Sébastien Puma

Nadine Matton

Pierre-Vincent Paubel

André Tricot

Cognitive Load Theory and Time Considerations: Using the Time-Based Resource Sharing Model

come

Introduction

Ever since the discovery of human cognitive resource limitation (e.g., [START_REF] Broadbent | Perception and Communication[END_REF], managing these limited resources has become a central issue in many fields. In education, it has been demonstrated that trying to solve a problem that overwhelms the student's available cognitive resources impairs learning [START_REF] Sweller | Cognitive Load During Problem Solving: Effects on Learning[END_REF]. Thus, managing cognitive load during instruction has become a matter of central importance. It is generally assumed that during explicit learning, students have to maintain information in working memory and manipulate it [START_REF] Cowan | Working Memory Underpins Cognitive Development, Learning, and Education[END_REF]. When the information to be held exceeds working memory capacity, cognitive overload is experienced. Therefore, studying working memory requirement during learning appears critical if learning efficiency is to be improved.

Cognitive Load Theory is an influential framework dividing cognitive resource allocation during explicit learning into three different loads: extraneous, intrinsic and germane (e.g., [START_REF] Sweller | Cognitive architecture and Instructional design[END_REF]. In this framework, cognitive overload arises from an excessive requirement of cognitive resources, described mainly as working memory capacity [START_REF] Sweller | Cognitive architecture and Instructional design[END_REF]; see Sweller, Ayres &Kalyuga, 2011 for a review). Cognitive Load Theory uses working memory models to identify empirical effects reducing cognitive load during learning. One typical finding, the modality effect, occurs when learning is more efficient when a text referring to a map, graph, diagram or tabular information, is presented orally than visually (Leahy & Sweller, 2016). This effect appears when information to be processed is related (e.g., Tindall-Ford et al., 1997). Furthermore, it does not benefit expert learners [START_REF] Kalyuga | The Expertise Reversal Effect[END_REF]. While investigating the modality effect (see [START_REF] Ginns | Meta-Analysis of the Modality Effect[END_REF] for a review), several studies found an impact of the pace of information presentation. Indeed, if the learner controls the pace of information presentation, then presenting information both visually and orally does not improve learning (e.g., [START_REF] Schmidt-Weigand | A closer look at split visual attention in system-and self-paced instruction in multimedia learning[END_REF]see De Jong, 2010 for a review, [START_REF] Moreno | Cognitive Load and Learning Effects of Having Students Organize Pictures and Words in Multimedia Environments: The Role of Student Interactivity and Feedback[END_REF], experiment 2, Ginns, 2005;[START_REF] Sweller | Cognitive Load Theory[END_REF][START_REF] Leahy | Cognitive Load Theory, Modality of Presentation and the Transient Information Effect[END_REF]. This pace of presentation effect is also found in studies on the transience of information, the information presented being no longer available after its presentation [START_REF] Sweller | Cognitive Load Theory[END_REF] for a review). Even if caution needs to be taken when considering these disappearing effects, these experiments altogether suggest an effect of pace of presentation on learning. Furthermore, in a second experiment, Schmidt-Weigand et al. showed that for the same experimental material, reducing pace of presentation had a positive effect on learning outcome.

The commonly used working memory models (e.g., [START_REF] Baddeley | Working Memory[END_REF][START_REF] Baddeley | Working memory. The psychology of learning and motivation[END_REF][START_REF] Ericsson | Long-term working memory[END_REF] do not allow this pace of presentation effect to be described.

Previous studies suggested that a working memory model taking time into account would be necessary in cognitive load theory [START_REF] Spanjers | A Theoretical Analysis of How Segmentation of Dynamic Visualizations Optimizes Students[END_REF][START_REF] Van Gog | The Mirror Neuron System and Observational Learning: Implications for the Effectiveness of Dynamic Visualizations[END_REF]. 1 To do so, they evoked the Time based Resource Sharing model [START_REF] Barrouillet | Time Constraints and Resource Sharing in Adults' Working Memory Spans[END_REF] The Time Based Resource Sharing model

The Time Based Resource Sharing (TBRS from now) model is a recent working memory model describing information maintenance and refreshing as a function of time (e.g., [START_REF] Barrouillet | Time Constraints and Resource Sharing in Adults' Working Memory Spans[END_REF][START_REF] Barrouillet | Working memory: loss and reconstruction[END_REF]. Following this model, elements in working memory are activated representations and their activation level decreases due to time decay. It assumes that attention is the single cognitive resource and can only be directed to one task at any given time. To counter time decay of information activation, attentional focus has to be applied on each chunk to refresh it, i.e., to raise its activation level [START_REF] Vergauwe | Evidence for a central pool of general resources in working memory[END_REF][START_REF] Cowan | Attention and memory: An integrated framework[END_REF] for a similar idea). If chunk activation decays too much for the information to be retrieved, it is forgotten (Barrouillet& Camos 2014). Thus, the TBRS model proposes to consider working memory as an attentional module maintaining information through attentional refreshing.

Since attentional focus can only be used for one controlled process at a time, it follows that multitasking is the result of frequent switching between tasks [START_REF] Salvucci | The multitasking mind[END_REF][START_REF] Barrouillet | Working memory: loss and reconstruction[END_REF] for a review). When attentional focus is used to process a concurrent task, it cannot be used to refresh information held in working memory. On the contrary, when it is used to refresh memory traces, it cannot be used to perform a concurrent task. It follows that holding items active in working memory while, for example, performing a judgment task will necessitate rapidly switching between memory trace refreshment and information processing. Each of these two tasks requires attentional focus for a given duration. From this conclusion, the authors infer that cognitive load can be modeled as the ratio between the time used to refresh memory traces and the time used to process the concurrent task. The longer the time available to refresh memory traces, and/or, the shorter the time needed to perform a concurrent task, the better the working memory performance will be. On the contrary, if the time available to refresh memory traces is shortened, or the time needed to perform a concurrent task lengthened, working memory performance will decrease. These predictions (see Figure 1) are opposite of those commonly used in Cognitive Load Theory research, based on working memory capacity conceptions. A lighter load might lead to better working memory performance with more distracter elements (but with sufficient time to process them), while fewer distracters might be associated with a heavier working memory load (with a short time to process them) and thus a lesser performance. Furthermore, if the time ratio remains constant, the number of concurrent distracters should have no effect on working memory performance (see [START_REF] Barrouillet | Working memory: loss and reconstruction[END_REF] for a review).

To test these hypotheses, [START_REF] Barrouillet | Time Constraints and Resource Sharing in Adults' Working Memory Spans[END_REF] used a complex span task. As with a classic span task, participants were presented series of items (e.g., letters or numbers) and at the end of the sequence had to recall them in the correct order. Contrary to a classic span task, after the presentation of each item, participants had to perform a series of distracting tasks. By manipulating the time needed to perform the distracting task and the total time available, the authors could manipulate the time ratio (i.e., the cognitive load).

[Insert here the Figure 1] performance is determined by the ratio between the time needed to process a distracting task and the remaining time allowing the refreshing of memory traces. Each item (here letters G and T) are presented serially and followed by series of interfering tasks (represented with empty squares). The width of a square represents the time needed for this process, kept constant in this example. Space between two successive squares represents the remaining time available to refresh memory traces. Thus, the first two examples should induce the same performance, although a different number of distracters is used. On the contrary, example 1 should impose a lesser load on working memory than example 3 although it has a higher number of distracters.

Example 2 should impose a higher load on working memory than example 4 even though it has a lesser number of distracters.

These counterintuitive hypotheses might help to explain some empirical results obtained in the field of Cognitive Load Theory research. In particular, the differences arising from the pace of presentation observed in learning outcomes using the modality effect might be explained using this model. For a fixed amount of information, learning outcome might be superior if presentation pace is slower, the time dedicated to process this information rising while the presentation pace decreases. The TBRS model has never been used in a learning context with meaningful material that can be chunked and related to long term memory, for which one can develop expertise.

The present study

In the present study, we aimed to assess the validity of the TBRS model We defined meaningful material as items that can be held and manipulated together in working memory, based on the content of long term memory, a definition close to that of element interactivity (see [START_REF] Sweller | Cognitive Load Theory[END_REF] for a review, see also [START_REF] Chanquoy | La charge cognitive: Théorie et applications[END_REF] for a model of load imposed by element interactivity). Contrary to meaningless items, meaningful ones can be gathered in chunks of various sizes based on the learner's expertise with the domain (e.g., [START_REF] Ericsson | Long-term working memory[END_REF]. Following Van Gog and her colleagues (2009) we will consider expertise as a continuum of knowledge, learners having more knowledge than others (i.e., able to perform better on domain relevant tasks) being more expert. Since expertise allows higher performance, two groups were formed based on the results of a pre-test to determine expertise differences. One group gathered participants with higher performance and the other gathered participants with lesser performance.

In these experiments, we used a complex span task while replacing meaningless items (used in most of the Barrouillet & Camos, 2015 experiments) by terms of mental arithmetic calculations. For example, three letters B, X and H do not mean anything. When processing these three letters, the participants have to maintain B, X and H. When processing 3 + 4 = ?, the participants have to maintain 7, i.e. just one digit instead of two digits and one calculation.

Common Cognitive Load Theory experimental results reveal that factors that facilitate learning of novices may impair learning of experts (named the "expertise reversal effect", [START_REF] Kalyuga | The Expertise Reversal Effect[END_REF][START_REF] Kalyuga | Expertise Reversal Effect and Its Implications for Learner-Tailored Instruction[END_REF]. Moreover, expertise is known as reducing element interactivity [START_REF] Chen | The Worked Example Effect, the Generation Effect, and Element Interactivity[END_REF]2016). It also has other effects on arithmetic, thus, when processing 3 + 4 = ?, expertise has a strong effect, i.e. the participants who do not know that the result is 7 have to maintain 3 + 4. Expertise is here seen as allowing the use of different strategies, for example, recalling arithmetic facts rather than computing the solution (e.g., Groen & Parkman, 1972;Zbrodoff & Logan, 2005 for a review). Expertise would thus not only reduce cognitive load but also allow the use of different strategies [START_REF] Chi | Two Approaches to the Study of Experts' Characteristics[END_REF][START_REF] Anderson | Cognitive Psychology and Its Implications[END_REF] which could affect the prediction of a working memory model. The aim of the present experiments was therefore to test different hypotheses allowed by the Time Based Resource Sharing model with meaningful items, by taking expertise differences into account. Indeed, as expertise allows automation and thus better performance on a task at a lesser cognitive cost, manipulation of the time ratio (i.e., of the cognitive cost) should principally affect less expert participants. For that reason, participants selected for these studies were children who did not rely completely on automated processes to compute mental calculation.

Experiment 1

Following the TBRS model assumptions, the time allowed to refresh working memory representations affects working memory performance. The longer the time allowed for refreshing, the better the working memory performance will be. If we consider complex span tasks, with a fixed trial duration, when the time needed to perform a distracting task increases, the time allowed to refresh memory traces will decrease. As a result, the working memory performance will decrease. However, expertise might affect this general assumption in many ways. Experts' representations held in working memory are larger and deeper (see [START_REF] Chi | Two Approaches to the Study of Experts' Characteristics[END_REF]Chi, Feltovitch & Glaser, 1988 for reviews) and chunks held in working memory last longer for experts than for novices (e.g., Ericson & Kintsch, 1995). Furthermore, since experts have automated many commonly used processes, they have automated routines for their expertise field [START_REF] Schneider | Training high performance skills: Fallacies and guidelines[END_REF]. Such effects could influence working memory span when considering meaningful items, but the TBRS model was never used with meaningful items to test this potential limit.

To address this limitation, we used terms of a mental calculation as items to be held and processed in working memory, since manipulation of mental calculation mainly relies on working memory resources [START_REF] Adams | Working memory and children's mental addition[END_REF]. Replacement of these items should allow chunking for expert participants but not for less expert participants. For expert participants, mental calculation is more automated than for novices. Thus, we reproduced a previous TBRS experiment (e.g., Portrat, Camos & Barrouillet, 2009, Experiment 1) by replacing items to be maintained in working memory with terms of a mental calculation. Following TBRS assumptions, performance on mental calculation should depend on the time ratio allowed to perform the distracting task. In other words, when the time ratio is smaller, performance on mental calculation should be better.

Two hypotheses were made. First, the time ratio affecting the working memory performance should have an effect on mental calculation performance. Second, as expertise allows the reduction of the reliance on working memory resources while performing cognitive arithmetic, the time ratio effect should principally affect novices. To investigate these hypotheses, participants had to perform the complex span task in both conditions of the interfering task. They were then split into two groups based on their performances during a pretest on mental calculation. Material and procedure. The procedure used in this experiment was similar to that used by [START_REF] Portrat | Working memory in children: A time constrained functioning similar to adults[END_REF], except for the series length and the items to be remembered. In this task, participants had to memorize terms of a mental calculation and perform this calculation in the order of presentation without consideration for the order of operation. They performed two complex span tasks, following the two conditions of the distracting task.

Method

The terms of a mental calculation were composed as the distracting task in Barrouillet, Bernardin and Camos (2004, experiment 2). First, a "root term" comprising only a single digit number was presented (for example, the number "7"). Then, the terms were composed of an operand and a single digit number (for example, the term "+ 2"). Calculations were to be performed in presentation order and none of the intermediary results could be a negative or decimal number. The final result was a single digit positive number. For example, the series "7", "-5", "x3" was decomposed as "7" and "-5" (equals 2) and ("2") "x3" (equals 6). The terms were randomly generated and then verified to conform to the criterion above.

After the presentation of each term, a series of eight distracting spatial judgment tasks was presented. Participants had to decide whether a square presented onscreen was located on the top or the bottom half of the screen, with two levels of difficulty (see Figure 2). The squares were black, with sides of 18mm, and were presented on a white screen. Each square was presented for 667ms and followed by a white screen for 333ms. The total length of a trial was 1s. In a distant condition (easy condition), the locations of the squares were 68mm apart from each other, whereas in a close condition (difficult condition), the locations were only 5mm apart, resulting in a partial overlap (13mm). Locations were randomly generated with half on the upper part of the screen and the other half on the lower part. This random selection served to control for a potential SNARC effect1 [START_REF] Dehaenne | The Mental Representation of Parity and Number Magnitude[END_REF].

[Insert here the figure 2] Fig. 2 the two conditions of the spatial judgment distracting task. On the left, the close square condition was the most demanding. On the right, the distant condition was the easiest, the squares being far apart from each other. The dotted line was added for more clarity.

A series of the complex span task started with a screen that presented the number of terms and the condition of the distracting task for 1500ms (for example: 3 terms / distant squares). Then a ready signal (*) was presented for 750ms and followed by a white screen for 500ms. After this, the root term was presented for 1500ms, followed by a post-term delay of 500ms and then by eight spatial judgment tasks (see figure 3). After the distracting tasks, a second term was presented for 1500ms and followed by a 500ms post-term delay. At the end of the series, the word "result" was presented and participants had to enter the result of the mental calculation. Stimuli were presented using E-Prime 2.0 software (Psychology Software Tools, Pittsburg, USA) [Insert here Figure 3] Fig. 3 the time ratio of the two conditions and the time course of a trial. Part A upper panel displays the difficult condition and lower panel the easy one. The easier condition is assumed to require attentional focus for a shorter duration (the squares are shorter). Part B the trial started with a presentation screen, followed by a ready signal. Then a root term (digit without operand) was followed by eight spatial judgment tasks before the second term. After the second term, a series of spatial judgment task was presented and then the next term and its following spatial judgment tasks. At the end of the trial, the world "result" was presented until

participants provided an answer.

The series started with three terms and this number increased up to a maximum of eight terms. Three calculations were presented for each series length and the experimental condition stopped if a participant failed on the three repetitions of a given series length. After a pause of a minimum of 30s, the second condition started.

The experiment began with three mental calculations to familiarize the participants with the exercise. Then, they performed a pre-test during which they had to perform as many mental calculations as possible in one minute. These calculations were three terms calculations, all terms being presented on screen simultaneously (for example, participants saw "3 + 9 -4" and had to answer 8 by pressing the corresponding keypad touch). They were then trained on the distracting task. Participants who failed to achieve a criterion of 80% success in this training were discarded from the data (n = 13), as in [START_REF] Portrat | Working memory in children: A time constrained functioning similar to adults[END_REF], to prevent participants neglecting the distracting task. After these training sessions, participants performed both conditions of the task, in a balanced order.

Dependent variables and statistical analyses.

Based on performance on the pre-test, two groups were created. A group called "Calc+" was composed of the 20 participants who had achieved the best results on the pre-test and group called "Calc-" gathered the 20 participants with the lowest performances. Performance was calculated as the number of correct calculations completed by the participants of each group. To test the hypothesis that difficulty would lead to a lower number of correct calculations performed, at least for the group with fewer automated mental calculations, a 2 group x 2 difficulty repeated measure ANOVA was performed. The average time needed to perform the distracting task was also measured for each series length (TR in milliseconds). To test the hypothesis that the close condition of the distracting task required attentional focus for a longer duration, the reaction times were compared using a Student t-test.

Results

The data are summarized in Table 1. The repeated measures ANOVA with group as a between subject factor showed no significant effect of the difficulty level (F(1,38) = 1.82, p = .186) but a significant difference between the groups (F(1,38) = 22.68, p < .001). The interaction between group and difficulty was not significant (F(1,38) = 1.04, p = .315).

Following [START_REF] Howell | Statistical Methods for Psychology[END_REF] commenting [START_REF] Wilcox | New Statistical Procedures for the Social Sciences[END_REF], pair comparisons using repeated Student t-tests were performed even for non significant factors. Pair comparisons allow for comparisons of two groups without taking variance of the other groups into account. This allows testing the effect of a variable on a group without considering the effect of this variable on another, independent, group. The "Calc+" group calculated as many correct calculations in the "distant" condition as in the "close" condition (M = 9.750, SD = 4.35 and M = 9.950, SD = 4.39 respectively, t(19) = -0.149, p = .883, d = 0.046). On the contrary, "Calc-" participants performed more correct calculations in the "distant" condition than in the "close" condition (M = 5.85, SD = 4.27 and M = 3.65, SD = 2.23 respectively, t(19) = 2.505, p = .022, d = 0.68).

Thus, time ratio manipulation affected participants from the "Calc-" group but not those from the "Calc+" group. For participants with less automated mental calculation, time ratio manipulation allowed higher performance while the number of distracters had remained constant.

In the "Calc-" group, participants took longer to perform the concurrent task in the "close" condition than in the "distant" condition (M = 383.09, SD = 106.58 and M = 354.58, SD = 91.97 respectively, t(19) = -2.97, p= .008, d= 0.287). The same result appeared for the "Calc+" group (M = 381.53, SD = 64.63 and M = 361.02, SD = 35.40 for "distant" and "close" conditions respectively, t(19) = -1.86, p= .079, d= 0.41) though the difference was only marginally significant. Both groups performed the distracting task at the same speed (t(38) = -0.29, p= .771, d= 0.10 and t(38) = 0.06, p= .956, d= 0.018 for the "distant" and "close" conditions respectively.

Number of correct calculations RT (s) on distracting task

Easy condition Difficult condition

Easy condition Difficult condition

Calc-

Discussion

In this experiment, we tested the hypothesis that manipulation of the time ratio would affect performance of mental calculation. We manipulated the time needed to perform a distracting task and left the inter-stimuli interval constant, thus a longer concurrent task reduced the remaining time. Following our hypothesis, performances on mental calculation were affected by the ratio between the time needed to perform the concurrent task and the time allowed for this, at least for the less proficient students in mental calculation. When the time needed to perform the distracting task was longer, the time allowed for maintaining and manipulating information decreased, resulting in an impaired mental calculation performance.

Due to the lesser automation of novices, mental calculation had a higher associated cognitive cost and thus took more time to perform. As a result, it was not performed during the remaining time after concurrent task completion. On the contrary, the most proficient students in mental calculation were probably able to perform mental calculation during the available time. This would have resulted in a low working memory load at any time during the experiment.

Consequently, this would explain the absence of differences between the experimental conditions, the different distracting tasks having the same effect on their mental calculation performance.

These results suggest a new interpretation of intrinsic and extraneous cognitive loads in the framework proposed by Cognitive Load Theory. Extraneous load might be viewed also as a proportion of time needed to manipulate information not relevant for the task at hand, rather than only the absolute number of information units to manipulate per se. Accordingly, intrinsic load could be viewed as time left to maintain and manipulate relevant information for learning rather than the number of elements of information only. Time ratio could therefore be used to describe both extraneous and intrinsic cognitive load. When the concurrent task requires attentional focus for a longer duration, the extraneous load increases. In the same way, if the time remaining to maintain and manipulate the relevant information decreases, then the intrinsic load increases accordingly. Thus, the cognitive load ratio defined by the TBRS model could be used in the Cognitive Load Theory framework to describe both intrinsic and extraneous load.

These loads are not only determined by the number of elements to be processed, but also by the time available and needed to process them. Participants having more automated mental calculation would be less affected by time ratio manipulation, because they needed less remaining time to manipulate the mental calculation terms. Expertise, seen as an automation of information manipulation, has reduced the sensitivity to extraneous load [START_REF] Kalyuga | The Expertise Reversal Effect[END_REF][START_REF] Kalyuga | Expertise Reversal Effect and Its Implications for Learner-Tailored Instruction[END_REF]. However, this new interpretation of expertise differs from the one used in Cognitive Load Theory. While Cognitive Load Theory suggests that irrelevant information might impair learning by becoming redundant in instructional procedures, the TBRS model considers effects of expertise on working memory processing. Here, expertise can be viewed as reducing the distracting task effect while this task impairs novices' performance.

Both groups performed the concurrent task with the same performance, thus mental calculation performance differences were not linked to different strategies used to carry out the mental calculation task and the spatial judgment task at the same time. The fact that the "close" condition of the spatial judgment task took longer to perform, indicates that attentional focus was captured for a longer duration, resulting in decreased working memory performance and thus in less error-free mental calculation, at least for participants with less automated mental calculation. For this group, result patterns are consistent with previous TBRS experiments (Portrat, Camos &Barrouillet, 2009), suggesting that less proficient participants had not "chunked" the terms by performing the calculation. Taken together, these results suggest that the Time Based Resource Sharing model might be used for Cognitive Load Theory research, providing that expertise of learners is controlled. If more time is available to maintain and manipulate information, this information will be processed more efficiently.

However, another interpretation of these results could be proposed. It is possible that the time ratio manipulation could have had an effect on the difficulty of the concurrent task.

The time ratio manipulation used two different distances for the squares. One might argue that this could have resulted in two different levels of interference. This would lead to the idea that at least some of the differences observed are due to an interference effect, variations in the concurrent task affecting participants according to their expertise. Participants of the more expert group could have had greater ability because they had superior working memory capacity to develop their superior expertise [START_REF] Bull | Short-term memory, working memory, and executive functioning in preschoolers: longitudinal predictors of mathematical achievement at age 7 years[END_REF]Raghubar, Barnes & Hecht, 2010 for review). Higher working memory capacity individuals are assumed to be better at inhibiting interference than those with lower working memory capacity [START_REF] Gulbinaite | Dissociable mechanisms underlying individual differences in visual working memory capacity[END_REF]. Thus, manipulation of the concurrent task could have resulted in a manipulation of induced interference. This manipulation would have had a detrimental effect on "novice" participants (i.e., participants with lower working memory capacity). On the other hand, it would not have affected participants from the "expert" group, who are better at inhibiting interference. Notwithstanding, other TBRS results ruling out this hypothesis [START_REF] Barrouillet | Working memory: loss and reconstruction[END_REF], we reproduced this experiment using the same concurrent task in both conditions to neutralize possible interference effect.

Experiment 2

The first experiment showed that typical predictions of the TBRS model were also observed with material that can be chunked, but only with participants who were less proficient with the principal task. However, reproducing a previous TBRS experiment (Portrat, Camos &Barrouillet, 2009), we used two different kinds of stimuli (close and distant conditions) to impose different processing times on our participants. This manipulation induced different time ratios between the time needed to perform the concurrent task and the remaining time allowed to refresh representations held in working memory.

However, since participants with different working memory capacity might rely on different strategies to maintain working memory representations active, the use of two different distracting tasks might have had a differential effect on our two groups of participants. At least some of the differences observed might be explained by variations in the load imposed by the interfering task for novices, who are more likely to be affected by interference. Consequently, the same experiment was reproduced while using another prediction of the TBRS hypothesis.

Following the TBRS model, only time ratio would affect working memory capacity. This ratio is affected by the time needed to perform the task if total time available is kept constant. On the other hand, if the time needed to perform the task is kept constant, then varying the total time available will affect the time ratio in the same way.

We thus reproduced Experiment 1 using only the "close" condition but varying total time available between each distracting task. This resulted in a "fast" condition and a "slow" condition. Our hypothesis was that the "slow" condition, providing more time to refresh items held in working memory, would induce a lower Cognitive Load and would result in higher mental calculation performance, at least for "novice" participants. This hypothesis was not in line with predictions allowed by previous conceptions of working memory, for which the main determinant of working memory performance is the number of elements held in working memory (see Oberauer, Farrell, Jarrold & Lewandowsky, 2016 for review). We proposed that the same number of distracting elements might have a differential effect on working memory performance even for less proficient students, while the commonly used model assumes that a given number of distractors will always have the same effect on working memory.

Method

Participants. Fifty seven8 th grade students (mean age = 13.46, SD = 0.57, 24 girls and 33 boys) of the same school as in Experiment 1 participated in this experiment. The parents of the children gave written informed consent and the children volunteered to participate in this study. The experiment took place at the school, in an equipped classroom. Participants performed this experiment in group sessions.

Material and procedure. The material and procedure used in this experiment were similar to those of Experiment 1, except for the distracting task. The squares used were the same as in Experiment 1 but the locations were those of the close condition. In a fast condition, participants were given 1s between each square presentation, as in Experiment 1. In a slow condition, the squares were presented for 667ms and followed by a white screen for 1333ms, resulting in a square presented every two seconds.

Dependent variable and statistical analyses.

Based on performances on the pre-test, two groups were created, using the same thresholds as those used in Experiment 1. Participants were gathered in the group "Calc+" (n=33) if they had more than 12 correct answers on the pretest and in the group called "Calc-" (n=11) if they had fewer than 8 correct answers on the same pre-test. The number of calculations correctly performed for each condition, fast and slow, was recorded. To test the hypothesis that the slow condition would result in better performances than the fast condition at least for the "calc-" group, a repeated measure ANOVA with the group as a between subject factor was performed on the number of correct calculations. Further pair condition respectively, t(11) = 0.13, p = .900). Participants of the "calc+" group also performed equally well the spatial judgment task in both conditions (M = 82.46, SD = 9.48 and M = 80.27, SD = 12.64 for slow and fast condition respectively, t(33) = 1.62, p = .115).

The presentation order had no effect on the number of correct calculations performed either during the "fast condition" (t(42) = -0.374, p = .710) or during the "slow condition" (t(42) = 1.143, p = .260).

Number of correct calculations RT (s) on distracting task

Slow condition Fast condition Distracter Slow condition

Distracter fast condition

Calc-

Discussion

In this experiment, we tested the hypothesis that manipulation of time ratio had an effect on working memory performance while ruling out interference based explanation. We reproduced the first experiment by using the exact same stimuli for the concurrent task and varying the inter-stimuli interval. Variations of the time remaining to refresh and manipulate information presented, resulted in variations in the number of correct calculations, at least for the least proficient students in mental calculation. Participants from the "expert" group showed no differences due to the time ratio, suggesting they were able to perform mental calculations during the time left by the "fast" condition. However, "Calc-" participants, having less automated mental calculation, performed better when the time ratio was lower.

Participants of both groups required the same time to perform the concurrent task, and this time was longer in the "slow" condition than in the "fast" condition. Despite this difference, the time ratio remained higher in the "fast" condition. A similar result appeared in previous experiments on the TBRS model and the authors concluded that their participants adapted their strategy to cope with a "speed-accuracy trade-off" [START_REF] Barrouillet | Time and Cognitive Load in Working Memory[END_REF].

Following a TBRS based hypothesis, time ratio affected working memory performance for the "Calc-" group while the concurrent task and the number of distracters were the same in the two conditions. This result rules out the hypothesis of an interference effect, which would have affected participants differently based on their working memory capacity. It is also inconsistent with predictions allowed by models based on spatial storage metaphors, which assume that the number of elements passing through working memory is the first determinant of working memory performance. Here, providing "novices" with more time to maintain and manipulate information held in working memory resulted in better performance.

The results of this experiment are consistent with those of the first experiment and extend them. Thus the proportion of time dedicated to process irrelevant information and relevant information affects extraneous and intrinsic cognitive loads. They are not only determined by the number of elements to be processed but also by the time available and needed to process them.

General discussion

New working memory models are required to derive a more complete understanding of learning processes and the TBRS model appears to be a promising alternative. In two experiments, we assessed its validity when considering the manipulation of meaningful information and participants of different expertise levels in mental calculation. The first experiment showed that for a given duration, the time needed to process distracting elements had an effect on arithmetic performance. The second experiment extended this result, showing that the same number of distracting elements might induce different cognitive load levels, depending on the pace of presentation. Thus, the TBRS model has the potential to provide the assistance that is considered necessary in Cognitive Load Theory research by taking time into account [START_REF] Paas | Cognitive load measurement as a means to advance cognitive load theory[END_REF][START_REF] Van Gog | The Mirror Neuron System and Observational Learning: Implications for the Effectiveness of Dynamic Visualizations[END_REF][START_REF] Spanjers | A Theoretical Analysis of How Segmentation of Dynamic Visualizations Optimizes Students[END_REF].

Our experiments emphasized the necessity of considering the level of expertise. Indeed, expertise affects the sensitivity to cognitive load induced by varying the time allowed to perform tasks (Experiment 1) and affects working memory performance (Experiment 2). This is consistent with previous Cognitive Load Theory research on the expertise effect [START_REF] Kalyuga | The Expertise Reversal Effect[END_REF][START_REF] Kalyuga | Expertise Reversal Effect and Its Implications for Learner-Tailored Instruction[END_REF] as well as with previous works on working memory and expertise (e.g., [START_REF] Ericsson | Long-term working memory[END_REF][START_REF] Ericsson | An introduction to Cambridge Handbook of Expertise and Expert Performance: Its Development, Organization and Content[END_REF][START_REF] Chi | Two Approaches to the Study of Experts' Characteristics[END_REF]. In experiments on Cognitive Load Theory, expertise has been known to reverse most empirical effects on instructional procedures [START_REF] Kalyuga | The Expertise Reversal Effect[END_REF][START_REF] Kalyuga | Expertise Reversal Effect and Its Implications for Learner-Tailored Instruction[END_REF][START_REF] Sweller | Cognitive Load Theory[END_REF]; see also [START_REF] Sweller | Element Interactivity and Intrinsic, Extraneous, and Germane Cognitive Load[END_REF] for a review on expertise and interactivity). However, the present experiments showed that the TBRS model allows for prediction on manipulation of meaningful elements providing that prior knowledge level is considered.

These results were obtained with very low interactivity material, since participants had to process the terms of calculation in the presentation order. Thus, there were no links between first and last terms presented, limiting the interactivity of the material. However, expertise still had an effect, suggesting that it did not only reduce the element interactivity. This might have affected the particular form of chunking used in these experiments. At least for more expert participants, able to perform operations as they were presented, there might be virtually no limit to the number of terms one can add. This form of chunking is both quite close but also different to the commonly accepted definition of the chunk, as gathering several elements into a single meaningful element. The chunking form used here consisted in adding new elements to the "chunk" at each step, a feature that was not included in a classic definition of chunking. This conception allowed the use of meaningful items that could be manipulated together in relation to the content of long-term memory, in this instance the terms of a calculation. Participants did not learn mental calculation during these experiments; their main focus was to investigate the Time Based Resources Sharing model while using meaningful items. This allowed the role of time as a determinant of cognitive load to be emphasized. To date, most of the experiments investigating working memory have used fixed durations (for example, of one minute) and varied the number of elements (for example, from five and ten). A higher number of elements was associated with a lower working memory performance, i.e., it was considered as having a detrimental effect on learning. The TBRS model allows a reconsideration of such results, with the assumption that five elements in one minute will be processed as efficiently as ten elements in two minutes.

While some authors argued for counting the number of elements and their links in order to define a cognitive load estimation [START_REF] Chanquoy | La charge cognitive: Théorie et applications[END_REF], the TBRS model enables a different reading of these relations. Extrinsic load could be viewed as a product of a number of distracting elements and of the time needed to process units of distracting information, rather than their sole number. As shown in experiment 1, the same number of distracting elements might impose different extrinsic load depending on the time needed to process them. Our results suggest that the time ratio affects task performance and classic studies on the TBRS model suggest that time ratio rather than interference affects working memory performance [START_REF] Barrouillet | Working memory: loss and reconstruction[END_REF] for a review).

Intrinsic load, on the other hand, would rely on the remaining time available to refresh memory traces and manipulate information in working memory. The longer this time is, the easier it will be to maintain and manipulate a large quantity of information. [START_REF] Sweller | Cognitive load theory[END_REF] stated that "intrinsic load refers to the intrinsic complexity of the information being processed" (p. 57) and that it is possible "to determine levels of intrinsic cognitive load by determining element interactivity" (p. 58), i.e., the number of elements to be processed simultaneously and their links. This resulted in a fixed amount of intrinsic load, at least for a given expertise level.

Experiment 2 introduced time as a factor to be taken into consideration. This implies that for a given learner and a given learning task, the intrinsic load will not be the same following the time available to process information. If a learner needs two seconds to process intrinsic load, performance (and by extension, learning outcome) will not be the same if one or three seconds are available.

Expertise would allow faster refreshing and manipulation of information in working memory, reducing the influence of the time needed for the manipulation of distracting elements.

Thus, expertise would decrease the sensitivity to time ratio manipulation. In the Cognitive Load Theory framework, expertise is viewed as decreasing interactivity between elements [START_REF] Chen | The Worked Example Effect, the Generation Effect, and Element Interactivity[END_REF]2016).

Fig 1

 1 Fig 1 predictions allowed by the TBRS model. In this model, working memory

  as a new working memory model in the field of Cognitive Load Theory research. Indeed, TBRS has so far never been used with meaningful material. On the contrary, Cognitive Load Theory research is particularly interested in the manipulation, and then learning of meaningful material. A working memory model which takes time into account could be of particular interest for Cognitive Load Theory, explaining the effect of information presentation pace and providing a theoretical framework for research on the transient information effect.

Participants.

  Sixty nine 7 th grade students (31 girls and 38 boys, mean age = 12.28 years, SD = 0.357) participated in this experiment. The parents of the children gave written informed consent and the children volunteered to participate in this study. The experiment took place at school, in a computer equipped classroom. Participants performed this experiment in group sessions.

  By reducing such interactivity, expertise reduces the efficacy of Cognitive Load Theory empirical effects. Most importantly, expertise reduces both intrinsic and extrinsic cognitive loads. Our results, in a low interactivity situation, extend this conception, considering expertise as allowing faster processing of information held in working memory and thus reducing sensitivity to time ratio manipulations. The TBRS model describes dynamic variations in working memory, and thereby allows time to be taken into account while studying working memory requirement. However, the same number of distracting tasks might result in different cognitive load levels, depending on the time they require attention for. The exact same task with the same distracters might also impose different cognitive load levels depending on the remaining time available to process intrinsic load elements. This allowed the explanation of variations of learning outcomes in the Schmidt-Weigand et al. (2010) study, the same learning material presented at different paces providing different results. Further studies should investigate the TBRS model in learning situations to extend the result of these experiments to the broad field of cognitive load theory research. In particular, it could help to provide a physiological measurement of cognitive load. It supports the idea that time should a greater role when considering the determinant of cognitive load, affecting the number of elements and their links.

Table 1 .Means (and Standard deviation) of the number of correct calculations for the easy (distant) and the difficult (close) conditions and of the reaction times in milliseconds on the distracting task.

 1 To control for learning effects, the number of correct calculations performed by participants was compared following the first condition completed. Starting with one condition or the other had no effect on the number of correct calculations in either the "distant" condition

		5,85 (4,27)	3,65 (4,23)	354,58 (91,97)	383,09 (106,58)
	Calc+	9,75 (4,35)	9,95 (4,39)	361,02 (35,40)	381,53 (34,63)

Table 2 . Means (and Standard deviations) of the number of correct calculations for the slow and fast conditions and of the reaction times (in milliseconds)on the distracting task

 2

The SNARC effect (Spatial Numerical Association of Response Code) shows an association between numbers and spatial position. Small numbers are associated with left or top part of the screen and larger number with right or lower part of the screen. It was originally found with manual responses, responses with left hand being faster than right hand for small numbers and conversely, but further extended to cross modal responses and to all associations of space and numbers.

comparisons were conducted using repeated student t-tests. As in experiment 1, the reaction time (in milliseconds) to perform the spatial judgment task was recorded and compared between experimental condition using t-tests.

Results

The results are summarized in Table 2. The repeated measure ANOVA with group as a between factor showed significant differences following the difficulty (F(1,44) = 8.82, p = .005) and following the group (F(1,44) = 3.09, p = .086) though this was only a marginally significant difference. The interaction between the two factors was not significant (F(1,44) = 2.09, p = .156). Further pair comparisons were conducted using repeated t-tests.

Participants of the "Calc-" group performed more correct calculations in the "slow" condition than during the "fast" one (M = 11.64, SD = 3.80 and M = 7.82, SD = 5.88, t(10) = 2.971, p = .014, d = 0.789). On the contrary, the number of correct calculations accomplished by the participants of the "Calc+" group did not vary according to the condition (M = 11.33, SD = 4.61 and M = 12.76, SD = 4.81 for the "fast" and "slow" conditions respectively, t(32) = 1.53, p = .136, d = 0.302). As during the first experiment, time ratio manipulation affected participants having less automated mental calculation only. These participants performed better in the slowest condition though there were the same number of distracters in both conditions. Participants from the "Calc+" group performed the concurrent task faster in the "fast" condition than in the "slow" condition (M =389.82, SD = 39.85 and M = 468.30, SD = 58.26 respectively, t(32) = 10.82, p < .001, d = 1.600). The same pattern appeared for the "Calc-" group (M = 393.27,SD = 83.49 and M = 479.82,SD = 50.53,t(10) = 4.98,p = .001,d = 1.292). Participants of both groups performed the concurrent task at the same speed for both "fast" and "slow" conditions (t(11.56) = 0.13, p = .897, d = 0.068 and t(42) = 0.58, p = .562, d = 0.204). Participants of the "calc-" group performed equally correctly in both conditions of the spatial judgment task (M = 72.14, SD = 15.38 and M = 72.56, SD = 16.93 for slow and fast


Antoine Lejeune
email: anlejeun@gmail.com

Audrey Cabrol

Ronan Lebullenger

Audrey Denicourt-Nowicki

Alain Roucoux

Annabelle Couvert

Pierre-Francois Biard

Pierre-François Biard

Novel and Sustainable Catalytic Ruthenium-Doped Glass Foam for Thermocatalytic Oxidation of Volatile Organic Compounds: An Experimental and Modeling Study

INTRODUCTION

Nowadays, air quality is a subject of major concern for human health and environment, and a special attention has to be paid towards Volatile Organic Compounds (VOCs). Many studies have highlighted their detrimental effects [START_REF] Huang | Chlorinated volatile organic compounds (Cl-VOCs) in environmentsources, potential human health impacts, and current remediation technologies[END_REF][START_REF] Guo | Risk assessment of exposure to volatile organic compounds in different indoor environments[END_REF][START_REF] Rodhe | A comparison of the contribution of various gases to the greenhouse effect[END_REF] and these compounds are present in many household products and are used in various industrial processes. For instance, they are responsible for eye and throat irritation, headaches and they are suspected to cause cancer in animals and humans. [START_REF] Lerner | Characterization and health risk assessment of VOCs in occupational environments in Buenos Aires, Argentina[END_REF] Various processes have already been designed and optimized to remove VOCs, based on physical, chemical or biological treatments. [START_REF] Khan | Removal of Volatile Organic Compounds from polluted air[END_REF] The choice of the most efficient and less expensive process is not easy and mainly depends on the concentration, the volume and the type of VOCs. There are two main groups of treatments based on either recovery or destruction, each presenting advantages and drawbacks. The use of oxidative processes seems to be currently one of the most efficient solution with some processes already developed at the industrial scale. Actually, thermal oxidation (fume incinerators) is efficient to remove a large variety of VOCs at high concentrations and flowrates but still requires high temperatures around 1,000 °C, rendering this process energy-consuming. [START_REF] Khan | Removal of Volatile Organic Compounds from polluted air[END_REF] To overcome this issue, catalysts have been developed and used to decrease the operating temperature down to 200-400 °C and reduce the energy requirement. The catalysts used are usually honeycomb structures with parallel channels coated with catalytic species (noble metals or metal oxides) 6-7-8 by different methods such as sol-gel deposition, impregnation or electrophoretic deposition. [START_REF] Meille | Review on methods to deposit catalysts on structured surfaces[END_REF] Many studies focused on the influence of the catalytic species to the removal of various VOCs such as toluene, [START_REF] Gallegos | Removal of VOCs by catalytic process. A study of MnZnO composites synthesized from waste alkaline and Zn/C batteries[END_REF][START_REF] Hu | Low content of CoOx supported on nanocrystalline CeO2 for toluene combustion: The importance of interfaces between active sites and supports[END_REF] benzene, [START_REF] Einaga | Catalytic oxidation of benzene in the gas phase over aluminasupported silver catalysts[END_REF][START_REF] Guo | Catalytic removal of benzene at mild temperature over manganese oxide catalysts[END_REF] formaldehyde, [START_REF] Li | Removal of formaldehyde over MnxCe1-xO2 catalysts: thermal catalytic oxidation versus ozone catalytic oxidation[END_REF] or ethanol. [START_REF] Wang | Effects of precursor and sulfation on OMS-2 catalyst for oxidation of ethanol and acetaldehyde at low temperatures[END_REF] However, these types of fixed bed catalysts suffer from several drawbacks: (i) the cost of some catalytic species and coating and (ii) the diffusional limitations. Some studies are still dedicated to overcome these issues and among the innovative solutions, the use of tortuous open-cell foams, composed of interconnected net pores, to face with mass transfer limitations is very promising [START_REF] Gao | Study on steam reforming of coal tar over NiCo/ceramic foam catalyst for hydrogen production: Effect of Ni/Co ratio[END_REF][START_REF] Giani | Washcoating method for Pd/γ-Al2O3 deposition on metallic foams[END_REF] and their structured shape can be easily integrated into already existing reactors. Ceramic and metallic foams were synthesized and characterized for some years. Even if pressure drops are higher with these catalysts compared to parallel channels, high mass transfer [START_REF] Groppi | Generalized Correlation for Gas/Solid Mass-Transfer Coefficients in Metallic and Ceramic Foams[END_REF][START_REF] Bracconi | A fundamental investigation of gas/solid mass transfer in open-cell foams using a combined experimental and CFD approach[END_REF][START_REF] Garrido | Mass transfer and pressure drop in ceramic foams: A description for different pore sizes and porosities[END_REF][START_REF] Lucci | Performance of randomized Kelvin cell structures as catalytic substrates: Mass-transfer based analysis[END_REF][START_REF] Richardson | Properties of ceramic foam catalyst supports: pressure drops[END_REF] and thermal [START_REF] Fratalocchi | Intensifying heat transfer in Fischer-Tropsch tubular reactors through the adoption of conductive packed foams[END_REF] rates are achieved. However, there are only few applications of structure foams as support for catalytic oxidation of VOCs [START_REF] Sanz | Aluminium foams as structured supports for volatile organic compounds (VOCs) oxidation[END_REF][START_REF] Li | Catalytic oxidation characteristics of CH4-air mixtures over metal foam monoliths[END_REF][START_REF] Ribeiro | Catalytic combustion of toluene on Pt zeolite coated cordierite foams[END_REF] and their widespread industrial use is limited by high costs of raw products and/or high operating costs for their synthesis. Nevertheless, recently, glass foams synthesized from recycled glass at milder conditions than other foams (temperature of 800-900°C against synthesis in many steps at more than 1,300°C for ceramic materials) were doped with zerovalent metal nanoparticles (aiming to 0.1 wt% metal) by a wet impregnation methodology in neat water at room temperature without washcoat layer, rendering these materials eco-friendly and cheaper than other foams. [START_REF] Biard | Nanoparticules métalliques supportées sur un support en mousse de verre et utilisations pour la catalyse de réactions chimiques[END_REF][START_REF] Lejeune | Development of a sustainable heterogeneous catalyst based on an open-cell glass foam support: application in gas-phase ozone decomposition[END_REF] Owing to their very small size in the range of 2-5 nm, the metal active nanospecies present high active surface area, and thus potentially affording relevant surface reactivities. These materials, wellcharacterized in terms of structure, pressure drops and surface charge, have proved to be relevant for the removal of ozone from air at room temperature. [START_REF] Lejeune | Development of a sustainable heterogeneous catalyst based on an open-cell glass foam support: application in gas-phase ozone decomposition[END_REF] In this study, these glass foams impregnated with ruthenium nanoparticles were investigated for the first time for the removal of several VOCs (ethanol, acetone, toluene and heptane) from air by thermocatalytic oxidation at temperatures ranging from 100 to 350°C. The first part of the paper will show the potential of catalytic glass foams for the abatement of these VOCs. In the second part, the influence of the operating conditions will be assessed to improve the efficiency of the catalyst. Finally, modeling and predictive simulations of the process will allow to consider upscaling in order to evaluate and compare large scale process performances.

MATERIAL AND METHODS

Synthesis of the catalytic glass foam

The synthesis and characterization of various catalytic glass foams were already detailed. [START_REF] Biard | Nanoparticules métalliques supportées sur un support en mousse de verre et utilisations pour la catalyse de réactions chimiques[END_REF][START_REF] Lejeune | Development of a sustainable heterogeneous catalyst based on an open-cell glass foam support: application in gas-phase ozone decomposition[END_REF] In this study, only one catalyst was used for all the experiments. Its synthesis and characterization are explained in Supplementary material S1.

Only thermal characterizations were added compared to the previous paper dealing with the characterization of catalytic glass foams. [START_REF] Lejeune | Development of a sustainable heterogeneous catalyst based on an open-cell glass foam support: application in gas-phase ozone decomposition[END_REF] Differential thermal and gravimetric analyses (DTA-TGA) were carried out on TA Instruments Model SDT 2960 equipment.

Measurements were done under synthetic air and a 10 K.min -1 heating rate. The dilation of the glass foam at high temperature was evaluated with a Rheotronic parallel-plate viscometer (from Theta-US). A glass foam sample of 1.65 cm diameter was used with an applied load of 200 g. The temperature of the analysis ranged between room temperature and 700°C.

Thermocatalytic oxidation setup

The thermocatalytic oxidation setup consisted of a continuous fixed-bed reactor fed with air polluted with a VOC at the desired concentration (Figure 1). A 40 L Tedlar® bag was filled at steady state with oxygen and then a liquid VOC was vaporized in it to reach the desired concentration. Then, the polluted air was pumped from the Tedlar bag using a membrane pump, specifically designed by KNF (Germany) for this application, to the glass foam catalyst (reactor) inserted in an oven whose temperature was controlled between 100°C and 400°C.

The accuracy of the oven temperature was 10°C. The temperature of the oven reached the desired value before starting the experiments about the removal of VOCs. The gas flow-rate (at room temperature) was controlled with a flow-meter (Brooks R-15-C) and it ranged between 6.6 L.h -1 and 21.9 L.h -1 . According to the size of the catalyst (16 mm diameter and 94 mm length), the gas velocity varied between 0.010 m.s -1 and 0.032 m.s -1 and the gas hourly space velocity (GHSV) between 288 h -1 and 1236 h -1 .

Gas samples were withdrawn with a gas-tight syringe at the inlet and outlet of the reactor. All experiments were performed during at least one hour in order to ensure steady state conditions (it was checked by taking several samples during the experiments and after some minutes the outlet concentration was constant) and no catalyst deactivation was observed.

VOCs and analyses

The removal of four VOCs (ethanol, acetone, toluene and heptane) was tested through a thermocatalytic oxidation process. These compounds were chosen since they belong to different families of chemicals and they are identified as detrimental for human health and environment. [START_REF] Kamal | Catalytic oxidation of volatile organic compounds (VOCs) -A review[END_REF] Table 1 gives the inlet concentrations implemented. Except for ethanol whose concentration was varied between 0.2 g.m -3 and 1.0 g.m -3 , the inlet concentrations were kept constant at 1.0 gm -3 (toluene, heptane) or 2.0 g.m -3 (acetone). These values were chosen in order to deal with industrial air treatment where such high concentrations can be measured.

The VOCs concentrations were quantified by Gas Chromatography (GC). The GC apparatus (Agilent 6890N) was equipped with a DB-624 column (30 m × 0.53 mm) and a Flame Ionisation Detector. The injector was heated at 150°C and the detector at 250°C. The gas vector was H2. Depending on the VOC analyzed, the oven of the GC was heated at different temperatures. The accuracy on the concentration was ±2%. Table 1 gives the temperature of the oven and the retention time for all the VOCs tested.

The removal efficiency (Eff, %) and rate of reaction (r, g.m -3 .s -1 ) were calculated according to the inlet and outlet concentrations, and residence time (equation (1) and equation (2), respectively).

Eff = [VOC] inlet -[VOC] outlet [VOC] inlet × 100 (1) r =
[VOC] inlet -[VOC] outlet τ (2)
With [VOC] inlet the VOC concentration at the inlet of the reactor (g.m -3 ), [VOC] outlet the VOC concentration at the outlet of the reactor (g.m -3 ) and τ the empty tube residence time (s).

The Turn-Over Frequency (TOF, h -1 ) was determined with equation (3).

TOF = ṅE tOH oxidized n Ru (3)
With ṅE tOH oxidized the number of moles of ethanol oxidized per time unit calculated with equation (4) (mol.h -1 ) and n Ru the number of moles of ruthenium on the glass foam determined with equation (5) assuming that the ruthenium loading was 0.1 wt.% (mol).

ṅE tOH oxidized = Q × Eff × [EtOH] inlet (4)
With Q the volumetric flowrate (m 3 .h -1 ).

n Ru = 0.1wt. % × m foam MW Ru (5) With MW Ru the molecular weight of Ru (g.mol -1 ) and m foam the mass of the glass foam (g).

RESULTS AND DISCUSSION

Characterization the catalytic glass foam

The catalytic glass foam has a porous structure (Figure 2) and possesses an open porosity of 92%, with a mean pore diameter of 0.59 mm. These values of open porosity and mean pore diameter are in the upper range for glass foams. [START_REF] Lejeune | Development of a sustainable heterogeneous catalyst based on an open-cell glass foam support: application in gas-phase ozone decomposition[END_REF] According to BET analysis, the surface area is 0.4±0.1 m 2 .g -1 . Compared with ceramic and metallic foams, the open porosity, mean pore size diameter and surface area of the glass foam are in the same range of values [START_REF] Giani | Washcoating method for Pd/γ-Al2O3 deposition on metallic foams[END_REF][START_REF] Groppi | Generalized Correlation for Gas/Solid Mass-Transfer Coefficients in Metallic and Ceramic Foams[END_REF][START_REF] Bracconi | A fundamental investigation of gas/solid mass transfer in open-cell foams using a combined experimental and CFD approach[END_REF][START_REF] Garrido | Mass transfer and pressure drop in ceramic foams: A description for different pore sizes and porosities[END_REF][START_REF] Lucci | Performance of randomized Kelvin cell structures as catalytic substrates: Mass-transfer based analysis[END_REF][START_REF] Richardson | Properties of ceramic foam catalyst supports: pressure drops[END_REF] but the synthesis of glass foam remains less expensive with cheaper raw materials (recycling of glass cullet), and milder synthesis conditions (around 800°C against 1,300°C for ceramic ones).

Figure 2 shows a real photo, SEM picture and TEM picture of the glass foam. The SEM picture confirms the mean pore diameter obtained with image treatment with ImageJ 1.52 software. On the TEM pictures, the ruthenium nanoparticles are clearly visible (black dots)

and well dispersed on the support. Spherical nanoparticles were observed with a diameter ranging from 2 to 5 nm and it was estimated through treatment of the image (with ImageJ 1.52 software) that around 23% of the glass foam surface was covered with nanoparticles. m.s -1 during 72h, representing 21 m 3 of air that passed through the catalyst) was already demonstrated and confirmed the quite strong interaction between the nanoparticles and the glass foam support. [START_REF] Lejeune | Development of a sustainable heterogeneous catalyst based on an open-cell glass foam support: application in gas-phase ozone decomposition[END_REF] The thermal stability of the catalytic glass foam at high temperature was also validated before using it for thermocatalytic oxidation.

Performances of the catalytic glass foam for the removal of various VOCs

The catalytic glass foam was evaluated for the removal of four VOCs presenting different functional groups (alcohol, ketone, aromatic and aliphatic), at a superficial gas velocity of 0.010 m.s -1 and inlet concentration of 1.0 g.m -3 or 2.0 g.m -3 depending on the VOC (Figure 24).

Abatements ranging from 8% to 100%, depending on the VOC and the temperature, were achieved, thus proving the potential of glass foams impregnated with ruthenium nanoparticles for thermocatalytic oxidation. From a general point of view, the higher the temperature is, the more efficient the removal is. This result is in agreement with literature data [START_REF] Kamal | Catalytic oxidation of volatile organic compounds (VOCs) -A review[END_REF] and can be explained by the fact that the energy required to initiate the oxidation is easier to overpass at high temperatures.

Ethanol is the easiest VOC to be removed and almost 100% of abatement was reached from 200°C. The removal of acetone was also very efficient with a sharp increase after 100°C and reaching a complete abatement at 250°C. Toluene and even more heptane required higher temperatures of 300-350°C to be fully eliminated. Nevertheless, high abatements were already achieved at 250°C for toluene (94%) and 300°C for heptane (88%), highlighting that full removal can be achieved with a longer reactor (namely a longer residence time) with these milder operating conditions. When 100% of abatement is achieved, no by-product is observed by GC analysis, thus confirming the complete mineralization of the VOCs.

Anyway, these results clearly highlight the efficiency of the catalytic glass foams as new catalyst for VOC treatment and illustrate the high oxidative power of ruthenium species even at a low load of only 0.1 wt.%. In addition with their moderate pressure drops, [START_REF] Lejeune | Development of a sustainable heterogeneous catalyst based on an open-cell glass foam support: application in gas-phase ozone decomposition[END_REF] these catalysts can be efficient alternative to conventional industrial materials. 3)) rather than abatements to consider the amount of catalytic active species involved in the process. The TOF were calculated at low conversion (around 20%) to ensure reliable values. Obviously, the TOF also depends on other parameters that may significantly change its value such as the gas velocity and inlet concentration, but the goal here is to draw an initial assessment of the performances of catalytic glass foams.

Moreover, the comparison is not exhaustive at all and other already existing catalysts may have better performances.

The TOF developed with the glass foam impregnated with ruthenium nanoparticles ranged between 2.30.4 h -1 (heptane and toluene) and 6.92.3 h -1 (acetone). The differences could be attributed to the various inlet VOC concentrations (in mol.m -3 ) and intrinsic VOC reactivity.

These TOF values remain significantly lower than orders of magnitude encountered for other catalytic applications, mainly because VOC treatment involved low VOC loading and competition with O2 for the active sites. In comparison with other applications for oxidation of VOCs, these values are close to the study of Sanz et al. [START_REF] Sanz | Aluminium foams as structured supports for volatile organic compounds (VOCs) oxidation[END_REF] with aluminium foam impregnated with Pt and Gallegos et al. [START_REF] Gallegos | Recovery of manganese oxides from spent alkaline and zinc-carbon batteries. An application as catalysts for VOCs elimination[END_REF] with manganese oxide active species. Zhao et al. [START_REF] Zhao | Novel monolithic catalysts derived from in-situ decoration of Co3O4 and hierarchical Co3O4@MnOx on Ni foam for VOC oxidation[END_REF] and Delimaris and Ioannides [START_REF] Delimaris | VOC oxidation over CuO-CeO2 catalysts prepared by a combustion method[END_REF] found lower TOF (10 times lower) because the amount of active species was high (around 10 wt%). On the other hand, higher TOFs were also found with other catalysts (around 10 times higher than the ones found in this study), [START_REF] Ribeiro | Catalytic combustion of toluene on Pt zeolite coated cordierite foams[END_REF][START_REF] Carabineiro | Gold supported on metal oxides for volatiles organic compounds total oxidation[END_REF] this result could be explained by a high feed flowrate and also to expensive Pt and gold particles involved in the process that achieved efficient catalytic oxidation (but they could be found in relatively high amount such as 1.0 wt% for the gold particles). Anyway, these results highlight that the ruthenium-doped catalytic glass foams are competitive with other catalysts recently developed. This good efficiency mainly comes from the high active surface area even at the low loading of metal active species (0.1 wt%). Associated to the previously explained eco-friendly synthesis and characteristics (recycling of glass waste, synthesis and impregnation under mild conditions and without washcoating, high porosity), the catalytic glass foams are competitive catalysts whose use could be considered in the chemical and environmental industries.

Influence of other operating conditions on ethanol removal

In addition to the temperature, the influence of two other operating conditions on the abatement was investigated: (i) the inlet concentration and (ii) the superficial gas velocity.

This evaluation was performed only with ethanol and similar behaviors are expected for the other VOCs. The effect of these two parameters was assessed at low temperatures (100°C, 125°C and 150°C) since the abatement can reach 100% at higher temperatures (Figure 24).

The results are summarized in Table 3 in terms of abatement, TOF and rate of reaction.

Acetaldehyde was the only by-product detected and quantified by GC during the experiment and so its outlet concentration was also recorded. Other researchers highlighted that acetaldehyde was the only by-product observed during the oxidation of ethanol. [START_REF] Ismagilov | Oxidation of ethanol on platinum/alumina and copper oxide catalysts[END_REF][START_REF] Rajesht | Complete Oxidation of Ethanol, Acetaldehyde, and Ethanol/Methanol Mixtures over Copper Oxide and Copper-Chromium Oxide Catalysts[END_REF][START_REF] Litt | An investigation of CuO/Fe2O3 catalysts for the gas-phase oxidation of ethanol[END_REF] It seemed that the other steps of the oxidation were very fast once acetaldehyde has been oxidized.

Therefore, a two-step mechanism was assumed (equation ( 6) and equation ( 7)). Equation (7) obviously means that for each mole of acetaldehyde oxidized, two moles of CO2 are produced.

Step 1, oxidation of ethanol: C2H5OH + 1/2 O2  C2H4O + H2O

Step 2, oxidation of acetaldehyde: C2H4O + 5/2 O2  2 CO2 + 2 H2O (7)

According to mass balance, the mineralization (quantity of ethanol oxidized into CO2) is calculated with equation ( 8):

Mineralization = n EtOH mineralized n EtOH inlet = [EtOH] inlet -[EtOH] outlet -[Acetaldehyde] outlet [EtOH] inlet (8)
With n EtOH mineralized the number of moles of ethanol mineralized into CO2 (mol), n EtOH inlet the number of moles of ethanol which entered in the process (mol), [EtOH] inlet the ethanol inlet concentration (mol.m -3 ), [EtOH] outlet the outlet ethanol concentration (mol.m -3 ) and

[Acetaldehyde] outlet the outlet acetaldehyde concentration (mol.m -3 ) at the temperature and pressure of the process.

Whatever the temperature, the rate of ethanol removal increased with an increase in the superficial gas velocity (Table 3). It shows that the process is still limited by mass transfer in the range of gas velocities tested and it is in agreement with the previous results about ozone removal in air at room temperature with similar catalytic glass foams. [START_REF] Lejeune | Development of a sustainable heterogeneous catalyst based on an open-cell glass foam support: application in gas-phase ozone decomposition[END_REF] At the same time, the ethanol abatement decreased (or remained almost constant) with an increase in the superficial gas velocity. Actually, two opposite effects are involved: on the one hand, the rate of reaction increases when the gas velocity rises (less mass transfer limitation) and on the other hand, the residence time decreases (from 8.8 s at 0.010 m.s -1 to 2.7 s at 0.032 m.s -1 ). Thus, for the same residence time, higher abatements would be expected at higher superficial gas velocity.

Another way to decrease the mass transfer limitations would be to play on the structure of the glass foam support (smaller pores and lower open porosities). However, Incera-Garrido et al. [START_REF] Garrido | Mass transfer and pressure drop in ceramic foams: A description for different pore sizes and porosities[END_REF] have already showed for ceramic foams that the effect of these parameters is small. In addition, the suggested modifications of the structure of the support significantly increases the pressure drops [START_REF] Lejeune | Development of a sustainable heterogeneous catalyst based on an open-cell glass foam support: application in gas-phase ozone decomposition[END_REF] and so the operating cost of the process.

The effect of the inlet concentration was also the same whatsoever the temperature and superficial gas velocity. The higher the inlet concentration is, the higher the reaction rate is.

The removal efficiency of ethanol decreased with higher inlet concentrations due to a noncompensation of the increase of the VOC molar flow rate by a better oxidation kinetics. It declined to 22% only at 100°C and 1.0 g.m -3 inlet concentration. However, these experiments were performed with high inlet concentrations and low catalyst load (0.1 wt.% of ruthenium).

The TOF values (at 1.0 g.m -3 inlet concentration and 0.010 m.s -1 ) increase according to the temperature in the following order: 1.1 h -1 at 100°C, 1.8 h -1 at 125°C and 3.3 h -1 at 150°C.

We could presume that at lower inlet ethanol concentration, very high removal efficiency would be achieved. Actually, the removal efficiency of ethanol reached 93% at 150°C, 0.2 g.m -3 inlet concentration and 0.010 m.s -1 superficial gas velocity.

Concerning the outlet acetaldehyde concentration, we observed that the higher the ethanol abatement is, the greater the acetaldehyde concentration is. In fact, the outlet acetaldehyde concentration increased with a raise in temperature and also in ethanol inlet concentration while it decreased when elevating the superficial gas velocity. Quite high values are achieved depending on the operating conditions, reaching 0.50 g.m -3 at 150°C, 0.010 m.s -1 and 1.0 g.m - 3 ethanol inlet concentration, which is half of the ethanol inlet concentration. It implied that the mineralization was quite low whatsoever the experiments (between 6% and 17%) because most of the oxidized ethanol remained acetaldehyde until the outlet of the process. A higher temperature or a higher residence time would be necessary to remove effectively acetaldehyde.

Finally, the experiment at 100°C, 0.010 m.s -1 and 1.0 g.m -3 inlet concentration was duplicated after around 40 hours of use of the catalyst. The same rate of reaction was found in both experiments highlighting that the catalyst was not deactivated after some tens of hours of use.

Moreover, this promising result also showed the good thermal resistance of the overall structured catalyst.

Modeling and simulations of ethanol abatement

Equations and assumptions of the model

In order to get more insights into the removal of ethanol by thermocatalytic oxidation with the catalytic glass foam, and to start thinking about upscaling, modeling and predictive simulations were performed. Several assumptions were done for the modeling: (i) temperature and pressure are constant, (ii) oxygen is in large excess for the oxidation reaction and so its concentration is assumed to be constant, (iii) only acetaldehyde is taken into account as byproduct, (iv) the glass foam catalyst is assumed to be a plug-flow reactor, (v) a steady-state flow is assumed and (vi) CO2 and H2O produced do not influence the kinetic of reaction. The same assumptions were already done by Rodríguez and Cadús 36 who modelled the oxidation of ethanol in a monolithic reactor.

A power law kinetic was chosen to deal with the influence of the ethanol concentration, as already used to try to model the removal of toluene by catalytic ozonation [START_REF] Hu | Novel mechanistic view of catalytic ozonation of gaseous toluene by dual-site kinetic modelling[END_REF] or for the removal of ethanol by thermocatalytic oxidation. [START_REF] Bedi | Modeling for catalytic oxidation of volatile organic compound (VOC) in a catalytic converter[END_REF] The Arrhenius law considered the influence of the temperature. [START_REF] Rodriguez | Mass transfer limitations in a monolithic reactor for the catalytic oxidation of ethanol[END_REF] Finally, the mass transfer resistance was taken into account. [START_REF] Rodriguez | Mass transfer limitations in a monolithic reactor for the catalytic oxidation of ethanol[END_REF] Owing to similar diffusion coefficients in air, the mass-transfer coefficients km for ethanol and acetaldehyde were considered identical.

On the basis of these assumptions and remarks, ethanol and acetaldehyde concentrations along the reactor in the gas phase and at the surface of the catalyst were modelled with equations ( 9) to (12). The ethanol reaction rate (equation ( 9) and equation ( 10)) is independent of the acetaldehyde behavior while the acetaldehyde concentration depends on the removal of ethanol (equation ( 11)).

v × d[EtOH] dx + k m × a v × ([EtOH] -[EtOH] surface ) = 0 (9)
k m × a v × ([EtOH] -[EtOH] surface ) = A EtOH × exp ( -E a,EtOH R×T ) × [EtOH] surface n ( 10
) v × d[Acetaldehyde] dx + k m × a v × ([Acetaldehyde] -[Acetaldehyde] surface ) = v × d[EtOH] dx + k m × a v × ([EtOH] -[EtOH] surface ) (11)
k m × a v × ([Acetaldehyde] -[Acetaldehyde] surface ) = A Acetaldehyde × exp ( -E a,Acetaldehyde R×T ) × [Acetaldehyde] surface m (12)
With v the empty tube superficial gas velocity (m.s -1 ), [EtOH] the ethanol concentration in the gas phase (mol.m -3 ), k m the mass transfer coefficient (m.s -1 ), a v the superficial area (m -1 ), [EtOH] surface the ethanol concentration at the surface of the catalyst (mol.m -3 ), A EtOH the preexponential factor for ethanol removal, E a,EtOH the activation energy for ethanol removal (kJ.mol -1 ), R the ideal gas constant (J.mol -1 .K -1 ), T the temperature (K), n the order of reaction for ethanol (-),[Acetaldehyde] the acetaldehyde concentration in the gas phase (mol.m -3 ), [Acetaldehyde] surface the acetaldehyde concentration at the surface of the catalyst (mol.m -3 ),

A Acetaldehyde the pre-exponential factor for acetaldehyde removal, E a,Acetaldehyde the activation energy for acetaldehyde removal (kJ.mol -1 ) and m the order of reaction for acetaldehyde (-).

In equations ( 9) to ( 12), the mass transfer was described with the term k m × a v . There are several correlations in the literature to calculate the mass transfer coefficient k m in ceramic and metallic foams. [START_REF] Groppi | Generalized Correlation for Gas/Solid Mass-Transfer Coefficients in Metallic and Ceramic Foams[END_REF][START_REF] Garrido | Mass transfer and pressure drop in ceramic foams: A description for different pore sizes and porosities[END_REF][START_REF] Richardson | Properties of ceramic foam catalyst supports : mass and heat transfer[END_REF] They depend on Reynolds and Schmidt numbers, and on the geometric properties of the foam such as the open porosity, mean pore diameter or shape of the struts. However, these equations are accurate for gas velocities higher than 0.5 m.s -1 , which is clearly higher than the values in this study (between 0.010 and 0.032 m.s -1 ). On this basis, a general power law correlation depending on the gas velocity v and 2 constants A and B, was used to deal with the mass transfer (equation ( 13)). It was also assumed that, in the range of temperatures tested (100-150°C), the mass transfer coefficient did not depend on the temperature. This assumption was strengthened by Richardson et al. [START_REF] Richardson | Properties of ceramic foam catalyst supports : mass and heat transfer[END_REF] who demonstrated that the mass transfer coefficient had a small dependence with the temperature for ceramic foams.

k m × a v = A × v B (13)
It makes a total of 8 unknown parameters (two for the mass transfer, three for the kinetics of ethanol abatement and three for the kinetics of acetaldehyde abatement) to fit with 23 experiments (46 data according to ethanol and acetaldehyde outlet concentrations). The differential equations system was solved with Scilab 6.1 with a space interval of 0.05 mm.

The inlet concentration was specified to carry out the calculation. Fitting of the parameters was performed with a Levenberg-Marquardt algorithm.

Preliminary analysis of the experimental data

In order to ease the fitting of the model parameters, a preliminary analysis was performed to roughly estimate some parameters before adjusting the whole model.

The energy of activation of ethanol oxidation was first evaluated. For a given gas velocity and inlet concentration, it was assumed that order of the kinetic power law was 1 and so the apparent kinetic constant of ethanol abatement (k EtOH in s -1 ) can be calculated with the inlet and outlet concentrations. The slope of the plot of the logarithm of the apparent kinetic constant in function of the inverse of the temperature give the energy of activation according to the law of Arrhenius (equation ( 14)).

ln(k EtOH ) = ln(A EtOH ) - E a,EtOH R×T (14)
The calculation was performed for each set of experimental superficial gas velocity and inlet concentration (Supplementary material S2). The values ranged between 24 kJ.mol -1 and 46 kJ.mol -1 that are in the range of experimental data found with other catalysts. [START_REF] Kamal | Catalytic oxidation of volatile organic compounds (VOCs) -A review[END_REF] The average value is of 37 kJ.mol -1 and was used as initial energy of activation for model fitting.

The order of the power law cannot be a priori determined. The regression of the ethanol and acetaldehyde outlet concentration versus the ethanol inlet concentration was nevertheless performed with a power law to estimate the values of n and m in equations ( 10) and (12), respectively. The average value of the order of the power law is 0.6 (for both ethanol and acetaldehyde) and was considered as initial model parameter.

Finally, the influence of superficial gas velocity on the rate of ethanol abatement was performed using a power law to estimate the value of B in Eq. ( 13). The value is 0.6 and was also used as initial model parameter.

Determination of the parameters of the model

According to the previously estimated initial model parameters, the model was adjusted to the experimental data. There is a good agreement between the experimental values of the outlet ethanol concentrations and those deduced from the model (12% of average relative error, Supplementary Material S3). The fitted parameters for ethanol were: A EtOH = 800 m 1.5 .mol - 0.5 .s -1 ; E a,EtOH = 38 kJ. mol -1 ; n=0.5 ; A=15 s 0.7 .m -0.7 and B=0.7. The fitted activation energy, order of kinetic reaction and order of power law mass transfer limitations were close to the estimated values, highlighting that the proposed methodology of estimation (see above part 3.4.2) can be accurately used. The dependence of the gas velocity to the mass transfer (B=0.7) is slightly higher than the literature data. Richardson et al. [START_REF] Richardson | Properties of ceramic foam catalyst supports : mass and heat transfer[END_REF] found an exponent of 0.565 to describe the dependence of the external mass transfer with the superficial velocity and Incera-Garrido et al. [START_REF] Garrido | Mass transfer and pressure drop in ceramic foams: A description for different pore sizes and porosities[END_REF] an average value of 0.47 for ceramic foams with porosities ranging from 75% to 85%. Nevertheless the comparison of the data has to be considered carefully because the gas velocities are very different between this study (around 0.01 m.s -1 ) and the literature cited (around 1 m.s -1 ).

There was also a quite good agreement between the model and the experiments for acetaldehyde, especially at temperatures of 125°C and 150°C (less than 15% of average error for most of the experiments, Supplementary Material S3). The fitted parameters for acetaldehyde were: A Acetaldehyde = 15 m 1.2 .mol -0.4 .s -1 ; E a,Acetaldehyde = 25 kJ. mol -1 and m=0.6, and the mass transfer parameters A and B were the same as for ethanol.

In order to improve the accuracy of the model, other types of equations based on a Langmuir-Hinshelwood mechanisms and taking into account the adsorption of the VOCs on the catalyst surface could be used. [START_REF] Kamal | Catalytic oxidation of volatile organic compounds (VOCs) -A review[END_REF][START_REF] Rodriguez | Mass transfer limitations in a monolithic reactor for the catalytic oxidation of ethanol[END_REF][START_REF] Hu | Novel mechanistic view of catalytic ozonation of gaseous toluene by dual-site kinetic modelling[END_REF][START_REF] Biard | Photocatalytic Degradation of Two Volatile Fatty Acids in an Annular Plug-Flow Reactor; Kinetic Modeling and Contribution of Mass Transfer Rate[END_REF][START_REF] Rodriguez | VOCs abatement in adiabatic monolithic reactors: Heat effects, transport limitations and design considerations[END_REF] In any case, the model developed here can be used to predict the abatement of ethanol (into acetaldehyde and CO2) with this catalytic glass foam in the range of operating conditions tested.

Predictive simulations

The model presented above was finally used to size an efficient catalytic reactor to get complete abatement of ethanol and full mineralization (no more acetaldehyde by-product)

with an inlet concentration of 140 ppmv (0.23 g.m -3 ).

A temperature of 150°C was first used and the superficial gas velocity was 0.010 m.s -1 . In these conditions, a reactor of 30 cm length allowed to completely remove ethanol until full mineralization (Figure 35-a). The ethanol concentration decreased fast and was null near the middle of the reactor. At the same time, acetaldehyde concentration increased up to 0.11 g.m -3 and slowly decreased until the outlet of the process where it was fully oxidized into CO2. At 100°C (Figure 35-b), a similar behavior was simulated but it needed a reactor of 75 cm length to get the same results as at 150°C. These results highlight that a compromise needs to be found between performances, energy consumption and compactness of the reactor. The rates of oxidation obviously increase with the temperature and are more than 10 times higher at 150°C than at 100°C (for ethanol: 1.9 × 10 -4 mol.m -3 .s -1 at 100°C and 6.4 × 10 -3 the one for ethanol meaning that acetaldehyde removal was the limiting step, highlighting the difficulty to fully remove acetaldehyde. To improve its removal, higher temperature (200°C for instance) could be applied in the second half of the reactor.

CONCLUSION

A heterogeneous catalyst composed of a glass foam support doped with ruthenium nanoparticles was synthesized, characterized (porosity, mean pore diameter and pressure drops) and applied for the first time to remove VOCs from air through a thermocatalytic oxidation process. This nanocomposite material presents many advantages: (i) it offers a reduced environmental footprint, being synthesized from recycled glass and easily doped with catalytic species by a mild wet impregnation method in neat water, without washcoating, (ii) relevant process performances are reached, whatsoever in terms of pressure drops, mass transfer efficiency due to its high tortuosity, and for the removal of various VOCs that could be obtained even at very low ruthenium loading of 0.1 wt.%. Actually, abatements up to 100% were achieved for ethanol, acetone, toluene and heptane at 350°C in a residence time of 8.8 seconds. Even lower temperatures (around 250°C) can be used to fully eliminate ethanol and acetone, making this catalyst competitive compared to the available technologies.

Even if the catalyst lifetime still needs to be evaluated (around 40 hours of use here and no deactivation observed) and remains a decisive index for implementation, scale-up could be envisaged to prove the feasibility for industrial applications. To this aim, the behavior of ethanol was modelled considering mass transfer limitations, power law reaction kinetic and acetaldehyde as the only by-product. An accurate predictive model was fitted with an energy of activation of ethanol oxidation of 38 kJ.mol -1 , an apparent kinetic of 0.5 order and the influence of the gas velocity followed a 0.7 order power law. Predictive simulations were finally carried out and showed that full abatement with full mineralization of ethanol into CO2 can be achieved at low temperature (150°C) with a moderate reactor dimension (30 cm). A tradeoff might be found between performances, energy consumption (temperature and pumping) and compactness of the process (reactor length) with a cost analysis.

Figure 1 .

 1 Figure 1. Layout of the setup for thermocatalytic oxidation of VOCs with a catalytic glass

Figure 2 .

 2 Figure 2. Real photo (a), SEM picture (b) and TEM picture (c) of the catalytic glass foam

Figure 3 Figure 3 .

 33 Figure 3. DTA-TGA curves obtained for the catalytic glass foam under air

Figure 24 .

 24 Figure 24. Removal efficiency of VOCs versus temperature (v = 10 mm.s -1residence time = 8.8 s) -▲: ethanol (inlet concentration: 1.0 g.m -3 ) -×: acetone (inlet concentration: 2.0 g.m - 3 ) -: toluene (inlet concentration: 1.0 g.m -3 ) -: heptane (inlet concentration: 1.0 g.m -3 )

Figure 35 .

 35 Figure 35. Concentrations of ethanol (full line), acetaldehyde (dashed line) and CO2 (pointed line) along the reactor simulated for v=0.010 m.s -1 and ethanol inlet concentration of 140 ppmv (0.23 g.m -3 )a) T=150°Cb) T=100°C

Table 1 . Inlet concentration of the VOCs and programming of the GC for analysis

 1

	VOC	Molecular	Inlet	concentration	GC analysis
		weight (g.mol -1 )	(g.m -3 / ppmv)	Oven temperature	Retention time
					(°C)	(min)
	Ethanol	46	0.2 -1.0 g.m -3 / 106 -	28	3.6
			532 ppmv
	Acetone 58	2.0 g.m -3 / 843 ppmv	28	4.2
	Toluene 92	1.0 g/m -3 / 266 ppmv	80	6.3
	Heptane 100	1.0 g.m -3 / 245 ppmv	80	4.1

Table 2

 2

compares the results for the removal of VOCs by thermocatalytic oxidation obtained with the catalytic glass foam and with other heterogeneous catalysts. The results are compared in terms of TOF (equation (

Table 2 . TOF values for oxidation of VOCs and comparison with literature data

 2

	VOC	Type of catalyst	Temperature (°C) TOF (h -1 )	Reference
	Ethanol	Glass foam impregnated with	200	4.9	This study
	Acetone	0.1 wt% Ru(0) NPs	250	6.9
	Toluene		300	3.6
	Heptane		350	2.3
	Toluene	Pt impregnated on aluminium	210	6.4	24
		foam
	Toluene	Pt zeolite coated cordierite	230	53.4
		foam
	Ethanol	Manganese oxide	200	4.3	29
	Heptane		450	4.3
	Acetone	Cobalt oxide	190	0.2	30
	Toluene		230	0.2
	Ethanol	CuO-CeO2	220	0.2	31
	Toluene		260	0.1
	Toluene	Au impregnated on different	264 ->400	56.1
		supports

Table 3 . Performances of the glass foam impregnated with ruthenium nanoparticles for the removal of ethanol -influence of the temperature, inlet concentration and superficial gas velocity

 3

	T	[EtOH]inlet	v (m.s -1 )	τ (s)	Eff (%) r (g.m -3 .s -1 ) TOF	[Acetaldehyde]outlet	Mineralization
	(°C)	(g.m -3 )					(h -1 )	(g.m -3 )	(%)
	100	1.0	0.010	8.8	22	0.026	1.1	0.11	7
	100	1.0	0.016	5.5	19	0.037	1.6	0.04	15
	100	1.0	0.023	3.7	17	0.049	2.1	0.03	15
	100	1.0	0.032	2.7	18	0.070	3.0	0.02	16
	100	0.2	0.010	8.8	38	0.009	0.4	0.06	8
	100	0.5	0.010	8.8	29	0.015	0.7	0.09	10
	100	0.8	0.010	8.8	22	0.020	0.9	0.09	11
	100	0.2	0.032	2.7	27	0.018	0.9	0.02	15
	125	1.0	0.010	8.8	39	0.042	1.8	0.30	10
	125	1.0	0.016	5.5	26	0.046	2.0	0.17	8
	125	1.0	0.023	3.7	24	0.061	2.6	0.08	16
	125	1.0	0.032	2.7	24	0.083	3.6	0.07	17
	125	0.2	0.010	8.8	74	0.017	0.7	0.12	10
	125	0.5	0.010	8.8	57	0.031	1.3	0.21	11
	125	0.8	0.010	8.8	42	0.034	1.5	0.24	8
	150	1.0	0.010	8.8	62	0.077	3.3	0.50	14
	150	1.0	0.016	5.5	45	0.083	3.5	0.38	6
	150	1.0	0.023	3.7	45	0.134	5.7	0.37	10
	150	1.0	0.032	2.7	38	0.157	6.7	0.29	11
	150	0.2	0.010	8.8	93	0.023	1.0	0.17	12
	150	0.5	0.010	8.8	85	0.052	2.2	0.37	14
	150	0.8	0.010	8.8	74	0.072	3.1	0.47	17
	150	0.2	0.032	2.7	73	0.051	2.2	0.10	16

.s -1 at 150°C). Whatsoever the temperature, the rate of acetaldehyde oxidation was lower than

ACKNOWLEDGMENTS

The authors thank the SATT Ouest Valorisation for financial support.

SUPPLEMENTARY MATERIALS

Supplementary material S1: Detailed synthesis and characterization of the catalytic glass foam Supplementary material S2: Estimated energy of activation of ethanol oxidation Supplementary material S3: Comparison between the model and the experimental data