Violette Mulot
email: violette.mulot@irstea.fr

Hayat Benkhelifa

Didier PATHIER (c Fatou-Toutie Ndoye

Measurement of food dehydration during freezing in mechanical and cryogenic freezing conditions

Keywords: Food dehydration, Weight loss, Freezing cabinet, Freezing, Cryogenic

The freezing of unpackaged foods induces water loss due to interactions with the surrounding medium. The weight loss resulting from this dehydration is up to 6 % according to the product and the freezing process. Food dehydration was studied for various operating conditions from mechanical to cryogenic ones with the same freezing device using Tylose as a food model material. The dehydration was studied for several surface states (smooth or streaked surface) and product porosities (full or perforated plates). It was found that weight loss is estimated with a good reproducibility in the developed freezer. The influence of freezing operating conditions and product characteristics on weight loss were clearly pointed out. From these results, weight loss could be related to the surface temperature evolution. In any case, these results confirm that to limit the weight loss, it is essential to decrease as quickly as possible the surface temperature of the product.

INTRODUCTION

Freezing is widely used for preservation in the food industry because it guarantees long preservation with relatively low impact on product quality. Two types of transfers occur during the freezing of unwrapped products:

• Heat transfer: the product in contact with cold air releases energy to the surrounding environment. This leads to a temperature gradient in the product inducing a heat transfer from its core to its surface and phase change (water crystallization) until reaching thermal equilibrium.

• Water transfer: the water vapor concentration in the surrounding air is lower than the water vapor concentration in the air in equilibrium with the product surface. Thus, a water transfer occurs between the product and its surroundings. As for heat transfer, a water concentration gradient appears in the product inducing a water transfer from its core to its surface and then to its surroundings. During the pre-cooling stage, water evaporates from the surface. When ice is formed, it sublimates from the surface causing the emergence of a dehydrated layer.

Dehydration during freezing implies a loss of quality especially within the dehydrated layer but also weight loss which means financial losses for industrials. Dehydration is strongly influenced by the product type, its initial temperature and the freezing process.

To predict weight loss in food during freezing, numerical solving of heat and mass transfer equations led to several models [START_REF] Andreasen | Modelling of Heat and Mass Transfer in Food Products[END_REF][START_REF] Campanone | Food freezing with simultaneous surface dehydration: approximate prediction of weight loss during freezing and storage[END_REF][START_REF] Campañone | Finite-difference method to solve coupled heat and mass balances with simultaneous surface dehydration during freezing[END_REF][START_REF] Pham | Modelling heat and mass transfer in frozen foods: a review[END_REF][START_REF] Pham | Model for food desiccation in frozen storage[END_REF][START_REF] Rouaud | Heat and Mass Transfer Modelling During Freezing of Foodstuffs Comsol Conference[END_REF][START_REF] Tocci | Numerical-models for the simulation of the simultaneous heat and mass[END_REF]. From these numerical models, simplified ones were also proposed [START_REF] Campañone | Weight loss during freezing and storage of unpackaged foods[END_REF]. All these models are valuable decision tools for selecting one technology (characterized by its range of temperature and air velocity) relatively to another in order to freeze a given product and limit its weight loss.

Models were validated and enriched with experimental data of freezing time and weight loss during freezing which help better understand transfer phenomena. Meat and fish products were widely studied [START_REF] Boonsumrej | Effects of freezing and thawing on the quality changes of tiger shrimp (Penaeus monodon) frozen by air-blast and cryogenic freezing[END_REF][START_REF] Bustabad | Weight loss during freezing and the storage of frozen meat[END_REF][START_REF] Campanone | Monitoring of weight losses in meat products during freezing and frozen storage[END_REF][START_REF] Espinoza Rodezno | Cryogenic and air blast freezing techniques and their effect on the quality of catfish fillets[END_REF][START_REF] Lambrinos | The weight loss of frozen meat. Experimentation and prediction by using tylose[END_REF][START_REF] Pham | Model for food desiccation in frozen storage[END_REF]. Few studies focus on highly porous products like pre-baked bread (Hamdami et al., 2004a(Hamdami et al., , 2004b)).

For these experimental studies, usually, a given product was placed in a freezer where the temperature and air velocity were controlled and measured. Air relative humidity was sometimes also measured but not controlled.

Temperature in the product was measured during freezing and the product was weighed before and after freezing or sometimes during freezing [START_REF] Campanone | Monitoring of weight losses in meat products during freezing and frozen storage[END_REF]. Most of the time, studies also took into account weight loss during the storage of the frozen products.

These studies highlight the fact that the product weight loss is closely linked to the freezing rate. Most of them compare freezing rates in the mechanical freezing field: air temperature between -15°C and -50°C and air velocity between 0 and 5 m s -1 . The air temperature has a high impact on weight loss whereas air velocity does not greatly influence it. A lower air temperature decreases the weight loss.

Few studies differentiate the two main categories of freezing processes: mechanical freezing and cryogenic freezing [START_REF] Boonsumrej | Effects of freezing and thawing on the quality changes of tiger shrimp (Penaeus monodon) frozen by air-blast and cryogenic freezing[END_REF][START_REF] Espinoza Rodezno | Cryogenic and air blast freezing techniques and their effect on the quality of catfish fillets[END_REF][START_REF] Rouaud | Heat and Mass Transfer Modelling During Freezing of Foodstuffs Comsol Conference[END_REF]. Mechanical freezing relates to slower freezing rates than cryogenic one. Indeed, cryogenic freezing allows reaching very low temperature (-78.5°C with CO 2 and -195.8°C with nitrogen) and fast freezing rates. [START_REF] Boonsumrej | Effects of freezing and thawing on the quality changes of tiger shrimp (Penaeus monodon) frozen by air-blast and cryogenic freezing[END_REF] used CO 2 cryogenic freezing with a cabinet temperature of -59°C. Only Espinoza [START_REF] Espinoza Rodezno | Cryogenic and air blast freezing techniques and their effect on the quality of catfish fillets[END_REF] used nitrogen injection that allowed reaching cryogenic temperatures from -70°C to -100°C. Nevertheless, both studies used two different types of technologies to study respectively mechanical and cryogenic freezing.

Moreover, the sample was taken out of the freezer to perform the weighing at the end of freezing, thus causing high mass variation.

The aim of the present work is to study the food dehydration during freezing in mechanical and cryogenic freezing conditions. For this, a reliable laboratory scale freezing cabinet was developed to study the total weight loss but also the variation of weight loss with time during the freezing process. It is able to simulate both mechanical and cryogenic freezing conditions in terms of temperature (using liquid nitrogen) and flow velocity.

The product is weighed directly in the cold medium during freezing without taking it out of the freezing cabinet.

This study presents experiments with Tylose (constant formula of water and methylcellulose) and the dehydration is studied for several food characteristics: the effect of the surface state by using smooth or streaked surface, the effect of the product porosity by using full plates or perforated plates and the effect of the initial temperature. Core temperature, surface temperature and total weight loss results are presented for different freezing conditions in mechanical and cryogenic freezing fields.

MATERIALS AND METHODS

Freezing equipment

A freezing cabinet was developed to recreate both mechanical and cryogenic freezing conditions in terms of temperature and gas flow velocity. Figure 1 presents the operating diagram of this designed freezer. Temperature is adjustable from room temperature to -100°C using a nitrogen injection coupled with a temperature measurement with a Pt100. The gas flow velocity is adjustable from 0 to 9 m s -1 thanks to a variable frequency fan connected to a differential pressure measurement with a Pitot tube.

A cold gas flow over a length of 2.8 m is obtained with the designed freezing cabinet. Samples are located in the measuring zone (Figure 1) during experiments. This zone is as far as possible over the gas flow length to get a well-established and uniform flow (temperatures and velocities). Some meshes were added before and after the measuring zone to homogenize this flow.

As liquid nitrogen is injected for the temperature control, there is no humidity in the freezing cabinet and relative humidity is close to 0.

Freezing cabinet characterization

Gas flow velocity, temperature, and heat transfer coefficient were measured in the measuring zone of the freezing cabinet in order to check their uniformity near sample locations. For these measurements, no samples were placed in the measuring zone.

Gas flow velocity

First, gas flow velocity was measured in the median plane of the measuring zone (Figure 1). A mapping was made to cover the entire width and height of this flow section with 30 measuring points, this mapping is presented on Figure 2.

Flow velocity measurements were carried out at 20°C with a hot-wire anemometer (0-50 m s -1 , Velocicalc ® , 9565). For each measuring point, 3 velocity readings were made. The fan motor was adjusted at its maximum rotational speed during all these measurements in order to verify the velocity uniformity and stability over time in the worst case.

Temperature

Then, temperature measurements were made in the median plane of the measuring zone at mid-height position, 3 equidistant calibrated type-T thermocouples (precision 0.1°C) were placed across the width of the flow section, on the left, on the middle and on the right position. For these measurements, flow velocity was fixed at 3.5 m s -1 and four temperatures were checked: 0°C, -30°C, -50°C and -100°C (whole temperature range of the freezing cabinet). Temperature was recorded for 360 s after stabilization of the freezing cabinet.

Heat transfer coefficient

Finally, convective heat transfer coefficients (HTC) were measured at mid-height position in the median plane of the measuring zone. For these measurements, three equidistant devices were placed along the width of the flow section (left, middle and right position). The devices are composed of a copper plate (50×50 mm) which is heated by an electrical resistance and insulated underneath. For each one, two type-T thermocouples measure the temperature of the copper surface and the gas temperature above it. A programmable controller performs temperature recording and flux calculation [START_REF] Eckert | Measurements in heat transfer[END_REF].

Three flow velocities were studied: 4.2, 6.6 and 8.4 m s -1 , temperature was set at 15°C. Heat transfer coefficients were recorded for 120 s once the freezing cabinet was stabilized.

Samples, sample temperature and sample weight

Sample preparation

To study food dehydration during freezing, Tylose plates (23 % methylcellulose, 76.4 % water and 0.5 % sodium chloride) were used as a model material (length=80 mm, width=45 mm, thickness=18 mm, mass=70.7-73.8 g). Their lateral faces were insulated with 1-cm-thickness (e) expanded polystyrene (λ p =0.033 W m -1 K -1 ) in order to consider quite only 1D heat and mass transfers. The lateral conductance, can be estimated from the lateral area of the product (S lateral ), the convective heat transfer coefficient (HTC) and the insulation thermal resistance:

. The conductance through the upper and lower surface (S upper/lower ) is: S upper/lower HTC.

Since for the measured HTC values, the lateral conductance is less than 4 % of the upper/lower conductance, the lateral heat flux should be very low compared to the upper/lower ones. Using the chart proposed by [START_REF] Cleland | Collection of accurate experimental data for testing the performance of simple methods for food freezing time prediction[END_REF], it was also found that the difference of freezing time with the ideal 1D case should be less than 4 %.

Three types of Tylose plate and surface state were studied (Figure 3): full plates with smooth surfaces (Figure 3a, initial temperature T i =20°C and T i =5°C), full plates with streaked surfaces (Figure 3b, initial temperature

T i =20°C
) and perforated plates with smooth surfaces (Figure 3c, initial temperature T i =20°C). To obtain streaked surfaces, the upper and lower surfaces of the Tylose block were scrapped with a saw blade. This type of surface aims to simulate products with rough surfaces, for example frozen patties. Perforated plates were made doing a regular perforation using a punch. This type of macro-porosity is found in product whose permeability is preferentially oriented in one direction (vertical) like blinis. It does not model micro-porous food as sponge cakes. The air/product interface area is increased by about 16 % for the streaked surface and about 41 % for the perforated plate . This different Tylose plates can be used as food model materials, with different surface states and different porosities.

In the freezing cabinet, samples were located in the median plane of the measuring zone (Figure 1) at mid-height position (Figure 4). Three samples were placed per run in the freezing cabinet on the left, on the middle and on the right position, they were separated equidistantly across the width of the measuring zone.

Sample temperature and sample weight

For temperature recording in the sample, two calibrated type-T thermocouples (precision 0.1°C) were used per sample, one dedicated for the upper surface temperature recording (1 mm under the upper surface) and the other for the core temperature recording. They were equipped with a needle so that they could be accurately positioned and inserted from the sample lateral side along likely isotherms, so that conduction along the thermocouples is minimized.

For weighing, two scales were used: Mettler Toledo ® PG1003S and Sartorius ® QUINTIX3102-1S. The weighing precision is 0.01 g. Scales were fitted with hangers for below-the-balance weighing. Thus, scales are kept outside the freezing cabinet while samples are in the cold zone.

Weight loss and water vaporization during food freezing

Weight loss is due to water vaporization from the product surface to the surroundings. The weight loss variation with time during freezing can be determined from the integral of the water vapor flux from the product surface over time [START_REF] Phimolsiripol | Verification of a simple product weight loss model for refrigerated storage of foods[END_REF]. The water vaporization flux (evaporation or sublimation) at the product surface is expressed with Equation (1).

φ = h S C -C !"# (1)
where hm is the external mass transfer coefficient and S the exchange area. Cvap-eq is the water vapor concentration in equilibrium with the product surface. C vap-sur is the water vapor concentration in the surrounding gas.

C vap-eq is estimated from the water activity at the product surface (a ws ) and the saturation water vapor concentration C vsat at the product surface temperature T s thanks to Equation ( 2).

C = a %! C ! '() * ) (2)
C vap-sur is estimated from the relative humidity (RH) in the cold environment and the saturation water vapor concentration at the gas temperature T g thanks to Equation (3).

C !"# = RH C ! '() . ) (3)
2.5.

.Experimental procedure First of all, experiments were made to measure the time required for thermal center of Tylose full plates with smooth surfaces (T i =20°C) to reach -18°C. This step was necessary to ensure that the left, middle and right samples were submitted to the same freezing conditions. Three replicates were made for the seven operating conditions. For a freezing run, when gas set point temperature and gas flow velocity were stable in the freezing cabinet, three samples, fitted with type-T thermocouples at core, were introduced in the freezing cabinet. Core temperatures of the three samples were recorded until they reached -18°C.

Secondly, Tylose plate dehydration due to freezing process was studied by measuring the total weight loss for the four types of plates. For a freezing run, two samples were dedicated to the weight recording (left and right samples) whereas the third one (middle sample) was used for core and upper surface temperature recording.

When operating conditions reached the stationary regime, process ventilation and nitrogen injection were switched off and samples were introduced in the freezing cabinet (Figure 4). The initial masses of samples suspended inside the cabinet were measured (M 0suspended ). Then, process ventilation and nitrogen injection were switched on. The freezing time is the time for the thermal center of the middle sample to reach -18°C. At the end of freezing, the freezing cabinet was switched off and the final masses of samples suspended inside the freezing cabinet were measured (Mfsuspended). The total relative weight loss (WL in %) was calculated using Equation (4).

WL = 100 M 4!"! 56 6 -M 7!"! 56 6 M 4)89:! (4) M 0Tylose is initial Tylose sample mass before freezing.

For full plates with smooth surfaces and an initial temperature of 20°C, seven freezing operating conditions (3 replicates, 6 weight loss measurements) were studied, three temperatures: -30°C, -50°C and -100°C and three gas flow velocities: 3 m s -1 , 3.9 m s -1 and 7.7 m s -1 . For full plates with smooth surfaces and Ti=5°C, full plates with streaked surfaces (T i =20°C) and perforated plates with smooth surfaces (T i =20°C), two extreme freezing operating conditions (1 replicate, 2 weight loss measurements) were studied: -30°C, 3.9 m s -1 and -100°C, 3.9 m s -1 (Table 1).

Finally, the weight loss variation during the freezing of full plates with smooth surfaces (T i= 20°c) was studied by measuring weight loss at regular time steps for the freezing operating condition -30°C, 3.9 m s -1 (3 replicates).

The protocol is the same as for the measurement of the total weight loss, but two intermediate weighing were performed: after 15 minutes and 30 minutes of freezing. The relative weight loss at each time step was still calculated using Equation ( 4). An additional experiment was done with 4 intermediate weighing (after 5, 10, 15 and 30 minutes) to validate the weight loss variation trend over time. Nevertheless, too many ventilation and nitrogen injection stops during weighing may disturb the freezing process.

RESULTS AND DISCUSSION

Freezing cabinet characterization

Gas flow velocity

The gas flow velocity results are summarized in Table 2. They show a very good repeatability between the three measurements of each measuring points (standard deviation<0.1) which means a good stability of the velocity for a same position over replicates and over time. Besides, for the upper and bottom wall, horizontal profiles show slightly lower velocities with higher variations (shaded part of Table 2). However, uniform horizontal and vertical profiles are noticeable at mid-height positions (unshaded part of Table 2) where samples are located during freezing which means that the three samples placed at three different horizontal positions are frozen with the same gas flow velocity.

Temperature

The temperature uniformity and stability over time at mid-height position in the measuring zone are summarized in Table 3. The standard deviation of each temperature recording is very low which indicates a good stability and a good temperature regulation system with measured temperatures close to set points. Moreover, results show temperature uniformity between the three positions (left, middle and right position) for a same temperature set point.

Heat transfer coefficient

Measurements with fluxmeters permit characterizing the stability over time and the uniformity of the convective heat transfer coefficient (HTC) between the three sample locations. Results are presented in Table 4. For each velocity set point, the standard deviation of each HTC recording is low relative to the average value which indicates a good stability over time. Moreover, HTC variations are not significant between the three positions.

These results validates the HTC uniformity and stability at a selected velocity set point where samples are located in the freezing cabinet.

Core temperature -Freezing time

The time required for the thermal center to reach -18°C in the case of full plates with smooth surfaces (T i =20°C)

was measured for seven operating conditions (3 replicates) and is defined as the freezing time. Table 5 presents, for each operating condition, the average freezing time with the standard deviation between the three replicates of each position and the average freezing time with the standard deviation between the three positions (9 replicates).

Whatever the operating conditions, the standard deviation between the three replicates of a same position is low relative to the total freezing time meaning a good repeatability between the three replicates. These results validate the fact that the designed freezing cabinet can be reliably used to repeat freezing tests under same operating conditions. Moreover, for same operating conditions, standard deviation is also low relative to the average freezing time between the three positions. This means that the three samples placed per freezing run are frozen in the same way.

These results coupled with those of the operating conditions uniformity and stability (gas flow velocity, temperature and heat transfer coefficient, Table 2, Table 3 andTable 4) validate identical and stable freezing conditions with a similar thermal treatment whatever the sample lateral position at mid-height of the measuring zone.

Total weight loss

Once the freezing equipment was validated, experiments were done with four types of Tylose plate to study total weight loss due to freezing process. Table 6 presents, for each operating condition the total relative weight loss (WL) when core temperature reaches -18°C.

Whatever the type of Tylose plate and operating conditions, results show a good repeatability between replicates with low standard deviations.

Figure 5a presents results of total relative weight loss for Tylose full plates with smooth surfaces (Ti=20°c) as a function of the gas temperature and the gas flow velocity. Figure 5b presents the total relative weight loss for the four types of plate as a function of the gas temperature (gas flow velocity=3.9 m s -1 ).

Influence of the freezing operating conditions

On both graphs of Figure 5, whatever the gas flow velocity and the type of plate, a large influence of the gas temperature on the weight loss is noticeable, the lower the gas temperature, the lower the weight loss.

Decreasing the gas temperature from -30°C to -100°C divides the total relative weight loss by 1.9 to 3.4 as a function of the type of plate.

Nevertheless, the influence of the gas flow velocity is less pronounced. Actually, increasing the flow velocity has opposite effects which compensate each other. On the one hand, increasing the flow velocity leads to shorter freezing time with a larger HTC; on the other hand, the mass transfer coefficient is also larger which leads to faster water loss rates. The influence of the gas flow velocity seems to be more significant at lower gas temperature. For high freezing temperatures, the gas flow velocity has no influence on the weight loss, whereas, for lower freezing temperatures, a higher flow velocity reduces the total relative weight loss (Figure 5a).

Influence of the initial temperature

The initial temperature of the product has a great influence on weight loss. For full plates with smooth surfaces, decreasing the initial temperature from 20°C to 5°C allows decreasing the total weight loss of 22 % for the operating conditions -30°C, 3.9 m s -1 and 46 % for the freezing condition -100°C, 3.9 m s -1 . Indeed, with a lower initial temperature, the total freezing time is shorter which decreases the total relative weight loss. The water evaporation kinetics at the product surface during the pre-cooling stage can mainly explain the weight loss reduction. This stage is shorter for Ti=5°C than for Ti=20°C because the initial temperature is closer to the initial freezing temperature (around -1.5°C) for Tylose as shown on Figure 6.

Influence of the type of Tylose plate

The freezing of full plates with streaked surfaces and perforated plates with smooth surfaces were studied.

Perforated plates aim to simulate a porous matrix. Both types of plate have larger exchange surfaces with the surrounding media than the full plate with smooth surfaces: +16 % for the streaked surface and +41 % for the perforated plate. On the one hand, heat transfer is facilitated so that the freezing time decreases, but, on the other hand, a larger surface leads to more water vaporization. Streaking the surface leads to a relative weight loss 1.1 times higher at -30°C and 1.3 times higher at -100°C for a respective freezing time 1.3 times lower and 1.2 times lower. Perforating the plate leads to a relative weight loss 1.1 times higher at -30°C and 1.2 times higher at -100°C for a freezing time 1.4 times lower for both cases. As the freezing time is enough reduced streaking the surface or perforating the plate, the weight loss does not significantly increase.

Variation of weight loss with time

The variation of weight loss with time was studied for full plates with smooth surfaces and for the freezing condition -30°C, 3.9 m s -1 (3 replicates). Two intermediate weighing were done at 15 minutes and at 30 minutes whereas the total freezing time is 45 min. An additional experiment with four intermediate weighing (after 5, 10, 15 and 30 minutes) was also carried out. Figure 7 shows the results of variation of weight loss during freezing for the two samples dedicated to the weight recording (left and right). The evolution of the surface temperature with time is represented on each graph. Results show repeatable experiments between replicates and between the two samples of a same run. For the experiment with four intermediate measurements, the values at 15, 30 and 45 minutes are slightly lower than for the experiments with only 2 intermediate measurements. Indeed, the two additional operating stops at the beginning of the freezing process slow down the weight loss kinetics but this experiment validates the nonlinear trend of the variation of weight loss with time during the freezing process.

On each graph, trends of weight loss variation with time are similar: the weight loss rate is high at the beginning of freezing and gradually slows down until the end of the freezing process. Based on the three experiments with the two intermediate weighing, during the first 15 minutes of freezing, 61 % of the global freezing weight loss is reached, then, 27 % from 15 minutes to 30 minutes and 12 % from 30 minutes to the end of the freezing process.

This trend is closely related to the surface temperature variation as it is shown in section 3.4.

Relation between weight loss and surface temperature

Variation of weight loss with time and surface temperature

In this part, measured weight loss variation with time and total weight loss are linked to the surface temperature variation as a function of the freezing time thanks to the theory presented in Section 2.4.

Considering Equation ( 1), C vap-sur and C vap-eq must be determined. In our case, the water vapor concentration in the cold environment, Cvap-sur, Equation (3), is constant and close to 0 during the freezing process since nitrogen is continuously injected in the freezing cabinet (RH=0). Considering C vap-eq , Tylose (like the majority of food) is mainly composed of water, so, the water activity at the product surface (a ws ) is initially close to one. Thus, based on Equation ( 2), C vap-eq is equal to C vsat(Ts) that is calculated with Clausius-Clapeyron [START_REF] Corriou | Thermodynamique chimique Diagrammes thermodynamiques[END_REF] and ideal gas equations considering the surface temperature variation during freezing. Figure 8a presents the variations of surface temperature Ts and calculated Cvsat(Ts) versus freezing time for a full plate with smooth surfaces (-30°C, 3.9 m s -1 ). C vsat decreases in the same way as the surface temperature.

From the simplification of Equation ( 1), the integral of the vaporization flux which is equal to the weight loss at time t can be calculated with Equation (5).

WL (') = h S ; C ! '() * ) dt ' 4 (5)
Thus, weight loss should be proportional to the integral of Cvsat(Ts) over time. The integral curve of Cvsat(Ts) has a trend comparable to the curve of weight loss variation with time (Figure 8b). Figure 8c shows the linear relation between the relative weight loss and the integral of C vsat(Ts) which is related to the surface temperature (R²=0.995).

In conclusion, the variation of the relative weight loss during freezing is strongly linked to the variation of the product surface temperature and contains 3 steps during the freezing process. At the very beginning of the freezing process, the relative weight loss quickly increases because C vsat(Ts) is high. During the pre-cooling stage, the weight loss rate decreases like C vsat(Ts) (slope of Figure 8b is decreasing between 0 and 6 min). Then, the surface temperature is almost constant during water crystallization as the evaporative flux. Finally, the surface temperature gradually continues decreasing during the sub-cooling stage slower and slower when it approaches the surroundings temperature. During this third stage, the weight loss rate decreases again.

Total weight loss and surface temperature

Figure 9 presents, for different operating conditions, the total weight loss (kg) (when core temperature reaches -18°C) versus the integral of C vsat(Ts) over the total freezing time.

It can be observed, as expected from Equation ( 5), that the total weight loss is proportional to the integral of C vsat(Ts) over the total freezing time, quite independently of the surrounding temperature and the initial product temperature. The proportionality coefficient (h m S) is the slope of the curve. This is why, when the product surface is increased, the slope of the curve increases. It could be also expected that increasing velocity would increase the slope because the mass transfer coefficient h m should be higher but it is seen that the influence of velocity is not very noticeable as already highlighted in Section 3.2. This could be due to surface dehydration at higher gas velocity that lowers the water activity.

In any case, these results confirm that to limit the weight loss, it is essential to decrease as quickly as possible the surface temperature of the product. Furthermore, knowing the experimental surface temperature variation over freezing time, it is possible to obtain an estimation of weight loss.

CONCLUSIONS

In this paper, it was shown that the designed freezing cabinet allows getting uniform and stable operating conditions, in terms of temperature, gas flow velocity and HTC.

Various operating conditions were selected to cover the range of mechanical and cryogenic freezing from -30°C, 3.9 m s -1 to -100°C, 7.7 m s -1 for the study of weight loss of various types of plate. Results show a good repeatability in weight loss measurements between replicates of a same operating condition and between the two sample positions. It was found that the gas temperature has a great influence weight loss: lowering the temperature decreases weight loss. The gas flow velocity has not a large effect on weight loss at -30°C, but the effect is significant at -50°C and at -100 °C: the weight loss decreases when the flow velocity rises.

The effect of the initial product temperature was also studied: decreasing the initial temperature from 20°C to 5°C allows decreasing the total weight loss by reducing the total freezing time and particularly the pre-cooling stage.

The effect of the product surface state and porosity were studied by considering different exchange surfaces. On the one hand, a larger surface in the case of streaked surfaces and perforated plate leads to more water vaporization but, on the other hand, it also leads to a higher heat transfer and a shorter freezing time. Finally, streaking the surface and perforating the plate do not significantly increase the weight loss.

To finish, the developed freezing cabinet allowed following the variation of weight loss with time for the operating condition -30°C, 3.9 m s -1 doing intermediate weighing during freezing. Results coupled with surface temperature reveal a consistent and specific trend. The vaporization rate as the product surface temperature first decreases, during the pre-cooling stage, then, remains almost constant during crystallization and decreases again during the sub-cooling stage.

These data for several food product characteristics and for cryogenic and mechanical freezing conditions will be especially useful to validate numerical models for weight loss prediction during freezing of food considering a water content in the cooling air close to 0. The hygrometry control for mechanical freezing could be an

T i =20°C T i =5°C T i =20°C T i =20°C
Tylose plate (45×80 mm)

Expanded polystyrene Ø=5mm

18 mm 1.9 mm 3.2 mm 1.9 mm

Figure 1 :2Figure 1 :Figure

 11 Figure 1: Operating diagram of the freezing cabinet-Top view ................................................................................. 2 Figure 2: Mapping of the median plane of the measuring zone for flow velocity measurements ................................ 2 Figure 3: Tylose plates insulated with 1 cm thickness expanded polystyrene............................................................. 2 Figure 4: Experimental procedure to introduce samples in the freezing cabinet and measure weight loss during freezing ............................................................................................................................................................. 2 Figure 5: Average total relative weight loss according to gas temperature ................................................................. 2 Figure 6: Core and surface temperature kinetics during freezing of full Tylose plate with smooth surfaces and an initial temperature of 20°C or 5°C (operating conditions -30°C, 3.9 m s -1 ) .......................................................... 2 Figure 7: Relative weight loss variation with time and upper surface temperature recording for the freezing operating condition -30°C, 3.9 m s -1 .................................................................................................................................. 2 Figure 8: Variation of Tylose surface temperature, calculated saturation water vapor concentration and weight loss during freezing (-30°C, 3.9 m s -1 ) ....................................................................................................................... 2 Figure 9: Total weight loss as a function of the integral of the saturated vapor concentration C vsat at the product surface over the total freezing time .................................................................................................................... 2

Figure 4 :

 4 Figure 4: Experimental procedure to introduce samples in the freezing cabinet and measure weight loss during freezing (a) Opening of the freezing cabinet at stationary regime, ventilation and nitrogen injection are switched off. (b) Introduction of samples inside the freezing cabinet. (c)Initial weighing of suspended samples. Then, ventilation and nitrogen injection are switched on.

Figure 5 :Figure 6 :

 56 Figure 5: Average total relative weight loss according to gas temperature (a) Tylose full plate with smooth surfaces (T i =20°C) according to gas flow velocity (b) Average total relative weight loss according to the type of Tylose plate (gas flow velocity=3.9 m s -1 )

Figure 7 :Figure 8 :

 78 Figure 7: Relative weight loss variation with time and upper surface temperature recording for the freezing operating condition -30°C, 3.9 m s -1 (a), (b) and (c) Three replicates with two intermediate weighing (d) Experiment with four intermediate weighing

Table 1 :

 1 Freezing operating conditions ..................................................................................................................... 2 Table 2: Gas flow velocity (m s -1 ) uniformity and stability ....................................................................................... 3 Table 3: Temperature (°C) uniformity and stability .................................................................................................. 4 Table 4: Heat transfer coefficient (W m -² K -1 ) uniformity and stability ...................................................................... 5 Table 5: Results of average freezing time (s) required for the thermal center of Tylose full plate with smooth surfaces (T i =20°C) to reach -18°C ................................................................................................................................... 6 Table 6: Results of total relative weight loss according to the type of Tylose plate and freezing operating conditions (average value of replicates ± standard deviation) .............................................................................................. 7

Table 1 : Freezing operating conditions

 1 For each run, two weight loss measurements and one temperature measurement (surface and core) are carried out.

			Full plate with	Full plate with	Full plate with	Perforated plate
	Temperature set point (°C)	Velocity set point (m s -1 )	smooth surfaces T i =20°C	smooth surfaces T i =5°C	streaked surfaces T i =20°C	with smooth surfaces T i =20°C
		3	×3
	-30	3.9	×3	×1	×1	×1
		7.7	×3
	-50	3.9 7.7	×3 ×3
	-100	3.9 7.7	×3 ×3	×1	×1	×1

Table 4 : Heat transfer coefficient (W m -² K -1 ) uniformity and stability

 4

	Velocity set point (m s -1 )	Left position	Middle position	Right position	Average
	4.2	63 ± 2	59 ± 2	62 ± 2	61 ± 2
	6.6	92 ± 2	84 ± 2	90 ± 3	89 ± 4
	8.4	115 ± 3	101 ± 4	110 ± 4	108 ± 7

Table 6 : Results of total relative weight loss according to the type of Tylose plate and freezing operating conditions (average value of replicates ± standard deviation)

 6

	Temperature set point (°C)	Velocity set point (m s -1 )	Full plate with smooth surfaces T I =20°C	Full plate with smooth surfaces TI=5°C	Full plate with streaked surfaces TI=20°C	Perforated plate with smooth surfaces TI=20°C
		3	1.70 ± 0.04
	-30	3,9	1.61 ± 0,05	1.26 ± 0.06	1.76 ± 0.03	1.83 ± 0.02
		7,7	1.56 ± 0,07
		3.9	0.98 ± 0.11
	-50
		7.7	0.85 ± 0.15
		3,9	0.71 ± 0,10	0.68 ± 0.01	0.89 ± 0.09	0.87 ± 0.02
	-100
		7,7	0.46 ± 0,03

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the financial support granted by the CIFRE department (Conventions Industrielles de Formation par la Recherche) from the French ANRT (Association Nationale Recherche et Technologie).

improvement of the experimental freezing cabinet as in these conditions, water vapor content in the cooling air is not null, leading to lower weight losses.

NOMENCLATURE a ws

Water activity C vap-eq Water vapor concentration in equilibrium with the product surface (kg m-3) Freezing operating conditions -30°C, 3.9 m s -1 -30°C, 7.7 m s -1 -50°C, 3.9 m s -1 -50°C, 7.7 m s -1 -100°C, 3.9 m s -1 -100°C, 7.7 m s -1


A. a,b , Saulais, L. c,b , Blumenthal, D. a , Delarue Galiñanes Plaza
email: julien.delarue@agroparistech.fr

Eating location as a reference point: differences in hedonic evaluation of dishes according to consumption situation

Introduction

In spite of numerous studies on the influence of context on consumers' evaluation of food products, mechanisms underlying this influence are not well known. This limits the pursuit of ecological validity of consumer tests of products, and in particular the attempts to contextualize controlled environments (Galiñanes Plaza, [START_REF] Galiñanes Plaza | The pursuit of ecological validity through contextual methodologies[END_REF]. To date, most published studies on context have focused on physical variables without addressing test participants' attitudes, expectations or mood states [START_REF] Edwards | The influence of eating location on the acceptability of identically prepared foods[END_REF][START_REF] King | The effect of meal situation, social interaction, physical environment and choice on food acceptability[END_REF][START_REF] Meiselman | Demonstrations of the influence of the eating environment on food acceptance[END_REF][START_REF] Stroebele | Effect of ambience on food intake and food choice[END_REF]. Nevertheless, consumers' attitudes, prior beliefs and past experiences have been highlighted as variables that may explain differences in liking and behavior from one consumption context to another [START_REF] Bernard | Are beliefs stronger than taste? A field experiment on organic and local apples[END_REF][START_REF] Cardello | Attitudes of consumers toward military and other institutional foods[END_REF][START_REF] Edwards | Institutional meals[END_REF][START_REF] Tuorila | School meal acceptance depends on the dish, student, and context[END_REF]. This is because people and locations are most often confounded variables, which makes generalization of measures to other contexts difficult [START_REF] Delarue | The effects of context on liking : implications for hedonic measurements in new product development[END_REF]. We may thus consider that depending on the consumption context, consumers' prior beliefs or expectations toward the location and the quality of the served food may predispose to a different state of mind, leading consumers to a different evaluation and behavior. This echoes the notion of reference point described by [START_REF] Tversky | Loss Aversion in Riskless Choice : A Reference-Dependent Model Author ( s ): Amos Tversky and Daniel Kahneman Published by[END_REF] in their Prospect Theory. It suggests that judgement and decision-making are reference-dependent. In other words, individuals do not make absolute judgements but base their evaluation on reference points. Following this theory, consumers can have a different reference point for each context, hence modifying their framework of evaluation.

We conducted a preliminary focus group study on beliefs about the food served in different consumption contexts. It revealed that consumers associate different eating places to different levels of quality, price and product types, which was expected. Moreover, they also associate eating places to different preparation modes: universities or company canteens, fast-food restaurants are strongly associated to readymade products, whereas brasseries and gastronomic restaurants are associated to 'homemade' preparation (Galiñanes Plaza, Saulais, & Delarue, 2018). Consumers' representations about the food preparation mode associated to each context may thus influence how food products are perceived and liked.

Therefore, we can hypothesize that consumers evaluate food within a framework of reference that may be determined by the consumption context itself. In this view, the purpose of this study was to examine the influence of context on consumers' attitudes towards food, as related to their expectations. In order to test this, we emphasized on the quality (readymade or homemade) of the served food with the hypothesis that consumers' expectations would depend on the evaluation context.

More specifically, we were interested in the extent to which expectations (considered as reference points) were met, or in other words, whether consumers were satisfied or dissatisfied by the food they were served.

Following a between-subject design, we measured consumers' liking for two variants of a given food (ham-olives cake) as well as the level of fulfillment of their expectations in two contexts: an experimental restaurant and a standard testing room (STR). Additionally, in each context, we tested the influence of information about the quality of the food (readymade or homemade).

Following the assumptions of prospect theory regarding reference points [START_REF] Tversky | Loss Aversion in Riskless Choice : A Reference-Dependent Model Author ( s ): Amos Tversky and Daniel Kahneman Published by[END_REF], we hypothesized that (i) in the realistic consumption context, consumers liking scores would be higher than in the controlled setting; (ii) information about homemade products would obtain higher rates than readymade products regardless of context; (iii) the impact of information regarding food quality would differ depending on the testing location.

Material and methods

Participants

Two hundred and eighty-three consumers were recruited via the database of the Research Centre of the Institut Paul Bocuse, social networks and local newspapers. Each participant was randomly appointed to either the "Living Lab" study (restaurant) or the standard testing room (STR) and within each context, to the informed or the non-informed condition (each condition was tested on a different day).

One hundred and forty-five participants took part in the restaurant study, (57.2% were female and 42.8% male; mean age 44.45±9.92). One hundred thirty-eight participants took part of the standard testing room (STR) study (61.6% were female and 38.4% male; mean age 43.86±9.93). Inclusion criteria were age (between 30 and 60 years old) and allergies (no known food allergy). Cooking habits and eating out frequency responses were collected to better characterize the studied population. Table 1 details their characteristics.

Participants were not financially compensated for their participation, but they were all invited to a free dinner at the restaurant, either as part of the experiment (for the restaurant groups) or as a follow up to the experiment (for the STR groups). Only the STR group knew, upon recruitment, that they would formally participate in a taste test in a controlled condition before the dinner.

At the beginning of the test, participants signed a consent form and then were invited to access the restaurant or to the central location test.

Products

Participants had to evaluate a ham-olives cake (Figure 1), which is a familiar appetizer product to French consumers. Two versions of the product were tested: (i) an industrial, commercially available version (referred to as readymade product in the rest of this article). From this readymade product, (ii) a homemade version (referred to as homemade product) was developed by a professional chef for the purpose of this experiment.

-Insert Figure 1 about here - Regarding the homemade version, the recipe was adapted using the following proportions: 150g ham (≈28.8%), 4 eggs (≈1.54%), wheat flour, canola oil, Emmental cheese, 150g green olives (≈28.8%), milk and yeast. Slight differences in sensory properties between these two versions were detected in an internal tasting session (notably, the readymade cake was perceived as drier than the homemade version, and the olive taste was less strongly perceived). Cakes were served in slices (1cm) and care was taken to make them equally thick in all conditions. The same quantity of product was thus served in the restaurant and in the STR contexts in order to avoid influences of food quantity or differences in the eating reference unit [START_REF] Rozin | A lack of appetite for information and computation. Simple heuristics in food choice[END_REF]. However, we did not measure the quantity of food that participants consumed.

The readymade cakes used throughout the experimental campaign came from a single batch and were stored in a cold chamber at 4.5°C. On each test day, five readymade cakes were removed from the cold chamber and placed at room temperature half an hour before the beginning of the service.

The homemade cakes were prepared using the same pan model as the readymade version to ensure that both variants had very similar appearance. They were made the same day and at the same hour for each testing session in order to limit sensory variations due to ageing and drying out.

Each product sample was assigned a 3-digit code displayed by a sticker on the presentation plate. All samples were presented sequentially at room temperature in a balanced and randomized order between and within sessions.

Settings

To compare participants' responses in natural and in controlled situations, the experiment was conducted in two settings: a restaurant setting (restaurant) and a standard testing room (STR).

Contextual variables such as portion size, presentation, cutlery, information, timing and social interaction were considered in the experimental design.

A. "Living Lab" restaurant

The natural setting was that of the "Living Lab" restaurant of the Institut Paul Bocuse (Figure 1.A.)

This restaurant is a real commercial restaurant, open to the public and known locally as such. It is also a living lab, in which a number of contextual and product variables can be controlled for, in order to conduct research. Each day, the tables were organized according to the reservation list and set up following a schema. Light and temperature were also set and controlled during each service. Once participants signed the consent form they were welcomed to the restaurant and conducted to their table. Before the dinner, a waiter proposed the cakes, presented as a set of two versions of an appetizer together with a drink, and indicated that participants would have to fill out a short questionnaire during and after the tasting. First of all, the drink (iced tea or water) was served and then the questionnaire was brought together with a pen. Prior to consumption, consumers had to indicate if they had any allergy or dietary restriction.

Appetizers were presented in a monadic sequential way. Once participants had rated the first sample, the second one was presented. Once the appetizer tasting was finished the rest of the dinner took place.

B. Standard Testing Room (STR)

Testing in the standard controlled environment took place in one of the classrooms adjacent to the Research Centre of the Institut Paul Bocuse. A picture of this STR can be seen in Figure 1.B.

Participants were seated and instructions about the test were given by a researcher. The procedure was the same as in setting A, except that in this case, water was the only drink offered.

-Insert Figure 2 about here -2.4. Experimental design 2.4.1. Information conditions Two information conditions were tested in each setting. In the non-informed condition, consumers were provided the two versions of the product with no information about the differences between the two product versions. In the informed condition, homemade cakes were presented together with a label displaying "fait maison", whereas the readymade version was presented with a label displaying "industriel".

Sessions

The experiment followed a 2 (setting) x 2 (information condition) design. For all conditions, the two products were first evaluated and then, participants had a dinner at the "Living Lab" restaurant. The experimental campaign was conducted over the course of two weeks (one per setting), and sessions were conducted at two time slots: 7pm and 7.30pm. This organization facilitated the service at the restaurant and the balance presentation of the two cake versions per day. Participants in the first time slot received the homemade version first, whereas in the second time slot participants received the readymade version first. This order was balanced over the week.

The two experimental conditions (non-informed and informed) were conducted on separate days to avoid confusion and uncontrolled information.

Experimental procedure and evaluation task

In all four experimental conditions, participants were presented with samples of the two product versions. The order of presentation of the products was balanced across subjects in each group.

Participants were asked to rate their liking for the appetizer (ham-olive cake) on a 11-point hedonic scale ranging from "dislike extremely" to "like extremely", and to rate the extent to which the product had met their expectations on a bipolar 11-point scale ranging from "lower than my expectations" to "higher than my expectations" with a midpoint corresponding to "meets my expectations". Finally, consumers also rated their preference between the two versions together with an open-ended question about their choice. All responses were collected using a paper form.

Demographic information (gender, age, and other consumers' characteristics) was also collected at the end of each questionnaire.

Data analysis

Liking and fulfillment of expectations data were analyzed using a multi-way analysis of variance with the subject effect nested in each group (information condition, setting, presentation order). All testable factors and interactions were tested and a step-by-step analysis was run to remove the non-significant interactions using Matlab 2017. The best models to explain liking (after 11 rounds) and fulfilment of expectations data (after 9 rounds) were selected and presented in the present paper. When the ANOVA showed a significant effect (p < 0.05), Tukey's test for pairwise comparisons was used (SPSS v.16, SPSS Statistics, Chicago, I).

With regards to fulfilment of expectations data, scores ranging from "lower than my expectations" to "meets my expectations" were converted in negative scores ranging from "-5" to "0" and those from "meets my expectations" to "higher than my expectations" were converted in positive scores ranging from "0" to "5".

In order to explore inter-individual differences in liking for each version, we distinguished between respondents who had reported that the product did not meet their expectations (they were named "deceived" consumers for that specific product (scores < 0)) and those who reported that the product met or exceeded their expectations (scores ≥ 0). They were named "satisfied" consumers, for that specific product.

Results

Liking

On average, the cakes were well liked by the participants in both settings (Figure 3). As expected, the homemade cake was more liked (x 7.0±1.7) than the readymade one (x 5.6±2.2) regardless of the experimental condition. The analysis of variance shows that the product version induced the most important differences in liking (Table 2). The liking scores also differed depending on the settings (scores being significantly higher in the restaurant than in the STR (p = 0.005)).

-Insert Figure 3 about here -

Effects of information

The presence of information as a main effect did not significantly influence participants' overall liking scores (F (1, 280) = 3.16; p = 0.076). Although we hypothesized that information would affect the liking differently depending on the context, we did not observe such an interaction. Nevertheless, the presence of information affected the liking differently depending on the product version, as revealed by the significant product*information interaction (F (1, 280) = 6.18; p = 0.014). Post hoc Tukey (HSD) pair-wise comparison showed that the homemade version was not affected by the presence of information (p = 0.964) while the use of the label negatively affected the liking scores of the readymade version (p = 0.024) (Figure 4). As a result, the difference in liking scores between the homemade and the readymade cakes was larger (1.8 points on the hedonic scale) when information was given.

-Insert Figure 4 about here -

Effects of sample presentation order

The order of sample presentation resulted in a significant difference in the overall liking scores of both product versions (F (1, 280) =7.76; p = 0.006). However, only the readymade cake was significantly affected (p < 0.001) -with liking scores dropping 1 unit (on the 11-point hedonic scale) -when tested second, after the homemade cake (Figure 5).

-Insert Figure 5 about here -

Fulfillment of expectations

After participants tasted each product, they were asked to rate the extent to which the product met their expectations or not. Results for the fulfillment of expectations scores showed a similar pattern as the liking scores. We observed a significant effect of product version, settings and order of sample presentation on the fulfillment of expectations scores (Table 3). Tukey (HSD) post hoc shows that participants' scores of fulfillment of expectations were significantly higher for the homemade version compared to the readymade one (p < 0.001). Participants also rated higher their fulfillment of expectations in the restaurant compared to the STR regardless of the product version, information condition and order of sample presentation (p = 0.009).

In order to explain those differences, we highlighted participants whose expectations were not met.

We indeed classified participants' responses into two groups: "satisfied" (whose expectations were met or exceed) represented in green and "deceived" (whose expectations were not met) in red. Overall, satisfied participants outnumbered deceived participants (11.6% in the STR, 4.2% in the restaurant).

However, the readymade version gave rise to more deceived participants (31.9% in the STR condition, 31.3% in the restaurant condition) than the homemade version (12.3%. in the STR, 8.3 in the restaurant). Participants are satisfied with the homemade cake no matter where it was tested and whether it was labelled or not. When this version is tested at the STR we can observed a slight trend of increase of the scores which may indicate that participants obtained something that they did not expected to find in that particular context (i.e. a homemade cake in a STR). However, in the case of the readymade version, bimodal responses are observed in both contexts.

-Insert Figure 10 about here -

Discussion

The purpose of this study was to assess the influence of the evaluation context on consumers' expectations regarding the quality (readymade or homemade) of the served food and on its subsequent evaluation. We hypothesized that consumers' prior expectations would depend on the evaluation context and that this would directly impact the liking scores.

Liking

Results indicate that participants liked the products significantly more in a natural consumption context than in a standard testing room (STR), supporting the notion that consumer product evaluation may be context-dependent [START_REF] Boutrolle | Central location test vs. home use test: Contrasting results depending on product type[END_REF][START_REF] Holthuysen | Welcome on board": Overall liking and just-about-right ratings of airplane meals in three different consumption contexts-laboratory, re-created airplane, and actual airplanethuysen[END_REF][START_REF] King | The effect of meal situation, social interaction, physical environment and choice on food acceptability[END_REF][START_REF] Meiselman | Demonstrations of the influence of the eating environment on food acceptance[END_REF]. Some contextual variables such as the ambiance and social facilitation at the restaurant may also have influenced those results. The environment at the restaurant was warm and friendly, whereas the ambiance at the STR was colder and participants did not have the possibility to discuss with each other. Some of the participants in the STR stated that they "felt like they were sitting in an exam" and this might have modulated participants' mood and therefore their liking [START_REF] Giboreau | Sensory and consumer research in culinary approaches to food[END_REF][START_REF] Porcherot | Measurement of selfreported affective feelings when an aperitif is consumed in an ecological setting[END_REF][START_REF] Sester | Having a drink in a bar": An immersive approach to explore the effects of context on drink choice[END_REF]. Moreover, the way products were consumed in each context could also explain differences in liking scores. In particular, in the restaurant, participants had the possibility to drink ice tea while they ate the cakes. This factor, which we consider as part of the context, could have contributed to the increase of liking scores in the restaurant. Indeed, several studies have shown an increase in the liking scores when specific combinations of food and drinks are consumed together [START_REF] Monaco | Effect of social interaction and meal accompaniments on acceptability of sourdough prepared croissants: An exploratory study[END_REF][START_REF] Hersleth | Effect of contextual factors on liking for wine-use of robust design methodology[END_REF]). Yet, a closer look at the responses from the 32% of participants who preferred to drink water does not show such an effect, although this could not be formally tested in our ANOVA model. Meanwhile, we cannot exclude that drinking ice tea could have modulated participants' perception of the cakes and therefore could have resulted in a product*testing condition interaction.

Another hypothesis is that the evaluation task itself, and not only the product, may have been perceived as different in those two contexts: participants may have integrated other aspects related to the consumption experience (environment, occasion, social facilitation, etc.) to their evaluations, increasing their scores at the restaurant regardless of the product versions. Conversely, at the STR, participants were more discriminant towards the two versions. This could be related to a greater attention placed on the sensory evaluation, and the lack of interaction with a drink (ice tea) [START_REF] Hetherington | Situational effects on meal intake: A comparison of eating alone and eating with others[END_REF][START_REF] Köster | From mood to food and from food to mood: A psychological perspective on the measurement of food-related emotions in consumer research[END_REF].

As regards product evaluation, results show that the homemade version was rated higher than the readymade one, regardless of the contexts and regardless of the information condition. As revealed during the internal tasting session, the readymade cake was perceived to have a drier texture and a weaker olive taste intensity, which was expected to be less appreciated even if these differences were small. We also observed that independently of the context there was a higher consensus on the evaluation and satisfaction of the homemade cake whereas the readymade product resulted in more variety of opinions. Nowadays, consumers are much more concerned about the food industry and the quality of processed food than they used to be [START_REF] Asioli | Making sense of the "clean label" trends: A review of consumer food choice behavior and discussion of industry implications[END_REF]. During our preliminary focus group study, consumers stated that they were able to differentiate a readymade product from a homemade one, underlining the importance of the quality of the food when eating out. Consumers expect to find certain type of quality (homemade) in a restaurant instead of a product they can have at the supermarket or even at home. However, this is different when it comes to the standard tests where consumers do not know what they are going to taste or tend to think that they will test industrial products, so the reference point of evaluation may differ (Galiñanes Plaza et al., 2018).

Besides, the liking for readymade cake was significantly affected by the presence of information.

Several studies have shown the effect of information on consumers' products evaluation as well as its relation to consumers' attitudes and beliefs [START_REF] Baer | The role of contextual information of luxury on emotional responses to perfumes[END_REF][START_REF] Bernard | Are beliefs stronger than taste? A field experiment on organic and local apples[END_REF]Schulte-Mecklenbeck, Sohn, de Bellis, Martin, & Hertwig, 2013;[START_REF] Van Den Heuvel | Why preferences change: Beliefs become more salient through provided (genomics) information[END_REF]. Priming on certain type of information, in our case "industriel", can make attitudes and beliefs about that particular information more salient, modifying the final response of the participants [START_REF] Reis | The role of information on consumer sensory, hedonic and wellbeing perception of sugar-reduced products: Case study with orange/pomegranate juice[END_REF][START_REF] Van Den Heuvel | Why preferences change: Beliefs become more salient through provided (genomics) information[END_REF]. Moreover, a significant effect of the order of sample presentation was also observed for the readymade version, especially when it was tested after the homemade version. [START_REF] Lahne | The great is the enemy of the good: Hedonic contrast in a coursed meal[END_REF] showed a similar effect when comparing the liking scores of a dish after a good and a mediocre appetizer. The fact that the homemade cake was higher rated could originate from a contrast effect between both cake versions that was manifest when the readymade version was tested second. The sample presentation order is known to have an effect on consumer hedonic evaluation [START_REF] Boutrolle | Central location test vs. home use test: Contrasting results depending on product type[END_REF]. However, to our knowledge this effect has not been explored in natural consumption contexts where consumers do not usually taste two similar products one after another. Conversely, in real life consumers may compare the product they eat to a personal reference point. This would correspond to a pure monadic testing mode. Here, having compared two similar products in a monadic way could have modulated participants' reference points of comparison from one product to another as well as their expectations.

Fulfillment of expectations scores

Concerning the fulfillment of expectations results, higher expectation scores were fulfilled at the restaurant compared to the STR. [START_REF] Cardello | Food quality: Relativity, context and consumer expectations[END_REF] described how the perceived food quality and the expectations about food quality of a same product may differ depending on the context of consumption, underlining how important consumers' mindset about a particular context is when evaluating a product.

In this study we considered those prior expectations about contexts and food quality as reference points. In the case of this restaurant we may assume that the reference point as regards the physical location was high because of its name associated to the prestige of Paul Bocuse. Consumers who came to the restaurant test at the Institut Paul Bocuse usually expect to find high food quality associated to the use of natural and local ingredients, tasty (and costly) food. However, in the STR the reference point was more ambiguous. Consumers usually associate this type of context to the test of industrial or processed products and not to a meal experience. Our data reflect these differences between the two contexts as regards food quality: at the restaurant participants' expectations were fulfilled for the homemade version whereas this was not always the case for the readymade version. Similar results

were obtained in the STR; however, the level of expectations in general in this context was lower as participants came to the STR with a « lower » overall framework which may relatively impact their evaluation. [START_REF] Cardello | Consumer concerns and expectations about novel food processing technologies: effects on product liking☆[END_REF] explains that when expectations are low -even if the perceived intrinsic quality is high -liking scores will decrease as the perceived liking will assimilate the lower expectation. This may explain the differences between both contexts and even more, the differences when the readymade version was labelled and presented before or after the homemade version [START_REF] Cardello | Consumer concerns and expectations about novel food processing technologies: effects on product liking☆[END_REF][START_REF] Piqueras-Fiszman | Sensory expectations based on product-extrinsic food cues: An interdisciplinary review of the empirical evidence and theoretical accounts[END_REF]. The reference point created may have been modulated for these two factors (product information and order of presentation), modifying the fulfillment of expectations scores.

Inter-individual differences

As regards the analysis of inter-individual differences, we observed that the distribution of liking scores differed depending on the product version and could be related to participants' fulfillment of expectations. Overall, the homemade version met or exceeded participants' expectations no matter where it was tested or how it was labelled; however, the readymade version was more disappointing showing a bimodal distribution of the liking scores and fulfillment of expectations. A possible explanation for this result is that a hedonic contrast between both versions and the product-context (inappropriate situation) may occur [START_REF] Cardello | Predictors of food acceptance, consumption and satisfaction in specific eating situations[END_REF][START_REF] Lahne | You'll spoil your dinner: Attenuating hedonic contrast in meals through cuisine mismatch[END_REF][START_REF] Lahne | The great is the enemy of the good: Hedonic contrast in a coursed meal[END_REF].

Conversely, some limitations should be noted and considered for further studies. This study was conducted in a specific location, the Institut Paul Bocuse, a name associated to one of the major references of gastronomy in France and worldwide. Participants came to the STR knowing that they would take part of a study. The STR was located inside of the Institut Paul Bocuse which may have contributed to create a certain degree of expectations that were not met in both contexts. Moreover, it is important to consider that, in both settings, participants were invited to the diner. We have previously mentioned that high food quality was related to higher prices. Thus, the fact that participants did not pay for their dinner may have led them to a lower engagement in either settings, which is a typical weakness of such hypothetical tests (as opposed to non-hypothetical tests implemented in experimental economics). Those limits may contribute to explain the fact that we did not observe any three-way interaction between the context, the product version and information.

Conclusion

The purpose of this study was to assess the influence of context on consumers' attitudes towards food by emphasizing the quality (readymade or homemade) of the served food. We hypothesized that consumers' prior expectations would depend on the evaluation context and that this would directly impact participants' evaluation.

The homemade version obtained a 'higher' reference score on average. This seems to make it less sensitive to variations of context than the less liked readymade version. Information about the product version played a key role on participants' evaluation that may be related to participants' prior beliefs and/or expectations. More generally, information may contribute to the modulation of participants' reference points.

Our results suggest that reference dependent theory may be an interesting way to look at consumers' mind-set when performing a context comparative study. By modulating this reference point or framework of evaluation we might be able to explain certain differences between contexts that may not be related to the physical environment itself but to the attitudes or prior experiences consumers have had with the served food in a similar context. Moreover, an important finding is that the context of the evaluation task had an effect stronger than the actual context of consumption (restaurant and STR). In the case of natural consumption contexts such as restaurants, a monadic sequential presentation of the products may decrease the ecological validity of the results. Our data also showed that product order modulate participants' hedonic evaluation as well as the fulfilment of their expectations. From a practical point of view, this result suggests that the task modulates the reference point from where consumers make their evaluation and set their expectations and should thus be carefully considered. Indeed, even in contextualized tests for the industry, resulting managerial decisions may depend on the evaluation task and test design.

  Figure 1

Table 1

 1 Characteristics of the participants in both studies: means (SD) or %

	Contexts

Table 2

 2 Summary of the effects of experimental factors on liking scores. Output from the final ANOVA model

	(calculated with type III sums of squares)
	Source	d.f.	F	p-value
	Consumers(Information Conditions, Settings, Presentation order)	279	1.25	0.031
	Products	1	80.20	<0.001
	Information conditions	1	3.16	0.076
	Settings	1	7.94	0.005
	Presentation order	1	7.76	0.006
	Products*Information Conditions	1	6.18	0.014
	Products*Presentation order	1	14.95	<0.001

Table 3

 3 Summary of the effects of experimental factors on expectations scores. Output from the final ANOVA model (calculated with type III sums of squares).

	Source

Acknowledgements

The authors thank all collaborators of the Institut Paul Bocuse for their assistance in this experiment. This work is part of a PhD project funded by the Société Scientifique d'Hygiène Alimentaire (SSHA).

Effects of information

Participants' scores of fulfillment of expectations were not affected by the information conditions (F (1, 279) = 2.01; p = 0.158). Nevertheless, a significant interaction between product and information conditions was observed (F (1, 279) = 4.02; p = 0.046). Higher scores were obtained for the homemade version than for the readymade version regardless of the information condition. Homemade version met participants' expectations and even overcame participants' expectations as shown on Figure 6. However, in the case of the readymade version, participants' scores of fulfillment of expectations decreased when information was presented, meaning that participants' expectations were not even achieved (negative scores were obtained), whereas in non-informed conditions the readymade version met participants' expectations (Figure 6).

-Insert Figure 6 about here -

Effects of sample presentation order

The sample presentation order also affected participants' fulfillment of expectations scores (F (1, 279) = 4.65; p = 0.032). Nevertheless, the two versions of the cakes were differently affected as Figure 7 shows. The order of sample presentation did not affect participants' scores of fulfillment of expectations for the homemade version (p=0.998). However, the scores of the readymade version were significantly lower (p < 0.001) when this version was tested second. Moreover, the three-way interaction product * information condition * presentation order was significant (F (1, 279) = 4.37; p = 0.037). It shows that the presence of information provoked even a higher deception among participants who scored this product as much lower than their expectations (Figure 8).

-Insert Figure 7 about here --Insert Figure 8 about here -3.3. Inter-individual differences: analysis of liking and scores of fulfillments of expectations In Figure 9, the first thing to note is that the overall shape of the liking score distribution is different for the homemade and the readymade versions. The homemade version shows a higher consensus on the liking scores whereas the readymade version shows a bimodal distribution, especially at the STR setting in non-informed condition.