Modeling the inactivation kinetics of lactic acid bacteria in a spray dryer

Abstract Changes in the viability of probiotic cells during spray drying were tracked, by developing an inactivation model of Lactobacillus rhamnosus GG (LGG) and coupling the model to the drying kinetics of spray drying using Computational Fluid Dynamics simulation. Six inactivation models in the Arrhenius-equation form were developed using single droplet drying experiments with average drying rates of 0.011–0.044 kg/kg/s; all gave reliable goodness-of-fit. In simulating spray drying process, the predicted moisture content of LGG-containing particles well followed experimental trends. However, only inactivation model 6, which incorporated droplet temperature, moisture content, rate of temperature change, and drying rate, accurately predicted the survival of LGG. Models 1–5 that incorporated fewer kinetics parameters with higher activation energy values underestimated the degree of inactivation. The findings highlighted the crucial effects of the rates of temperature and moisture content change on the inactivation of probiotics during rapid drying with average drying rates of 0.31–0.81 kg/kg/s.


Introduction
Lactic acid bacteria (LAB) are Gram-positive, oxygentolerant bacteria widely applied in food, pharmaceutical, and agricultural industries as starter cultures, probiotics, and biopreservatives. [1]In most applications, the viability of LAB is a key criterion for fermenting dairy substances, acting beneficially on the host's health, and modifying the environment.Converting the living culture grown in a liquid medium to an active powder form can extend the shelf life of LAB products remarkably, and is advantageous to transportation and further dosage formulation. [2]Compared to the conventional freeze drying technique to produce active LAB powders, spray drying is cost-effective, rapid in powder production, and viable for large-scale production. [3]In spray drying, liquid feed that contains viable LAB cells and protectants is atomized into billions of micron-sized droplets, and then mixed with hot airflow for rapid conversion to dry particles in several to tens of seconds.With the rapid decrease in moisture content, the temperature of the droplets rises, which may lead to severe dehydration and thermal stresses on LAB cells in the droplets. [4,5][8] However, relatively little is known about the deactivation of LAB during the droplet-to-particle transition inside the spray dryer, where significant loss of bacterial viability up to several orders of magnitude may occur with severe cellular injuries.
Since it is relatively difficult to take samples of individual flying droplets inside a spray dryer, experimental and numerical approaches have been developed to investigate the coupled physicochemical transitions during spray drying.With the single droplet drying experiments, the drying kinetics of an isolated droplet can be accurately measured under conditions analogous to spray drying, contributing fundamental data needed in modeling a spray drying process. [9,10]][12] Numerical simulation approaches such as Computational Fluid Dynamics (CFD) have also been developed to track the drying processes of individual droplets inside a spray dryer.Through three-dimensional simulation, velocity and temperature fields in the dryer and the corresponding changing processes of the physicochemical properties of individual droplets can be described.15][16] The simulation of the inactivation of LAB during spray drying should be achieved by correlating the inactivation to drying kinetics experienced by bacterial cells in atomized droplets.By coupling a reliable inactivation model of LAB to the drying process of atomized droplets using CFD, it would be feasible to describe the changes in LAB viability during droplet drying.In the thermal processing of food, the rate of change of a quality attribute (C) at different processing temperatures is conventionally described by the Arrhenius equation: [17] À dC dt ¼ kC where t is the time of exposure, herein drying time (s), T refers to the temperature during constant-temperature processing (K) and k is the corresponding rate constant of quality change, E is the activation energy needed for the change to occur, and k 0 is a pre-exponential factor.Fu et al. employed Equation (2) to describe the inactivation process of Lactococcus lactis ssp.cremoris during single droplet drying, taking the inactivation rate k d as the rate change of the survival of bacteria (N/N 0 , with N being the viable cell count of bacteria, cfu/mL) as drying progressed. [10]ith an E d of 105.50 kJ/mol and k 0 of 2.84 Â 10 14 , Equation (2) well described the inactivation profiles of L. cremoris at six single droplet drying conditions, that is, feed solid contents of 10 and 20 wt% and drying temperatures of 70, 90, and 110 C. [10] In spray drying, the majority of water in atomized droplets can be removed in several to tens of seconds, which is much shorter than the drying time of around 2-10 min in a single droplet drying process.The associated high rates of temperature change and water removal may cause a higher loss of bacterial viability than a slow application of the stresses. [18,19]Such a characteristic might be linked to the nature of living microorganisms, which show significant differences from bioactive chemicals such as proteins and vitamins toward stresses. [8]For instance, bacterial cells could experience multiple cellular injuries during dehydration, [20,21] and may repair the injuries and continue multiplying under suitable conditions.Chen and Patel proposed a series of modified Arrhenius equations to account for the effects of the rate of temperature change (dT/dt) and drying rate (-dX/dt) on the inactivation of bacteria (Table 1), where X is moisture content on a dry basis (kg/kg). [22]Huang et al. applied the equations to describe the inactivation of yeast during infrared drying. [23]It was found that the model that incorporated T, dT/dt, and -dX/dt gave a more accurate prediction of the experimental survival curve than the simple Arrhenius equation that included T as the only parameter. [23]However, it has remained unclear to what extent the drying kinetics parameters affected the inactivation of bacteria and how the effects vary with different drying conditions, which are crucial to developing a suitable inactivation model for various drying applications.To date, there is yet an inactivation model that can capture the changes in the viability of bacterial cells during spray drying.
The objective of the present study is to describe the inactivation process of LAB inside a spray dryer numerically, by developing an inactivation model that takes into account the effects of drying kinetics parameters and coupling the model to the drying kinetics of spray drying using CFD.Six inactivation models of a model probiotic strain, Lactobacillus rhamnosus GG, were established based on reported single droplet drying data. [5,24]The inactivation models were coupled to the dryer scale Multiphysics drying kinetics model of a microfluidic jet spray dryer on the FLUENT platform.The spray dryer generated monodisperse atomized droplets for dehydration under well-controlled drying conditions, so the produced particles were uniform in size, morphology, and properties. [25]The simulation results were compared to the experimental results of the spray drying of L. rhamnosus GG to identify the appropriate inactivation model.Changes in the viability of L. rhamnosus GG inside the spray dryer were unveiled, and the effects of drying kinetics parameters on the viability of the bacteria in spray drying, a typical rapid drying process, were discussed.

Problem statement and system description
A schematic of the spray dryer studied in the present study is shown in Figure 1a.Its working principles and experimental procedures have been described in detail in previous studies. [25]To produce active L. rhamnosus GG powder, monodisperse droplets containing viable L. rhamnosus GG cells with reconstituted skim milk (RSM) as protectant are injected into the drying chamber from the nozzle.The hot air flows co-currently into the tower from tiny holes that are evenly distributed on the ceiling of the drying tower.Dried particles can be directly collected at the outlet of the cylindrical chamber.In typical experimental studies, the remaining viability of L. rhamnosus GG in spray-dried powder is analyzed, and compared to the value in the feed to calculate the survival of the bacteria after spray drying. [26]Clearly, survival at the outlet of the dryer is the cumulative result of the inactivation process of the bacteria inside the dryer, during which viable cells are carried in atomized droplets and experience changes in the droplet environment as droplets are transformed into particles.Such changes in bacterial viability, also known as inactivation history, are complicated to track experimentally.The structure of the spray dryer does not allow frequent and convenient sampling of droplets flying in the drying chamber.CFD simulation offers a quantitative approach to unveil the complex physicochemical transitions inside a spray dryer.

Governing equations
The drying air flow is modeled with 3D Navier-Stokes conservation equations integrated with RNG k-e turbulent model to capture the slightly turbulent flow in the chamber. [27]The interactive heat and mass transfer between air (bulk fluid) and atomized droplets (discrete particles) is described with the discrete phase model (DPM), and the evaporation process of individual droplets is modeled with the Reaction Engineering Approach (REA).Most importantly, in this work, to describe changes in the viability of bacteria in the droplets, the key is the development of a model that is capable of correlating bacterial viability (N) to the kinetic parameters (i.e., temperature, moisture content, and their changing rates) of the droplets being dried.The governing equations for the droplet model are listed below.

Droplet trajectory determination
During drying, droplets and the flow field affect each other interactively.The trajectories of the droplets are mainly determined by the initial speed and the drag force of the fluid.The following equations for spherical droplets are used: where u p ! is the velocity of droplets (m/s), u ! is the velocity of hot air (m/s), D p is the diameter of a droplet, and C d is the drag coefficient calculated using an empirical correlation between C d and Re. [28]oplet shrinkage model A falling droplet is assumed spherical and shrinks uniformly as water is removed from the droplet.The correlation between droplet diameter D p and its moisture content X (kg/kg) is described by the linear shrinkage model as reported by Line and Chen: [29] where a is taken as 0.51, 0.59, and 0.69 for 10 wt%, 20, and 30 wt% RSM droplets, respectively.The conservation of heat during spray drying and the heat balance between droplets and gas involving moisture evaporation are calculated using the following equations: where T p and T b are droplet temperature and bulk air temperature (K), respectively, h is the heat transfer coefficient (W/(m 2 ÁK)), and DH l is the specific enthalpy of water evaporation (J/kg).The second expression of Equation ( 5) is the energy conservation equation solved in FLUENT, where k eff is the effective thermal conductivity (W/(mÁK)), and J ! j is the diffusion flux of species j (Kg/(m 2 Ás)).The last term on the right of the second expression refers to energy transfer due to water evaporation.

Droplet evaporation model
Evaporation causes the transfer of moisture from the droplets to the gas phase under the driving force of the difference in vapor density between the droplet surface and bulk gas.The rate of drying (-dm p /dt) can be mathematically denoted as: where m s is the mass of solids in the droplets (kg), h m represents the mass transfer coefficient (m/s), and q v, sur and q v, b are water vapor density at the droplet surface and the flow field (kg/m 3 ), respectively.Since q v, sur is in a transient state during drying, a fractionality coefficient w is introduced to correlate it with the saturated vapor density at the droplet surface (q v, sat ) according to the REA model: [30] q v, sur where T sur is the surface temperature of the droplet (K).For micron-sized droplets like atomized droplets during spray drying, the temperature gradient in the radial direction may be neglected, [30] and T sur is approximated as the average temperature of the droplet T p in the present study.
In describing droplet drying kinetics, the lumped REA (L-REA) model considers the evaporation of water as an activation-energy-based process that needs to overcome an energy barrier to occur.The fractionality coefficient w can be correlated with the apparent activation energy of evaporation, DE v , using an Arrhenius-type equation: Extensive studies have demonstrated that changes in the activation energy DE v during the drying of a given material can be correlated with the changes in its moisture content using a generalized equation for varying drying conditions, as far as the initial solid content of the material is the same: [30] where DE v, b is the maximum activation energy when the moisture content of the material reaches equilibrium with the bulk gas at a specific drying condition, and X e is the corresponding equilibrium moisture content.X e can be calculated with the GAB equation in the following form: where a w is the water activity of the bulk gas, m 0 is the monolayer moisture content, and parameters C and K are functions of gas temperature.In the present study, RSM is used as protectant, and the mass of LAB cells is considered negligible compared to the mass of milk solids, so the parameters of RSM are used, that is, m 0 , C 0 , DH 1 , K 0 , DH 2 values of 0.06156 kg/kg, 0.001645, 24831 J/mol, 5.710, and À5118 J/mol, respectively. [30]or drying a given material, Equation ( 10) is a characteristic fingerprint model established with the REA concept.The specific form of the equation can be determined through a minimum number of experiments, and then the established model can be used to describe drying kinetics under other conditions.The model used for the drying of RSM droplets in the present study is reported by Chen and Lin: [30] Inactivation model of viable bacteria Models 1-6 in Table 1 provide several possibilities for developing an inactivation model in the Arrheniusequation form.The corresponding model parameters, a, b, and c, should be determined before the inactivation model can be coupled with a CFD model of spray drying.In this study, the inactivation data of L. rhamnosus GG reported in previous single droplet drying studies [5,24] are used to fit Models 1-6 to determine the parameters for each model.Specifically, single droplet drying experiments offer dynamic data on the survival of bacteria (N=N 0 ) throughout the complete drying process.Fitting the models to the experimental data is achieved by solving the optimization problem  2), to examine the predictive performance of each equation.The resulting six inactivation models are coupled to the CFD model of the spray drying of L. rhamnosus GG through user defined functions (UDFs), respectively.The survival of the bacteria at the dryer outlet predicted by each inactivation model is compared to the experimental survival in spray-dried L. rhamnosus GG powders, to determine the model that gives the most accurate description of the inactivation of the bacteria during spray drying.

Boundary and initial conditions
Table 3 summarizes the boundary conditions of airflow used in the calculation of the main drying chamber.Following the conditions used in the spray drying experiments, three inlet temperatures of 106, 118, and 134 C are used to control the outlet temperature of the drying chamber at 58, 63, and 68 C, respectively.The heat loss of the spray dryer is considered by incorporating the convective heat transfer coefficient of the dryer wall, as shown in Table 3. Table 4 summarizes the initial conditions of the discrete phase and the corresponding experimental results obtained with the microfluidic jet spray dryer.The injected droplets are considered monodisperse, with an initial droplet size of 155 mm. [25]At the outlet temperature of 58 C, skim milk at three initial solid contents (10, 20, and 30 wt%) are used as the protectant of L. rhamnosus GG, respectively.At 63 C, 20 wt% skim milk is used.

Results and discussion
Establishment of a kinetic model for the inactivation of L. rhamnosus GG using the single droplet drying experiment Experimental data from four single droplet drying experiments (Trial 1, 2, 4, and 5 in Table 2) were used to obtain parameters a, b, and c in Models 1-6 (Table 1), and the predictive performance of the resulting six models on the inactivation of L. rhamnosus GG during convective droplet drying was evaluated by comparing to Trial 3. To gain a better understanding of the different forms of the kinetic model, the inactivation processes of L. cremoris under eight conditions were also modeled with Models 1-6, in which experimental data from six conditions were used to obtain parameters a, b, and c for each model, and the other two experiments were used to evaluate the predictive performance (Table S1, supplementary material).The optimal parameters for each model to describe the inactivation of L. rhamnosus GG and L. cremoris are shown in Table 5 and Table S2 (supplementary material), respectively.
In describing the inactivation of L. rhamnosus GG, the trends given by all six models well followed the experimental data as shown in Figure 2, with R 2 larger than 0.90 (Table 5).On a normal scale between 0 and 100%, the six curves were close to each other at each tested condition (Figure 2a-d), whereas divergence was observed at a later drying stage when the data were plotted on a logarithmic scale (Figure 2A-D).In Figure 2B and D, Model 1 which only considered the effect of T showed the lowest similarity to experimental data, while in Figure 2A and C it was Model 2, which considered the effects of both X and T. Models 3-6 that took the effects of the rates of change into account showed similar goodness-of-fit, giving higher R 2 (larger than 0.92) than Models 1 and 2. To verify the reliability of these equations, the survival data of L. rhamnosus GG during Trial 3 were predicted with each model.The resulting six curves nearly overlapped each other (Figure 3).
It is worthwhile to note that the incorporation of an increasing number of kinetic parameters appeared to be associated with a perceptible decrease in the activation energy for the inactivation of LAB (E d in Table 5).
The highest E d of 124,000 J/mol in deactivating L. rhamnosus GG was given by Model 1, whereas the lowest E d of 80,014 J/mol was achieved with Model 4 which involved T, X, and -dX/dt.Model 6 which considered the effect of four parameters (T, X, dT/dt, and -dX/dt) showed the second lowest E d of 93,711 J/mol.A similar trend was observed in modeling the inactivation of L. cremoris during convective droplet drying (Table S2, supplementary material).With the increase in the number of kinetic parameters, E d gradually decreased from 117,500 J/mol in Model 1 to 69,634 J/ mol in Model 6.The low activation energy value may indicate that the inactivation reaction could occur at a faster rate by overcoming a relatively low energy barrier.Moreover, the reaction with a low activation energy value is less sensitive to the change of temperature than that with a high value.By contrast, the inactivation model that incorporated fewer kinetic parameters might overestimate the activation energy, so the predicted degree of inactivation is likely lower than that predicted by a model with lower activation energy under the same reaction condition.Wall: The setting of inlet temperature was to control the outlet temperature of drying chamber at 58, 63, and 68 C, respectively, in accordance with the experiment conditions used to produce L. rhamnosus GG powders.
In describing the inactivation of L. cremoris (Table S2, supplementary material), Model 5, which considered the effect of T, X, and dT/dt, showed the worst description both in fitting the data from six experiments and in predicting the data from two separate experiments (R 2 of 0.9133 and 0.8755, respectively).Compared to the description results of L. rhamnosus GG, the trends given by the six models on the inactivation of L. cremoris showed considerable discrepancy at each drying condition, for example, in Fig. S1B, S1E, S1F, S2A, and S2B (supplementary material).
The goodness-of-fit of each model in describing the inactivation processes of L. rhamnosus GG and L. cremoris was analyzed with the Akaike information criterion (AIC), as shown in Table 5 and Table S2 (supplementary material).For the inactivation of L. rhamnosus GG (Table 5), the incorporation of -dX/dt, which was a rate parameter, in Model 3 led to a perceptibly lowered AIC value (-188.50)compared to Models 1 and 2 which only considered the effects of T and X (-181.27and-178.21,respectively), indicating a better fit.The incorporation of more drying kinetics parameters in Models 4, 5, and 6 slightly increased the AIC value by 3-5.In general, the AIC values of the six models were in a similar range between À188.50 and À178.21, although the number of model parameters varied from 2 to 5 (Table 5).For the inactivation of L. cremoris, the lowest AIC values were observed with Models 1 and 2 (-382.45 and À382.46, respectively; Table S2, supplementary material).With the increase in the number of drying kinetics parameters, the AIC values gradually increased, indicating the penalty of AIC on the number of variables.Models 1-4 and 6 showed AIC values in a similar range between À382.46 and À360.58, whereas Model 5 gave the highest AIC of À319.64, indicating the worst fitting in describing the inactivation processes of L. cremoris.
Two criteria may be helpful in developing a suitable model to describe the inactivation of microorganisms.First, the parameters in the model should be interpretable with clear biological or physical meanings, and second, it should be capable of describing multiple inactivation processes under varying conditions using one set of parameters. [31]Apart from the    2.
first-order kinetics model coupled with the activation energy theory used in the present study, the Weibull distribution model is another widely utilized inactivation model. [32]The Weibull model considers the inactivation of bacterial populations as the cumulative result of the distribution of lethal events, namely the inactivation of individual bacterial cells with varying stress resistance in the population.The model with an empirical nature has been successfully applied in describing a variety of inactivation processes during both thermal and nonthermal processes. [33,34]urthermore, when the heat treatment is non-isothermal, the temperature history experienced by the bacteria can be correlated to model parameters to improve the accuracy of the description. [35]onetheless, during a dynamic drying process, bacterial cells experience dramatic changes in both environmental temperature and moisture content.The Arrhenius-type equations in Table 1 show high flexibility in incorporating kinetic parameters including the rates of change.
In a previous study, the survival of the spores of Bacillus thuringiensis after spray drying was correlated to the inlet and outlet temperatures of the spray dryer, respectively, using the Arrhenius equation. [36]Since the size and geometrical structure of spray dryer vary considerably from dryer to dryer, the survival of LAB could show remarkable differences when different dryers are used, even with the same inlet and outlet temperatures.In the present study, the droplet temperature is used to accurately capture the effect of temperature history experienced by LAB cells during convective droplet drying, and the histories of other kinetic parameters have also been taken into account.
The results in Figure 2, 3, S1, and S2 (supplementary material) validated the reasonableness of such modifications, namely, using droplet temperature instead of drying air temperature to develop the inactivation model.Since the goodness-of-fit and goodness-ofpredication were similar regardless of the form of kinetic inactivation models, all six models for the inactivation of L. rhamnosus GG were coupled to the CFD model of spray drying process using parameters summarized in Table 5.

Description of the inactivation process of L. rhamnosus GG during spray drying using kinetic inactivation models
The verification of CFD simulation to the experimental process of the microfluidic jet spray dryer was first carried out on the flow field without the injection of atomized droplets.Three outlet temperatures of 58, 63, and 68 C were tested, achieved with inlet temperatures of 106, 118, and 134 C, respectively (Figure 1b).The predicted temperatures at the location of thermocouple placement well matched the measured values under all three conditions.Then particles that simulated atomized droplets were injected into the flow field using the DPM model, with initial conditions shown in Table 4.The major constitute in the droplets was the protectant for LAB cells, namely RSM, with three initial solid contents of 10, 20, and 30 wt%, respectively.Four spray drying conditions were studied: three initial solid contents at an outlet temperature of 58 C and the initial solid content of 20 wt% at 63 C (Table 4).After the state of injected droplets reached steady, their temperature, moisture content, diameter, and residence time profiles along the axis of the simulated spray dryer are shown in Figure 4.As the droplets traveled from the top inlet to the bottom outlet of the dryer, their temperature histories can be characterized with different drying stages (Figure 4a).In the spray drying of 10 wt% droplets at 58 C, a pre-heating stage, a wet-bulb temperature range, a rapid heating stage, followed by a temperature-decreasing stage were observed. [24]With the increase in solid content, droplet temperature started to rise at the wet-bulb temperature range, and no wet-bulb stage was observed for the drying of 30 wt% RSM droplets at 58 C. Increasing the outlet temperature from 58 to 63 C resulted in an upward shift of the droplet temperature curve for the drying processes with 20 wt% RSM.The decrease in droplet temperature at the later drying stage was because droplet temperature reached the temperature of the flow field, and then decreased with the decline in the field temperature as the droplets approached the outlet.The decrease in the field temperature at the later drying stage mainly arose from the heat loss of the spray dryer.The droplet temperature profiles in general resembled those reported by Rogers et al., [37] which were calculated using onedimensional modeling for the spray drying of RSM.At 58 C, RSM droplets with 10 wt% solids experienced the highest peak temperature, which was attributed to the lowest mass content as reflected in Figure 4c. [37]he decrease in the moisture content of 10 wt% droplets became minimal at around 2.5 m from the top of the dryer, whereas that of 20 and 30 wt% droplets continued till the bottom outlet at the same outlet temperature (Figure 4b).Gong et al. took samples from the different heights of a spray dryer, and found that a significant loss of LAB viability (>90%) occurred when the droplet moisture content was lower than 0.31 kg/kg, associated with substantial damages on cellular membrane. [20]At 58 C, the moisture content of atomized droplets reached lower than 0.31 kg/kg at around 1.8-1.9m of the spray dryer, irrespective of the different initial moisture contents (Figure 4b).Nevertheless, the residence time of 30 wt% droplets was remarkably shorter than that of droplets with lower solid contents (Figure 4d).The shortened exposure time to a high-temperature environment may help retain the viability of LAB cells, making 30 wt% RSM potentially a more effective protectant than 10 and 20 wt% RSM.Increasing the outlet temperature from 58 to 63 C led to perceptibly faster moisture removal and correspondingly faster droplet shrinkage during spray drying (Figure 4b and c).The moisture content of droplets at the outlet of the simulated spray dryer was compared to the corresponding experimental value of spray dried particles in Figure 5.The experimental trends were correctly described, and the predicted values were similar to the experimental moisture content of LAB powders for all four conditions tested.The results verified the reliability of the simulated drying kinetics.
Figure 6 presented the inactivation profiles of L. rhamnosus GG, which were calculated by coupling the six inactivation models in Table 1 to the droplet drying kinetics in Figure 4 for each drying condition.The six models generated distinct inactivation profiles for each spray drying process, contrasting the similar trends given by different models in the single droplet drying experiments (Figures 1 and 2, Figure S1, S2, supplementary material).Significant loss of the viability of L. rhamnosus GG was only observed with Model 6, which not only considered the effects of T and X, but also took the corresponding rates of change into account (dT=dt and ÀdX=dt).At the initial stage of drying, the viability of the bacteria was maintained at the initial level for a short period (Figure 6), which was a similar trend to the single droplet drying experiments.As drying progressed further, bacterial viability started to decrease.The drying process with 30 wt% skim milk as the protectant at 58 C showed the earliest decrease in bacterial viability.Nevertheless, it gave the highest survival of 37.31 ± 21.90% at the outlet of the drying tower (Figure 6c), which was very close to the experimental value (33.94 ± 17.97%).Model 6 also accurately described the survival of L. rhamnosus GG in spraydried powders when 10 and 20 wt% RSM were used as protectants at 58 C, respectively (14.15 ± 14.33% and 25.69 ± 19.88%, respectively; Figure 6a, b).At a higher temperature of 63 C, the predicted survival by Model 6 at the spray dryer outlet (10.24 ± 12.54%) was marginally lower than the experimental result (19.77 ± 3.12%).Nevertheless, the prediction accuracy was still much better than that of the other five models, which substantially overestimated the residual viability of L. rhamnosus GG at the outlet (Figure 6d).
With Models 1-5, the degree of overestimation of bacterial survival varied with the form of the inactivation model (Figure 6).The viability curves calculated with Models 1 and 2 barely showed any downward trend throughout the drying process, with survivals higher than 98% at the outlet under all four drying conditions.Model 3 which considered the effect of T and -dX/dt and Model 5 which considered the effect of T, X, and dT/dt gave slightly higher deactivation; however, the residual viability remained greater than or equal to 95%.Involving T, X, and -dX/dt as parameters, the viability curves predicted with Model 4 showed a descending trend from the middle section of the drying tower, with residual viability between 73% and 82% as affected by drying conditions.Models containing fewer drying kinetics parameters tend to have higher values of activation energy E d (Table 5, Table S2, supplementary material), suggesting a relatively slow reaction rate and an increased difficulty for the inactivation reaction to occur.The trends in Figure 6 highlighted the importance of the rates of change in accurately describing the inactivation of LAB cells during a rapid dehydration process such as spray drying.
The different capacity of the six models to describe the inactivation of L. rhamnosus GG during spray drying was double-checked using one-dimensional modeling, which assumed that the spray dryer was a 1-D plug-flow reactor. [38]Similar to the trends in Figure 6, only Model 6 accurately predicted the survival of L. rhamnosus GG at the outlet of the spray dryer, whereas the other five models all overestimated the residual viability of the bacteria (data not shown).For Models 2-5, the predicted survivals of spray-dried LGG calculated using 1-D modeling and using CFD showed differences between 3.5% and 25% at the outlet, while the viability curve predicted with Model 1 using 1-D modeling was maintained approximately at the initial value throughout the spray drying process.In the study of George et al., [38] the 1-D modeling provided a reasonable description to the moisture content of skim milk particles produced using a microfluidic jet spray dryer.Perdana et al. modeled the inactivation processes of Lactobacillus plantarum WCFS1 in a pilot-scale spray dryer, assuming that the dryer was an ideal-mixed system and a plug flow system, respectively. [39]It was suggested that the actual drying profile should be between the two ideal cases. [39]In the present study, both CFD modeling and 1-D modeling demonstrated the better capacity of Model 6 in describing the inactivation of L. rhamnosus GG under wider dehydration conditions in comparison to Models 1-5.
Models 1-5 which were capable of describing the inactivation process of LAB during single droplet drying gave poor predictions about the survival of LAB after spray drying.The discrepancy might be linked to the difference in the rates of change between the two processes, which was up to 1-2 orders of magnitude.With 10 and 20 wt% RSM as the protectant, the time of drying during single droplet drying at 70 and 90 C was between 200 and 400 s, giving averaged drying rates of 0.011-0.044kg/kg/s.By contrast, the residence time of atomized droplets in spray drying ranged between 7 and 11 s (Figure 4d), with averaged drying rates up to 0.31-0.81kg/kg/s.The detrimental effects of the rates of change on LAB cells may be reasonably neglected in single droplet drying because of the low values, whereas in spray drying such effects could become critical, with such a high drying rate and the corresponding high rate of temperature change.The remarkable difference in both the time scale and the rates of change between single droplet drying and spray drying could be linked to the different initial sizes of the drying droplet (1.28-1.56mm in single droplet drying and 155 mm in simulated spray drying).
Comparing the inactivation curves between Models 4, 5, and 6 in Figure 6, both dT/dt and -dX/dt appeared indispensable to the accurate description of LAB inactivation during spray drying, which could be related to the simultaneous heat-and mass-transfer nature of drying.Bacterial cells that contain complex cellular structures and a high intracellular water content could be sensitive to rapid changes in environmental conditions.Rapid dehydration may cause a large moisture content gradient across the cellular membrane, substantially increasing the level of osmotic stress exposure on cells. [18]Similarly, a large temperature gradient caused by rapid heating may also be detrimental to cellular integrity and biological functions. [40]ploring the temporal and spatial changes for the inactivation of L. rhamnosus GG during spray drying The dryer-wide simulation is capable of generating a large amount of data at intermediate drying stages, which are crucial to a better understanding of spray drying behavior and are difficult to monitor experimentally.First, the drying behavior before the injected droplets reached a steady state was studied.After a spray drying process was started, the initially injected droplets flew in the co-current hot airflow while the contained water was removed, reaching the bottom outlet of the dryer as dried particles in around 7-11 s (Figure 4d).The evaporation of water from the droplets lowered the temperature and increased the humidity of the flow field, which further impacted the evaporation behavior of subsequently injected droplets.To understand how the multiphase flow reached a steady state under different drying conditions, the temperature, moisture content, and survival profiles of atomized droplets at 10, 30, 60, 90, and 120 s after spray drying was started were compared in Figure 7.At the same outlet temperature of 58 C, the three solid contents demonstrated distinct behaviors, despite the same initial droplet size of 155 mm and the same mass spray rate of 2.2 Â 10 À5 kgÁs À1 .At 10 s after spray drying was started, the droplet temperature of 10 wt% RSM soared to 341 K following the web-bulb temperature range at around 305-308 K (Figure 7a).Heat transfer from the continuous gas phase to the evaporating droplets and the low temperature of injected droplets (298 K) lowered the temperature of the gas phase, which further led to a decrease of the peak temperature that the droplets could reach as spray drying was continued for a longer time.After spray drying was continued for 30 s, the droplet temperature curve was substantially lower than that of 10 s, with a difference larger than 15 K in peak temperature.The steady state was reached by 60 s of spray drying, as indicated by the overlapping temperature curves (Figure 7a).The difference in moisture content curves became negligible at 30 s after spray drying was started (Figure 7b).The survival of L. rhamnosus GG at the outlet significantly increased from 0.06% at 10 s to 14.01% at 60 s, showing a difference of larger than two orders of magnitude (Figure 7c).The survival curve reached steady after 60 s rather than 30 s, indicating the dominating effect of droplet temperature on bacterial viability.
With the increase in the solid content of the protectant, atomized droplets took a longer time to reach the steady state in the continuous gas phase (Figure 7d-i).Since the flow field was kept identical for the three conditions before the injection of droplets, the difference may likely be linked to hindrance to mass transfer by the high solids.In the drying process with 30 wt% solids content, a minor difference was observed between the survival curves after 90 and 120 s (Figure 7i).The use of a higher drying temperature of 63 C accelerated water removal from atomized droplets and led to higher inactivation of L. rhamnosus GG than the drying process at 58 C (comparing Figure 7l and f).Nevertheless, with the same initial solids content of 20 wt%, the shift of the temperature and moisture content profiles in the initial 120 s of spray drying was similar for the drying LAB cells were found sensitive to drying kinetics in that a minor difference in drying kinetics could give rise to significant variations in the viability, membrane integrity, and digestive stability of dried bacteria; in the meantime, other particle properties such as particle morphology and rehydration behavior remained similar. [5]The sensitivity of LAB was supported by the varying survival curves in Figure 7c, f, i, and l, showing differences in viability for more than two orders of magnitude within the initial 2 min of spray drying.In the industrial production of common bioactive materials, a short unstable period at the beginning of spray drying is often negligible since the drying process often continues for hours.Nonetheless, the significantly lower viability of probiotics powder produced during the unstable period is disadvantageous to the quality of active probiotics products.It is probably better to separate the powders with low viability retention from those produced during the steady state period.
Next, the extent of the uniformity of LAB survival at the steady state was investigated (Figure 8 and 9).The simulated spray drying processes replicated the experimental processes of a microfluidic jet spray dryer, in which monodisperse droplets were dehydrated in optimized air dynamics to produce particles with identical size, morphology, and properties. [25,41]rom the simulation, the flying droplets demonstrated noticeable variations in the survival of L. rhamnosus GG in the middle section of the spray dryer (Figure 8).As the droplets flew toward the bottom outlet, the decrease in the viability of L. rhamnosus GG was first observed for droplets close to the wall of the dryer.Droplets at the center region maintained high viability till a later drying stage, as indicated by the gradually diminishing red and orange dots along the axial direction of the spray dryer (Figure 8a-d).The trend was in correspondence with the lower droplet temperature and higher moisture content shown by the droplets at the center region when they reached the middle section of the dryer (Figure 9).The relatively uneven distribution of droplet properties and L. rhamnosus GG survival in the cross-section may likely be linked to the degree of crowding of droplets.After injection, the stream of droplets quickly dispersed to achieve a more efficient mixing with the co-current airflow.Nevertheless, the center region concentrated a higher number of droplets, as can be seen from the bottom view of the simulated spray dryer (Figures 8 and 9).Such a flow pattern of droplets may help reduce wall deposition and thus improve the yield of spray-dried particles.As droplets approached the outlet, the difference in droplet properties became minimal, as reflected by error bars in Figure 4a-c.In future studies, further improvement in the similarity of the drying histories of atomized droplets may be achieved by optimizing the mixing behavior of droplets and hot air.
Compared to the curves in Figure 4a and b, the dot plots in Figure 9 provided additional information on the drying behavior of atomized droplets.The three moisture content curves of 10, 20, and 30 wt% RSM at 58 C in Figure 4b showed substantial differences because of the different initial moisture contents.Nevertheless, when changes in moisture content were normalized to the same color scale, the trends of the decrease in particle moisture content were relatively similar between the three drying processes (Figure 9e-g).
A significant decrease in the viability of L. rhamnosus GG was observed at the bottom half of the drying tower when 10 wt% RSM was used as the protectant at 58 C, as indicated by the large number of dark blue dots in Figure 8a.The extent of inactivation was lessened with 20 wt% RSM (Figure 8b).The drying process of 30 wt% RSM showed a remarkably lower degree of inactivation than that with 10 and 20 wt% RSM (Figure 8c).The trend was in agreement with the report of Ghandi et al., [42] which showed that the protective effect of a composite protectant increased as solid content was increased from 10, 25, to 35 wt% in the spray drying of L. cremoris.These results indicated that the relatively mild kinetics of temperature change and moisture content change given by a protectant of a high solid content is advantageous to the preservation of bacterial viability through spray drying.
Previous studies attempted to model the inactivation of spray-dried LAB cells using various approaches.Empirical modeling, such as response surface methodology, has been used to correlate the survival of LAB to the operation conditions of the specific spray dryer. [43,44]or describing changes in the viability of LAB inside a spray dryer, Perdana et al. utilized a modeling software pack entitled DryProf to model droplet drying kinetics based on the effective diffusion concept. [45]The retention of the viability of LAB was calculated using the Weibull model.Optimal spray drying conditions with LAB residual viability larger than 80% were recommended as small initial droplet size, hollow particle morphology, low outlet temperature, and an ideal-mixed dryer system. [45]Menshutina et al. combined mass, momentum, and energy conservation equations for the gaseous and dispersed phases to model a spray drying process, and the loss of the viability of Bifidobacterium bifidum caused by thermal stress was described using the standard Arrhenius equation as shown in Equation ( 2). [46]The present study demonstrated that the incorporation of the rates of temperature and moisture content change in the inactivation model allows the model to be used under wider drying conditions, including both slow and rapid droplet drying.In addition, CFD simulation enabled investigations on the variation of LAB viability with the time of spray drying and the distribution of LAB viability inside the spray dryer.

Conclusions
This study proposed a model that can accurately describe the inactivation process of L. rhamnosus GG, a model LAB strain, during both single droplet drying and spray drying.The inactivation profile of L. rhamnosus GG inside a spray dryer was monitored, by coupling the proposed inactivation model to the drying kinetics of a microfluidic jet spray dryer on the ANSYS FLUENT platform.A total of six inactivation models were tested, all in the form of Arrhenius-type equations but considering different combinations of drying kinetics parameters, namely, droplet temperature (T), moisture content (X), the rate of temperature change (dT/dt), and drying rate (-dX/dt).All six models well described the inactivation process of L. rhamnosus GG during single droplet drying, a comparatively slow drying process analogous to spray drying.By contrast, only Model 6 which incorporated all four parameters accurately predicted the survival of L. rhamnosus GG in spray-dried particles.The results highlighted the importance of the rates of temperature and moisture content change on the viability of LAB cells in the rapidly changing droplet environment during spray drying, with average drying rates of 0.31-0.81kg/kg/s.The successful modeling of the inactivation process of LAB allowed the quantitative analysis of the temporal and  The proposed inactivation model is potential to be applied in other types of spray dryers through coupling with the drying kinetics of the specific dryer.Since the model was developed with a limited number of single droplet drying experiments, future studies may work on the optimization of the model to further improve the accuracy of prediction.

DE v
The apparent activation energy of evaporation (J/mol) DH l The specific enthalpy of water evaporation (J/kg) RTT, X, dT dt , À dX dt Ã C refers to the survival of bacteria (N/N 0 ), and the subscript d represents deactivation.

Figure 1 .
Figure 1.(a) The schematic of microfluidic jet spray dryer used to produce L. rhamnosus GG powder in the current study (not to scale in mm); (b) comparison of the temperature profile of flow field in the CFD simulation to the experimental values measured by four thermocouples placed in the spray dryer.

Figure 2 .
Figure 2. The description of the inactivation process of L. rhamnosus GG during four single droplet drying processes, by Models 1-6 incorporating optimal parameters in Table 5. (a-d) The survival of L. rhamnosus GG plotted on a normal scale; (A-D) the viable cell count of the bacteria plotted on a logarithmic scale.(a, A) Trial 1, (b, B) Trial 2, (c, C) Trial 4, and (d, D) Trial 5 in Table2.

Figure 3 .
Figure 3.The validation of optimal parameters for each inactivation model, by comparing model prediction to the results of single droplet drying experiment No. 3 in Table 2. (a) The survival of L. rhamnosus GG plotted on a normal scale; (b) the viable cell count of the bacteria plotted on a logarithmic scale.

Figure 4 .
Figure 4. Changes in the physicochemical properties of L. rhamnosus GG-containing droplets along the axial direction of spray dryer, after flow field reached steady state in the CFD simulation.Error bars refer to the standard deviation of 2000 particles collected at the individual cross section.(a) Droplet temperature; (b) the moisture content of droplet; (c) droplet diameter; (d) residence time.For the outlet temperature of 58 C, the protectant of 10, 20, and 30 wt% RSM was used, respectively.For the outlet temperature of 63 C, the protectant was 20 wt% RSM.

Figure 5 .
Figure 5.Comparison of the predicted moisture content of L. rhamnosus GG particles at the outlet of spray dryer to experimental results.Error bars of CFD data refer to the standard deviation of 2000 particles collected at the outlet plane.The temperatures of 58 and 63 C referred to the outlet temperature of spray dryer.

Figure 6 .
Figure 6.The inactivation process of L. rhamnosus GG along the axial direction of spray dryer in the CFD simulation, predicted by coupling Models 1-6 to the drying kinetics in Figure 4. (a) Using 10 wt% RSM as protectant at the outlet temperature of 58 C; (b) using 20 wt% RSM as protectant at the outlet temperature of 58 C; (c) using 30 wt% RSM as protectant at the outlet temperature of 58 C; (d) using 20 wt% RSM as protectant at the outlet temperature of 63 C.

Figure 7 .
Figure 7. Changes in (a, d, g, j) the temperature of droplets, (b, e, h, k) the moisture content of droplets, and (c, f, i, l) the survival of L. rhamnosus GG along the axial direction of spray dryer, before the flow field reached steady state.(a-c) Using 10 wt% RSM as protectant at the outlet temperature of 58 C; (d-f) using 20 wt% RSM as protectant at the outlet temperature of 58 C; (g-i) using 30 wt% RSM as protectant at the outlet temperature of 58 C; (j-l) using 20 wt% RSM as protectant at the outlet temperature of 63 C.

Figure 8 .
Figure 8.The spatial distribution of the survival of L. rhamnosus GG at the steady state from the front view and bottom view.(a) Using 10 wt% RSM as protectant at the outlet temperature of 58 C; (b) using 20 wt% RSM as protectant at the outlet temperature of 58 C; (c) using 30 wt% RSM as protectant at the outlet temperature of 58 C; (d) using 20 wt% RSM as protectant at the outlet temperature of 63 C.

Figure 9 .
Figure 9.The spatial distribution of (a-d) the temperature of droplets and (e-h) the moisture content of droplets at the steady state from the front view and bottom view.(a, e) Using 10 wt% RSM as protectant at the outlet temperature of 58 C; (b, f) using 20 wt% RSM as protectant at the outlet temperature of 58 C; (c, g) using 30 wt% RSM as protectant at the outlet temperature of 58 C; (d, h) using 20 wt% RSM as protectant at the outlet temperature of 63 C.

Table 1 .
Arrhenius equation and modified Arrhenius equations describing the inactivation of lactic acid bacteria during convective drying.
as the target function, where i is the index of sampling time instant and h is the set containing model parameters, a, b, and c.The experimental data used to develop the parameters for each model are from four single droplet drying conditions (Trial 1, 2, 4, and 5 in Table2), with varying initial droplet size (1 or 2 mL), initial solids content (10 or 20 wt%), drying air temperature (70 or 90 C), and airflow velocity (0.45, 0.75, and 1 m/s).The obtained a, b, and c values are employed to predict the survival of L. rhamnosus GG for a separate single droplet drying condition (Trial 3 in Table

Table 2 .
Experimental conditions used in the single droplet drying of L. rhamnosus GG, with reconstituted skim milk (RSM) as protectant.

Table 3 .
Boundary conditions of the spray drying chamber in the CFD simulation.

Table 5 .
Optimal parameters for Models 1-6 to describe the inactivation of L. rhamnosus GG during convective droplet drying.Fitting performance refers to the comparison between model description and the experimental results of single droplet drying experiments No. 1, 2, 4, and 5 in Table 2.After the model parameters were determined with the four experiments, the prediction performance of each model was examined by comparing the model description and experimental results of single droplet drying experiment No. 3.

Table 4 .
Initial conditions of skim milk droplets containing L. rhamnosus GG for injection to the spray drying chamber in the CFD simulation, and the experimental survival of the bacteria and the moisture content of powders after spray drying under different conditions.
Surface area (m 2 ) CA given quality attribute of food material, herein the survival of lactic acid bacteria (N/N 0 )