of the intermediate domain is usually referred as random loose packing, it occurs at volume fractions which could be much below random close packing, and depend on cohesive and frictional interactions [START_REF] Silbert | Jamming of frictional spheres and random loose packing[END_REF][START_REF] Dong | Role of Interparticle Forces in the Formation of Random Loose Packing[END_REF] . Finally, the concentrated domain corresponds to a domain where particles highly deform and decrease their volume to fit the available space and to be able to flow.

It is therefore necessary to consider the particle compressibility in determining their volume fraction at a given concentration. The presence of cells fragments also restricts the use of a linear relationship between volume fraction and insoluble solid content. If plant particle suspensions are composed of cell walls having maintained their cell integrity, cell fragments are also present in the suspension. In diluted domain, cell fragments occupy a hydrodynamic volume comparable to the one of an entire cell (Figure 2). In contrast, in intermediate or concentrated domains, their hydrodynamic volumes may be significantly lower than the ones occupied by entire cells (Figure 2). Thus, if the insoluble solids content is the same, the hydrodynamic volume occupied by cell fragments in diluted or in more concentrated domains can be strongly different.

The apparent volume fraction of soft particles can also be evaluated by defining the volume fraction as the ratio of the concentration to a critical concentration. This approach is widely used in polymers' rheology where the apparent volume fraction occupied by the polymers is often defined as * / , where * is the overlap concentration of polymers [START_REF] Koumakis | Direct comparison of the rheology of model hard and soft particle glasses[END_REF][START_REF] Mendoza | Model for the Shear Viscosity of Suspensions of Star Polymers and Other Soft Particles[END_REF] . The overlap concentration is obtained using the polymer molecular weight and the radius of the sphere equivalent, considering the particles dimensions as if they were hard spheres [START_REF] Koumakis | Direct comparison of the rheology of model hard and soft particle glasses[END_REF][START_REF] Mendoza | Model for the Shear Viscosity of Suspensions of Star Polymers and Other Soft Particles[END_REF] . It is worth noting that this approach allows volume fractions greater than 1, due to the possible interpenetration of particles [START_REF] Koumakis | Direct comparison of the rheology of model hard and soft particle glasses[END_REF] and that it allows to distinguish the concentration domains.

A similar approach was applied on plant particles by Day et [START_REF] Day | Dynamic rheological properties of plant cell-wall particle dispersions[END_REF] or flow [START_REF] Leverrier | Influence of Particle Size and Concentration on Rheological Behaviour of Reconstituted Apple Purees[END_REF][START_REF] Leverrier | Design of Model Apple Cells Suspensions: Rheological Properties and Impact of the Continuous Phase[END_REF] properties of the suspensions when the particle concentration is increased. It corresponds to the concentration at which the particles fill all the available space and from which the particles begin to squeeze [START_REF] Leverrier | Influence of Particle Size and Concentration on Rheological Behaviour of Reconstituted Apple Purees[END_REF] , represented in Figure 1 as ≈ 1.

Both on carrot, broccoli and apple cell suspensions [START_REF] Leverrier | Influence of Particle Size and Concentration on Rheological Behaviour of Reconstituted Apple Purees[END_REF][START_REF] Day | Dynamic rheological properties of plant cell-wall particle dispersions[END_REF][START_REF] Leverrier | Design of Model Apple Cells Suspensions: Rheological Properties and Impact of the Continuous Phase[END_REF] this approach highlights concentration domains and materializes the transition between the intermediate and concentrated domains, thus defining a relevant parameter to evaluate the volume fraction of plant particle suspensions.

Following this approach, we define the apparent volume fraction of plant particles as: *

where is the insoluble solids content of the suspension and * is the critical insoluble solids content at the intersection between the intermediate and concentrated domains [START_REF] Leverrier | Design of Model Apple Cells Suspensions: Rheological Properties and Impact of the Continuous Phase[END_REF] , obtained from rheological measurements.

Presentation of the model

Here, the proposed modelling of plant particle suspension viscosity is based on a previous work from Mendoza & Santamaría-Holek (2009) which showed that the viscosity of colloidal particles suspensions can be modelled by :

$ × 21 -1 - 3 ( (4)
where is the continuous phase viscosity, is an exponent without unit which can be assimilated to the intrinsic viscosity of the suspension (specific viscosity of the suspension for → 0), and is defined as follow:

1 - (5)
Where is the critical volume fraction defined as the maximum volume fraction that can be reached by the system.

This expression takes into account the excluded volume and hydrodynamic interactions, and has been shown to fit with high accuracy suspensions of hard spheres [START_REF] Mendoza | The rheology of hard sphere suspensions at arbitrary volume fractions: An improved differential viscosity model[END_REF] , droplets [START_REF] Mendoza | Rheology of concentrated emulsions of spherical droplets[END_REF] , arbitrarily-shaped hard particles [START_REF] Santamaría-Holek | The rheology of concentrated suspensions of arbitrarily-shaped particles[END_REF] or rigid core-shell permeable particles [START_REF] Mendoza | Effective static and high-frequency viscosities of concentrated suspensions of soft particles[END_REF] . However, Eq. ( 4)

did not apply to very soft particle suspensions [START_REF] Mendoza | Model for the Shear Viscosity of Suspensions of Star Polymers and Other Soft Particles[END_REF] , able to decrease their volume or to interpenetrate. Considering suspensions of star polymers and other soft particles,

Mendoza [START_REF] Mendoza | Model for the Shear Viscosity of Suspensions of Star Polymers and Other Soft Particles[END_REF] suggested that a critical volume fraction greater than (volume fraction at random close packing) may be reached since the particles can interpenetrate, and he proposes that the critical volume fraction follows :

" 6 (6)
where and are two adjustable parameters without unit.

This gradual increase of the critical volume fraction with the current volume fraction of the suspension, that is associated with increasing levels of particles compression, is undoubtedly the major innovation of this model.

For spherical and permeable particles, Mendoza [START_REF] Mendoza | Model for the Shear Viscosity of Suspensions of Star Polymers and Other Soft Particles[END_REF] defined the intrinsic viscosity [η] as :

5 2 9 : ; (7)
where and are the respective radius of the (impermeable) core and the entire particles, considering a shell-permeable periphery of thickness -.

This model, that was conceived for soft particles and applied to star polymers suspensions, is intended primarily to describe the shear viscosity of colloidal-size particles suspensions. Such models can however often be applied to non-colloidal (granular-scale) systems, as commonly done for the Krieger's equation [START_REF] Krieger | A Mechanism for Non-Newtonian Flow in Suspensions of Rigid Spheres[END_REF] for example [START_REF] Mendoza | Model for the Shear Viscosity of Suspensions of Star Polymers and Other Soft Particles[END_REF][START_REF] Adams | Influence of particle modulus on the rheological properties of agar microgel suspensions[END_REF][START_REF] Ellis | Manufacture and characterisation of agarose microparticles[END_REF] .

However for plant particles, Eq. ( 7) cannot be used as such since particles are not spherical in shape. Moreover, the solvent permeability of the plant particles concerns the entire cell wall, and not only a surrounding area. Instead of [η], we chose here to use a more general parameter , which value may vary with the particle Sphericity (or Shape), Softness, Surface irregularities and Size distribution of the suspension. Using in addition the apparent volume fraction of the particles as given by Eq. ( 3), the initial model from Mendoza therefore becomes:

< = × > ? @ 1 - 1 -A 1 - - 6 " 6 B C D E (F (8)
In the following sections, we will first demonstrate that this model can be successfully applied to plant suspensions. To facilitate interpretations of the model parameters, we will first set the value of at 0.637, corresponding to the random close packing fraction of monodisperse hard spheres [START_REF] Mendoza | Model for the Shear Viscosity of Suspensions of Star Polymers and Other Soft Particles[END_REF] . We are aware that this is not fully appropriate since our system is heterogeneous in size and not spherical in shape but we used it as a first approach.

The impact of the polydispersity of apple cell suspensions on value will also be discussed. Then, we will study the impact of the continuous phase on the parameters of the model. And finally, we will propose some adjustments to the current model.

Validation of the model

First, the effect of the particles properties on the model parameters will be evaluated. To do so, we will compare three different suspensions, characterized by different size distributions but also different particles properties (in terms of rigidity and shape). Second, we will evaluate how the volume fraction at random closed packing, , which depends on the sample polydispersity, affects the quality of the fit. Third, we will evaluate the impact of the continuous phase, which does not impact particles intrinsic properties but can affect frictional interactions through lubrication. It is noteworthy that the model presented in Eq. ( 8) describe remarkably well the data (Figure 3) for the three purees investigated. Two purees present a bimodal particle size distributions: they contain in different proportions both very large particles up to 1000 µm (clustered cells [START_REF] Leverrier | Influence of Particle Size and Concentration on Rheological Behaviour of Reconstituted Apple Purees[END_REF][START_REF] Espinosa-Muñoz | Structural parameters that determine the rheological properties of apple puree[END_REF] ) and smaller particles of about 150 µm (individual cells [START_REF] Leverrier | Influence of Particle Size and Concentration on Rheological Behaviour of Reconstituted Apple Purees[END_REF][START_REF] Espinosa-Muñoz | Structural parameters that determine the rheological properties of apple puree[END_REF] ), and one puree presents a monomodal size distribution, centered on 150 µm. Fitting parameters used in Figure 3 are itemised in Table 1. They all increase when the average particle size decreases. However, the decrease in global particle size also reflects the presence of particles of different kind in the medium, as illustrated in Figure 4. Large particles are clusters of cells, irregular in shape and quite rigid thanks to their complex architecture. Small particles are individual cells, more regular and spherical in shape, and probably less rigid due to their purely liquid content. Grinding thus induces a decrease in particle size, but also an increase of particle sphericity and a decrease of their rigidity and their surface irregularities, which are difficult to decorrelate. The fitting parameters , , and S depend on the suspension properties, and are therefore link to the particles physical properties. In the following, we investigate how their value depend on the particles rigidity and shape.

Impact of the particle size distribution

values here obtained are 0.913, 1.035 and 1.177 respectively for the purees (1), ( 2) and (3).

In the work of Mendoza (2013) [START_REF] Mendoza | Model for the Shear Viscosity of Suspensions of Star Polymers and Other Soft Particles[END_REF] , is related to the particle deformability: the softer is the particle, the greater is : values between 0.244 and 0.966 were observed for 128 arms and 32 arms star polymer particles, respectively. This is consistent with our results, in which we observe that the higher the proportion of large clusters, the lower the value of . Indeed, the complex architecture of clusters could generate a greater overall rigidity of the particle 6 , thus here also is higher when the particles are softer (smaller particles in our case). It is noteworthy that the values of individual cells are much higher than the softer star polymer ones (with only 32 arms), while stiffer cells clusters exhibit a closer value confirming that plant particles are highly deformable objects.

Regarding , the values obtained on the apple purees (2.10-2.16) are slightly higher than those obtained on star polymer suspensions [START_REF] Mendoza | Model for the Shear Viscosity of Suspensions of Star Polymers and Other Soft Particles[END_REF] (1.9-1.74 for 128 and 32 arms particles, respectively). In the case of star polymer suspensions, decreases when particle deformability increases, while we observe here the opposite effect, the greatest value of being obtained for the puree (3).

We hypothesize that this may be related to the sphericity of the particles or to their surface irregularities. Indeed, on apple purees, when the particle size decreases, the deformability increases, but surface irregularities are decreased and particle sphericity increases.

However, in star polymer suspensions, the opposite effect could be anticipated: Indeed, star polymer particles with many arms are very close to hard spheres. If the number of arms decreases, particle deformability increases but particle sphericity could only be reduced, thus possibly increasing surface irregularities.

Regarding , we observe that it increases when the particle size decreases and the deformability increases. This is similar to the / parameter evolution in star polymer suspensions [START_REF] Mendoza | Model for the Shear Viscosity of Suspensions of Star Polymers and Other Soft Particles[END_REF] which was previously associated with particle permeability.

It should be noted that is consistently above 2.5, while in existing models for spherical and deformable particles, the power parameter is often presented as equal to [START_REF] Mendoza | Model for the Shear Viscosity of Suspensions of Star Polymers and Other Soft Particles[END_REF] or less than 2.5 [START_REF] Taylor | The viscosity of a fluid containing small drops of another fluid[END_REF][START_REF] Quemada | Modélisation rhéologique structurelle : dispersions concentrées et fluides complexes[END_REF][START_REF] Quemada | Rheology of concentrated disperse systems and minimum energy dissipation principle I . Viscosity-concentration relationship[END_REF] . Higher values of the Einstein coefficient were however reported for non-sperical particles [START_REF] Mueller | The rheology of suspensions of solid particles[END_REF] . This high value of determined with plant particles could therefore be due to their non-spherical shape.

It is noteworthy that Eq. ( 8) offers, to our knowledge for the first time, the possibility to describe the viscosity dependence towards concentration of complex, non-colloidal suspensions of soft particles. The good agreement of the model with experimental data is due to the use of a critical volume fraction that evolve with the actual concentration of particles (Eq. ( 6)). In other words, due to their compressibility, the effective volume fraction of the particles do not increase as the insoluble solids content does.

Impact of the random close packing volume fraction

Up to here, the maximum packing volume fraction was taken as 0.637 for all fittings, the random close packing value for monomodal hard spheres. The impact of polydispersity on this type of highly deformable non-spherical particle suspensions was evaluated. To do so, a similar approach to the one used by Shewan et al. Then, we determined the new model parameters in each case, they are itemized in Tableau 2. As one can see, no significant improvement is noted on the fit quality, and the impact of the particle size distribution on the parameters , and remains the same as discussed in previous section. The impact of polydispersity on the maximum volume fraction seems to be negligible when modelling the data. These results are consistent with observations made in our previous work [START_REF] Leverrier | Design of Model Apple Cells Suspensions: Rheological Properties and Impact of the Continuous Phase[END_REF] : Particles having non-spherical shapes and high surface irregularities dominate the global rheological properties of suspensions, and polydispersity effect is almost negligible. For the sake of simplicity, the value of corresponding to monodisperse spheres 0.637 will thus be used for the rest of this work.

Tableau 2. Fitting parameters of the model used for the Figure 3

Impact of the viscosity of the continuous phase

In this section, model suspensions of individual apple cells varying in continuous phase viscosity and composition will be considered (data taken from Leverrier et al. (2017) [START_REF] Leverrier | Design of Model Apple Cells Suspensions: Rheological Properties and Impact of the Continuous Phase[END_REF] ). Such suspensions are composed of the same batch of particles, characterized by a monomodal distribution, centered on 180 µm (Figure 5). It allows us to assume that all particles have the same deformability, sphericity, surface irregularities and polydispersity, and to investigate here more specifically how a phenomenon like lubrication, which depends on the continuous phase properties, could affect the suspension viscosity other the full range of volume fraction investigate. Figure 6 represents the resulting fittings of Eq. ( 8) on these suspensions varying only in continuous phase. It is noteworthy that Eq. ( 8) fits again quite well the data, whatever the continuous phase composition. Fitting parameters are itemised in Table 3. We observe that when the continuous phase viscosity increases, and increase and decreases. (circles) and carboxy-methyl-cellulose solution at 3.2% (squares). Solid lines represent the fittings resulting from Eq. ( 8) for each continuous phase.

Previously, and in agreement with Mendoza's approach, we have shown that and parameters were related to particles' deformability and sphericity (or surface irregularities).

At a first look, it might seem surprising that the continuous phase composition impacts the model parameters, however, we remind here the reader that apple cells are granular, nonbrownian particles. In such suspensions, frictional forces play a key role in rheological properties [START_REF] Menut | Does size matter? Elasticity of compressed suspensions of colloidal-and granular-scale microgels[END_REF][START_REF] Denn | Rheology of Non-Brownian Suspensions[END_REF][START_REF] Ancey | A theoretical framework for granular suspensions in a steady simple shear flow[END_REF] . One additional consequence is that these particles are not sensitive to the depletion effects that can be observed in colloidal systems.

The increase of with the increasing continuous phase viscosity could be due to a lubricating effect [START_REF] Leverrier | Design of Model Apple Cells Suspensions: Rheological Properties and Impact of the Continuous Phase[END_REF] . By increasing the viscosity of the continuous phase or the presence of polymers in the medium, frictions between particles are decreased.

This lower friction could have an impact on apparent surface irregularities, leading to an apparent more spherical shape of the particles. The increase of with the viscosity of the continuous phase could be related to crowd effects. Indeed, in all cases, the viscosity of the continuous phase has been increased by introducing polymers in the continuous phase.

These polymers, whose concentration increases with the continuous phase viscosity, have an intrinsic volume and thus occupy space in the medium. If the rheological properties of the suspensions are predominantly driven by the particles [START_REF] Leverrier | Influence of Particle Size and Concentration on Rheological Behaviour of Reconstituted Apple Purees[END_REF][START_REF] Leverrier | Design of Model Apple Cells Suspensions: Rheological Properties and Impact of the Continuous Phase[END_REF] , the presence of polymers in the continuous phase can force particles to deform to a greater extent, thus leading to higher values.

We also observe that , previously associated with the particle's permeability, decreases when the continuous phase viscosity increases.

Here, higher viscosities are associated with higher polymer content: in such cases, the continuous phase goes through particles less easily, giving rise to lower apparent permeabilities

Adjustments of the model

This work highlights the interest of a model that goes beyond a constant random close packing defined for swollen particles. However, a clear limitation of the model is that Eq. ( 6)

implies that a finite value of the critical volume fraction cannot be determined from a set of data, since it increases monotonically with the particle volume fraction : for different volume fractions , different values of are determined. Still, at sufficiently high concentrations, cells should become incompressible, and therefore, the volume fraction reaches a finite, maximum value. This maximum volume fraction, , is an important characteristic of a given system, as it gives a clear indication of the maximum compression level that can be reached physically, which should depend on the particles structure and composition. To circumvent this limitation, we propose to modify the existing model so that this maximum volume fraction could be included, as indicate in the following equation:

" - 1 " _a^b-Λ< -=c (9)
As proposed by Mendoza, the critical volume fraction evolves here with the particle concentration above the random close packing volume fraction defined for hard spheres.

However, rather than using a power law model, leading to an infinite critical volume fraction, we use a sigmoidal law, so that a finite maximal volume fraction ( $ will be reached eventually.

While this equation involves an additional variable, it seems more physically realistic to the vegetable particles of ours. As it includes a sigmoid function, it allows to model the viscosity evolution with volume fraction in a wider range of concentrations, including the divergence that should occur at extremely high volume fractions. The maximum attainable volume fraction included in Eq. ( 9) allows us to translate the incompressibility limit encountered by the particles at high volume fraction, which, in our case, results in a divergence of the viscosity at high volume fraction, assuming that particles are not able to shrink or deform anymore. It is however less accurate for very diluted systems: for extremely low values of , the critical volume fraction remains slightly higher than in our model. Still, food suspensions are rarely highly diluted system and Einstein's law remains the best way to fit very diluted systems.

In Eq. ( 9), the model parameters can be associated with different physical properties. Λ defines the spreading of sigmoid (i. e., the slope of the sigmoid at the inflection point) and defines the value of the inflection point which corresponds to the points for which the particle compressibility towards particles concentration is maximum. The sigmoid is also defined by two asymptotes, the first one is equal to zero, and the second one is defined by the parameter . This parameter set the critical volume in a finite range between and , and allows the estimation of the latter from experimental data

To summarize, we fitted in Figure 7 4), ( 5) and ( 9)). The parameters used to fit our data points are summarized in Table 4. The Einstein model, the only theoretical model describing the evolution of viscosity with the apparent volume fraction, does not allow to model concentrated systems. Thus, as expected, it does not fit our data over the entire range of concentrations studied. The Quemada and Krieger-Dougherty models also do not fit our data correctly, because in these models the viscosity increases more and more as the volume fraction increases, till it diverges at volume fractions much lower than the ones reached experimentally. The Mendoza model, as we have seen in this work, allows us to successfully model the entire range of concentration that was experimentally investigated. However, in this model the viscosity will continuously increases with the volume fraction, as an upper limit for will never be reached, whatever the value of . As it can be observed, the model we propose allows by contrast to fit the whole range of our data (from diluted to highly concentrated) while having a volume fraction upper limit.

Conclusion

In this work, an indirect way of accessing the effective volume fraction of the particles and a model describing the concentration dependence of the viscosity of soft plant cells suspensions over a wide range of concentration were proposed.

The model, initially proposed for soft colloidal particles and applied to star polymers [START_REF] Mendoza | Model for the Shear Viscosity of Suspensions of Star Polymers and Other Soft Particles[END_REF] , was successfully applied to real apple purees of several grindings and to monodispersed suspensions of apples cells in several continuous phases. Three adjustment parameters are defined and related to the particle's intrinsic physical properties: deformability, sphericity and porosity.

We also showed that for such non-colloidal suspensions, in which friction forces play an important role in the rheological properties, those parameters are also related to the continuous phase properties that may act as a lubricant and decrease frictional interactions.

To represent the predictable divergence of the viscosity at the maximum packing fraction, we successfully introduced a sigmoid-type term in the model, which allows the prediction of the viscosity in the entire range of volume fraction. This new model necessitates additional parameters, however these parameters now include a key characteristic of a compressible suspension, namely the maximum volume fraction, , that is reached when particles are fully compressed. For the system investigated here, we found =16, which demonstrates the extremely high compressibility of apple cells. This estimation calls for future work:

investigating apple cells suspensions rheological properties in extremely concentrated states would allow to confirm the validity of the model in this limit. The predicted divergence of the viscosity while approaching indeed assumes that in this limit, particles become incompressible but also cannot deform anymore, which seems reasonable considering the high level of entanglement, but have not been confirmed experimentally to date to our knowledge Also, future work should be done on others food soft granular suspension to evaluate how this model could be applied to other systems.

This model represents a significant advance in the understanding of processed fruit and vegetables systems and offers clear industrial prospects.

We believe the attempt to link macroscopic behavior with local properties such as compressibility or friction in such systems would benefit from in-depth investigation at the particles scale, both experimentally and numerically, that would certainly in the future allow a better description of their behavior.

  core of star polymer particle Radius of the entire star polymer particle Current model fitting parameter Λ Spreading of the sigmoid

Figure 1 .

 1 Figure 1. Schematic representation of the impact of the concentration on the particles shape and size adapted from Leverrier et al. (2017).

  and 2.5 (hard spheres). Relying on the work of Nawab & Mason reported in Macosko (1996), 1.7 was used for individual apple cells 20 . Their voluminosity was then determined from viscosity measurements on diluted suspensions, allowing to define the apparent volume fraction of apple cells suspensions as 1.3 .

Figure 2 .

 2 Figure 2. Schematic representation of two of the plant particles specificities: cell wall porosity allows a (limited) flow through the particle (up), and presence of cell fragment allow particles interlocking in concentrated suspensions. Both phenomena may result in lower hydrodynamic volumes than expected.

Figure 3 .

 3 Figure 3. Modelling using Eq.(8) for three apple purees varying in particle size distributions. Data were taken from Leverrier (2016) 6 . Particle size distributions are represented on the upper side. Relative viscosity is represented as a function of the apparent volume fraction on the bottom side. Black squares, circles and black triangles stand for experimental data and the solid lines represent the modelling.

Figure 4 .

 4 Figure 4. Microscopic observations of the three particle size distributions. Some of the particles have been highlighted to facilitate reading.

  (2015) 21 on agar microgel suspensions was used. Based on the particle size distribution of our suspensions, we determined the distribution's width MN O P,R O R,S . Using the results obtained by Farr et al. (2009) 39 , we determined the random close packing volume fraction of each suspensions, based on their polydispersity. We obtained values of 0.715, 0.705 and 0.70 for the purees (1), (2), (3) respectively.

Figure 5 .

 5 Figure 5. Particle size distribution of monomodal model suspensions.

  our data with the most widely used models in the literature (i.e. the Einstein model, the Quemada model and the Krieger-Dougherty model), with the model proposed by Mendoza and with the model we propose here (combining equations (

Figure 7 .

 7 Figure 7. Modelling of model suspensions in apple serum with theoretical and phenomenological models describing the evolution of the viscosity with the apparent volume fraction. Model and parameter used are summarized in Table 4

Table 1 .

 1 Fitting parameters of the model used for the Figure3 with

	0.637.
	#

  considering the particle size distribution effect on .

						#
	1$	0.914 0.021$	2.285 0.018$	3.880 0.042$	0.715	0.999
	2$	1.053 0.044$	2.292 0.028$	4.057 0.072$	0.705	0.999
	3$	1.223 0.081$	2.309 0.035$	4.090 0.105$	0.70	0.999

Table 3 .

 3 Fitting parameters of the model used for the Figure6.

	WX . Y$

Figure 6. Modelling using Eq. (8) for model suspensions in 4 different continuous phases. Symbols represent experimental data for model suspensions, in NaCl 1% (triangles), apple serum (diamonds), carboxy-methyl-cellulose solution at 1%

Table 4 .

 4 Models used for the Figure7

	Models	Equation and parameters used in Figure 7
	Einstein			$	1 " d $
					d	2.5
	Quemada			$	e1 -	f (g
			h 2.0 ;	0.637
	Krieger-Dougherty		$		e1 -	f (j k l %mn
			d	2.5 ;	0.637
	Mendoza		$ 1 -	21 -1 -;	3 ( "	6
		1.964 ;		0.851 ;	0.637 ;	3.226
	Current model	1 -	;	$	3 1 " exp -Λ -$ (F 21 -1 -" -
		Λ 1.87 ;	2.38 ;		16 ;	0.637 ;	3.76

Acknowledgements

The research leading to these results has received funding from the European Union's Seventh Framework Programme for research, technological development and demonstration under grant agreement number 311754. The authors wish to thank Adeline Boire, for fruitful discussions.