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Ohmic heating of blended citrus juice: Numerical modeling of process and bacterial inactivation kinetics
Innovative Food Science and Emerging Technologies 52 (2019) 313–324
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Innovative Food Science and Emerging Technologies journal homepage: www.elsevier.com/locate/ifset
Ohmic heating of blended citrus juice: Numerical modeling of process and bacterial inactivation kinetics
T
Seyed Mohammad Bagher Hashemia, , Reza Roohib ⁎
a b
Department of Food Science and Technology, College of Agriculture, Fasa University, Fasa, Iran Department of Mechanical Engineering, Fasa University, Fasa, Iran
ARTICLE INFO
ABSTRACT
Keywords: Foodborne bacteria Ohmic heating Weibull model Modified Gompertz model Inactivation
A comprehensive 3D, transient-free convection, and multiphase model was developed to determine the performance of ohmic heating (150, 200 and 250 V; 120 s; 99.4 °C) and conventional heating (90 °C; 15 min) for the inactivation of Escherichia coli, Staphylococcus aureus, Salmonella enterica subsp. enterica serovar Paratyphi A, Salmonella Typhi, Shigella dysenteriae, and Shigella flexneri in blended citrus juice (sweet lemon and orange). Results indicated the computed temperatures were in good agreement with the experimentally measured data (below 5% deviation). The examination of velocity and temperature patterns throughout the computational domain explained the reasons for significant differences between the conventional and ohmic heating process. The homogeneously distributed vortices in ohmic heating lead to a more uniform and rapid temperature rise in temperature (from 26 to 99.4 °C) while compared with the conventional method with a stratified flow pattern. Based on the evaluation of temperature rise, increasing in the applied voltage from 150 to 250 V was deducted to reduce the inactivation time about 20–30% for the investigated pathogens. The inactivation rate of pathogens during ohmic heating process was maximum for S. aureus, followed by E. coli, S. enterica subsp. enterica serovar Paratyphi A, S. Typhi, S. dysenteriae and S. flexneri. In conclusion, the developed numerical modeling can be conveniently applied to simulate and predict the ohmic heating for the inactivation of pathogenic bacteria. Industrial relevance: Several thermophysical phenomena affect the optimization and design of ohmic heating systems such as heat and mass transport as well as electrical field distribution. The implementation of the computational fluid dynamics (CFD) method is an efficient and economical technique that can provide valuable data for researchers. Moreover, the determination of off-design thermal spots, heat-loss magnitude and apparatus efficiency can be determined via numerical calculations.
1. Introduction Pasteurization as a thermal processing technique has been applied for inactivation of pathogenic and spoilage microorganisms to ensure safety and extend shelf-life of a diversity of foods. However, the novel thermal technologies compared to the traditional thermal treatments enhance retention of nutrients, texture, color and flavors of food products. Therefore, the development of novel thermal process technologies has attracted notable attention over last decades (Hashemi, Mousavi Khaneghah, Fidelis, & Granato, 2018; Pereira & Vicente, 2010). Ohmic heating can be used as an effective thermal processing for consistently heating of food products by the passage of electric currents through food matrices. Thus, ohmic heating can circumvent the limitations of conventional pasteurization by using electricity (Hashemi
⁎
et al., 2017; Tavakolpour et al., 2017). However, understanding of the ohmic heating process for pasteurization of food products is crucial in order to guarantee the safety and suitability of the process. In this context, a vast number of models have been applied to explain nonlinear microbial inactivation kinetics, such as the modified Gompertz equation, the Weibull distribution function and the log-logistic model (Siguemoto, Gut, Martinez, & Rodrigo, 2018; Wang, Hu, & Wang, 2010). For instance, the Weibull model has been used for the modeling of the inactivation of Alicyclobacillus acidiphilus treated with high hydrostatic pressure (Buzrul, Alpas, & Bozoglu, 2005). However, no model regarding kinetics of inactivation of pathogenic bacteria in citrus juice by ohmic heating is available. The numerical simulation of applied methods in food processing has gained considerable attention due to their accuracy and efficiency, as well as the economical aspects in comparison with experimental
Corresponding author. E-mail address: [email protected] (S.M.B. Hashemi).
https://doi.org/10.1016/j.ifset.2019.01.012 Received 4 December 2018; Received in revised form 10 January 2019; Accepted 22 January 2019 Available online 23 January 2019 1466-8564/ © 2019 Elsevier Ltd. All rights reserved.
Innovative Food Science and Emerging Technologies 52 (2019) 313–324
S.M.B. Hashemi, R. Roohi
examinations (Fryer, Knoerzer, & Juliano, 2011; Kiani, Karimi, Labbafi, & Fathi, 2018; Norton, Tiwari, & Sun, 2013). The implementation of computational fluid dynamics (CFD) as a simulation approach, can provide insights regarding the several mutually affecting mechanisms in food procedures such as heat and mass transfer, chemical reactions, and flow turbulence (Caccavale, De Bonis, & Ruocco, 2016; Crilly & Fryer, 1993). The numerical simulation and modeling of ohmic heating has been performed by several investigations to evaluate the major aspects of ohmic heating process such as the generated temperature field, the effect of mixture electrical conductivity, the role of electrodes' sizing and their position inside the sample (Sastry & Palaniappan, 1992; Sastry & Salengke, 1998; Jun & Sastry, 2005; Davies & Fryer, 2001; Shim, Lee, & Jun, 2010; Gally, Rouaud, Jury, & Le-Bail, 2016). However, to the best of our knowledge, simulation of heat and mass transfer through ohmic heating of citrus juice process has not been examined. Hence, in the present study, the ohmic heating and heating processes for inactivation of pathogenic bacteria were numerically simulated with a 3D, laminar, and transient model and the results were compared with those using a conventional approach. Moreover, the mixture model was utilized for the multiphase flow, and the ohmic heating generation was simulated based on the calculation of the potential electrical field. The variations of temperature and velocity fields during the process were determined and compared to experimental data for ohmic heating and conventional methods. Additionally, two mathematical models (Weibull and modified Gompertz) were applied to the experimentally captured data set and the effect of utilized voltages on the inactivation of pathogens was investigated.
Ohmic treatments were carried out in a 1000-mL capacity laboratory-scale reactor at three voltages (150, 200 and 250 V). The reactor part included a Teflon chamber in cylindrical form (7-cm internal diameter and 25-cm length) and was prepared with two titanium electrodes. The fully automated system for the control of current (0–16) A, voltage (0–300) V, and temperature, allowed recording data through the experiment. For all samples, 600 mL of citrus juice was poured into the chamber and treatments were carried out for 120 s. Each one of the treatments was carried out in triplicate. 2.3. Microbial enumeration For microbial enumeration, 1-mL aliquots of each samples were serially diluted in 0.1% peptone water and 0.1 mL of proper diluents were spread plated onto each appropriate medium. Sorbitol Mac Conkey agar (PO0232, Oxoid, UK) and Baird-parker Agar (PO0168, Oxoid, UK) were used as appropriate media for the enumeration of E. coli and S. aureus, respectively. Nutrient agar (CM0003, Oxoid, UK) was used for other pathogens. All the plates were incubated at 37 °C for 24–48 h, colonies were counted. All tests were duplicate-plated and replicated three times (Hashemi, Amininezhad, Shirzadinezhad, Farahani, & Yousefabad, 2016). 2.4. Governing equations Several approaches were proposed to simulate the behavior of multiphase flows, namely Eulerian, mixture and volume of fluid (VOF) model (Ghiji, Goldsworthy, Brandner, Garaniya, & Hield, 2017). According to the mixture model, the conservation equations including continuity, momentum, and energy as well as volume fraction equation (for secondary phases) were considered. In addition, an algebraic expression was implemented to calculation of relative velocity of phases. On the other hand, based on the VOF model, the dynamics of several immiscible phases can be determined via the solution of a single momentum equation while the continuity equation was considered separately for each phase. Based on the Eulerian method, to calculate the domain characteristics the governing equations (i.e., continuity, momentum and energy equations) should be solved separately for each phase; however, a single pressure equation was assigned to all of the phases. Moreover, the interaction between phases was simulated using the calculated drag and lift forces (Mirmasoumi & Behzadmehr, 2008). Each model offers benefits as well as computational complexities. In the present study, the mixture model was chosen based on its capability for simulation of nearly uniform flows with a relative velocity of phases. The transient form of the mass conservation equation for the mixture of n phases is:
2. Materials and methods 2.1. Chemicals and microorganisms Escherichia coli PTCC 1399, Staphylococcus aureus PTCC 1764, Salmonella enterica subsp. enterica serovar Paratyphi A PTCC 1230, Salmonella Typhi PTCC 160, Shigella dysenteriae PTCC 1188 and Shigella flexneri PTCC 1865 were obtained from the Iranian Research Organization for Science and Technology, Tehran, Iran. All strains were reactivated in Mueller Hinton broth (CM0405, Oxoid, UK) and incubated at 37 °C overnight. All chemicals were of analytical reagent grade and purchased from Sigma (ST. Louis, MO). 2.2. Sample and treatments Sweet lemon and orange were purchased from a local market in Fasa city (Autumn of 2017), Fars province, Iran. Samples were washed and manually peeled. The juices were prepared by a domestic juicer (Pars Khazar, VITAFRUIT model, Gilan, Iran) under aseptic conditions. After mixing the juices (50:50 (v/v) %; pH 4.04 and 14.7°Brix), the blended citrus juice was transferred into sealed glass tubes. Then, the tubes were submerged simultaneously into the water bath (Fan Azema Gostar, WB 22, Tehran, Iran), which was maintained at 90 °C for 15 min. After cooling the tubes, each strain of pathogenic bacteria was inoculated separately into blended juice. Following reactivation of each strain in Mueller Hinton broth, cells were collected by centrifugation at 4000 ×g for 15 min. The supernatant was removed and 10 mL of 0.2% peptone water was mixed with the pellet to wash cells. Cells were centrifuged and the washing step was repeated. Following the washing step, the pellets were resuspended in blended juice to get the desired concentration of cells (~6–6.2 log CFU/mL). Approximately 600 mL of the blended citrus juice was poured in 1000-mL sealed glass tubes for conventional heating. Four tubes per test were immersed in a water bath under control temperature (75 °C for 30 min). A digital thermometer (106 Model, Testo, Germany) fitted to a reference tube was applied to measure the blended citrus juice temperature during the thermal examination. After thermal treatment, the tubes were quickly cooled.
t
(
m)
+
·(
m Vm )
=0
(1)
where ρm and Vm represent the mixture averaged density and velocity, respectively. Assume φk, as the kth phase volume fraction, ρm and Vm can be calculated using Eqs. (2) and (3):
Vm =
n k=1
k k Vk
(2)
m
m
=
n k=1
k k
(3)
The momentum equation of the mixture model is derived based on the summation of the momentum equation of each phase as: 314
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t
(
m Vm )
+
.(
m Vm Vm )
=
p+ + +
m mg
.
(
. [µm ( Vm + (T
diameter and outer fluid conductivity coefficient, respectively. Based on Eqs. (12) and (13) the convective heat transfer coefficient of the outer container walls is assumed to be a function of system geometrical and operational conditions. Additionally, RaD and Pr are the Rayleigh and Prandtl numbers defined as:
T
Vm )]
T0)
n k=1
k k Vdr , k Vdr , k
)
(4)
In Eq. (4), p, μm, T, and dr denote the pressure, mixture viscosity, matrix transpose and drift, respectively. βm is the volumetric expansion coefficient and can be calculated as: m
1
=
RaD =
k k
m
(5)
n
k µk
k=1
vdr , k = vk
(6) (7)
vm
The conservation of the energy equation has the following form:
t
(
n k=1
k k Ek
)+
n k=1
k vk ( k Ek
+ p) =
·(keff
T ) + Sohmi c (8)
where keff is the effective mixture conductivity, Ek is the kth phase energy and Sohmic is thermal heat source due to the ohmic heating. The ohmic heating is referring to the phenomena of heat generation due to the electrical passage through conductors with electrical resistivity (Davies & Fryer, 2001). It should be noted that the applied voltage can be altered, in this context; the electrical potential, current, and the generated power are time-dependent. The root means square value of these variables over time cycles were calculated and used in the energy equation. The electrical potential distribution is required to estimate the produced electrical current and consequently the generated thermal power as:
·(
To mathematically describe the variations of the pathogens' quantity as a function of time two commonly used models were selected.
where σ and Φ represent the electrical conductivity and potential, respectively. Hence, the current density (J) and the Sohmic can be estimated as:
1) The modified Gompertz model: The modified Gompertz model was acknowledged for its capability in the prediction of smooth curves (Chen & Hoover, 2003). This kinetic model has three tunable variables of C, B and M.
(10)
J= Sohmic =
J·J
(11)
log
2.5. Boundary conditions
h=
NuD ·k D
0.387RaD1/6 [1 + (0.559/ Pr )9/16]8/27
1012
C exp( exp( B × (t
M )))
(16)
The Weibull kinetic model is the general case of the linear model, in which the decreasing of the inspected parameter is assumed to have various rates during the process (Mafart, Couvert, Gaillard, & Leguérinel, 2002).
log
N = N0
bt n
(17)
where b and n are representatives of the scale and shape factor (the slope of the line in a probability plot), respectively.
2
, RaD
N = C exp( exp(B × M )) N0
2) The Weibull model:
To determine the flow and thermal fields, the governing equations should be solved accompanied by a proper set of boundary and initial conditions. For the momentum equation the no-slip condition was assigned to all of the domain wall boundaries. The wall boundaries were defined as the system surfaces where the fluid phase was in contact with the solid domain. Moreover, as the outer container walls were in contact with surrounding air (for ohmic heating) and water (for the conventional case), the appropriate convection heat transfer coefficient was applied as (Churchill & Chu, 1975):
NuD = 0.6 +
(15)
2.6. Statistical simulation of pathogens
(9)
)=0
(14)
In addition to the container's outer walls, the adiabatic (zero heat flux) boundary condition was set at other domain walls (i.e., the electrode's walls). It should be noted that regarding the insulation applied at the electrodes connection point to the containers caps, the adiabatic boundary condition is valid. For the electrical potential equation, constant values were assigned to the anode and cathode electrodes, while the zero gradient boundary condition was set for the other boundaries. It should be noted that constant voltage values were referred to the amplitude of the applied voltage and instantaneous apparatus voltage varied as a sinusoidal function during the time. The initial conditions were determined based on the system properties before the exposing to ohmic system. Hence, the field temperature was set to be 26 °C, phases were assumed to be stagnant (zero velocity) and the domain electrical potential was set to zero. The water level was also calculated and set based on the volume of the liquid initially placed in the container, while the rest of the container was filled with air. The governing equations were solved numerically using the open source code program of OpenFOAM. The numerical simulation was performed with the aid of a computer system with following characteristics: Intel Core i7 [email protected], 16 GB of DDR4 RAM. Each simulation was converged in about 16 h to the final results.
Due to the small values of velocity magnitude, the flow field is assumed to be laminar. Mixture viscosity (μm) and drift velocity (the difference between phase and averaged mixture velocity), vdr , k , can be obtained using:
µm =
TD3
Pr =
n k=1
g
2.7. Mathematical model accuracy evaluation
(12)
Two main measures were utilized to assess the accuracy of the fitted correlations, adjusted R2 and RMSE:
(13)
where in the above equations, h , NuD , D and k are the averaged convection heat transfer coefficient, averaged Nusselt number, cylinder
Adjusted R2 = 1
315
(n
i)(1 R2) n p
(18)
Innovative Food Science and Emerging Technologies 52 (2019) 313–324
S.M.B. Hashemi, R. Roohi
(a)
(b)
(c)
(d)
Fig. 1. Schematic of geometry (a: ohmic heating, b: conventional method) and computational domain grids (c: overall grid's view and d: internal cell distribution via sectioned view).
where n indicates the number of the measured data, p is the number of parameters and i as the indicator variable with the value of 1 for happening of an intercept in the model and 0 for other situations (Diels, Wuytack, & Michiels, 2003). Moreover, RMSE is a measure of the average difference between the estimated and observed data as:
RMSE =
(observed predicted )2 n 1
To assure the sufficiency of the number of utilized cells, the grid independence test was carried out for three unstructured grids with the amount of 880,457, 930,876 and 1,102,635 computational cells. Based on the effect of cell numbers on the velocity profile at the center of the container and the computational cost, the grid with the medium number of cells (930,876) was selected, and the hereafter results were obtained based on the mentioned grid.
(19)
2.9. Solution method The governing equations including the conservation laws of mass, momentum, energy, electrical potential and drift velocity of phases were solved simultaneously to determine the flow and thermal fields' characteristics. To do so, a transient, laminar and multiphase CFD code was employed. The SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm was implemented for pressure-velocity coupling. Besides, the central and second-order upwind schemes were applied for the discretization of diffusive and convective terms, respectively. The convergence criteria for mass, momentum, energy and electrical potential equations were set to 10−4, 10−5, 10−6 and 10−8, respectively.
2.8. Geometry and computational grids The assumed geometry was based on the actual configuration of the inactivation apparatus. The container for both cases of ohmic inactivation and conventional method was a cylinder with an internal diameter of 7-cm and 25-cm in height. Besides, for the ohmic process, two electrode rods with diameter and length of 1 cm and 2.5 cm were added to the left and right sides of the container (Fig. 1a and b). The created geometry should be divided into several small control volumes (computational cells), and the discretized form of the governing equation was solved consequently. Thus, the quality and quantity of the utilized grids had a significant effect on the CFD simulation results accuracy and computational cost. In the present investigation, the grids density was increased near the zones with a higher gradient of variables, i.e., zones beside the walls, at the interface between phases and around the electrodes. Moreover, to determine the flow behavior inside the boundary layers near the walls, five layers of structured grids with gradually increasing height was implemented at the device walls (Fig. 1c and d).
3. Results and discussion The fact that the ohmic heating is better than conventional methods for the inactivation process was well demonstrated in several previous studies (Pereira & Vicente, 2010). However, the physical background of ohmic heating and conventional methods as well as the impact of operating conditions on the velocity and thermal fields were listed as the main goals of the current study. In other words, the pathogens 316
Innovative Food Science and Emerging Technologies 52 (2019) 313–324
S.M.B. Hashemi, R. Roohi
(a)
(b)
(c)
(d)
Fig. 2. The velocity (a) and temperature (b–d) contours: a) t = 30 min, b) t = 10 min s, c) t = 20 min s and d = 30 min for conventional method.
Fig. 3. The electrical potential distribution at various planes for ΔV = 200 v for ohmic heating process. 317
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(a)
(b)
(c)
(d)
Fig. 4. The velocity magnitude contours at various time instances: a) t = 25 s, b) t = 45 s, c) t = 60 s and d = 90 s for ohmic heating process.
inactivation is due to increase in temperature and the numerical simulation was dealing with the determination of temperature throughout the domain. Therefore, the temperature field was the common link between the simulation and the inactivation process. The numerical modeling was used to describe the reasons of establishment of a more rapid and uniform temperature rise during ohmic heating in comparison to the conventional method. Moreover, developing numerical models for heating and inactivation processes (which both were done in the present study in addition to the experimental data) with high accuracy, aids to determine the inactivation process outputs using merely theoretical simulations.
and ohmic inactivation experiments. The results of the conventional modeling are illustrated in Fig. 2. The container with a specified amount of liquid was placed inside a Bain-marie bath and heat was transferred to the mixture from the surrounding walls due to the temperature difference between the fluids on both sides of the container walls. As the temperature in the container liquid zone (the lower part) was slightly higher near the walls, the upward liquid stream was observed due to the density reduction and the buoyancy force (Fig. 2a). The time history of temperature variations is depicted in Fig. 2b to d at some internal planes. According to the lower value of the specific heat capacity of the gas phase (upper zone) in comparison to the liquid phase (lower zone), the temperature level was more elevated in the gas containing zone. The gas phase (evaporated liquid) formation was initiated in hot spots where the temperature was above the saturation temperature at the local pressure. Additionally, it should be stated that
3.1. Numerical simulation The numerical simulation was performed for both of conventional 318
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S.M.B. Hashemi, R. Roohi
(a)
(b)
(c)
(d)
Fig. 5. The temperature contours and velocity vectors at various time instances: a) t = 25 s, b) t = 45 s, c) t = 60 s and d = 90 s for ohmic heating process.
as the heat from all of the peripheral boundaries was transferred to the container, the fluid circulation due to the natural convection was substantially decreased. Therefore, the required time for the liquid to reach the desired point was increased significantly in comparison to the other examined heating method (ca. 30 min for the conventional method and 120 s for the ohmic heating). For the ohmic inactivation process, the generated heat due to the passage of the electrical current was strongly related to the distribution of the electrical potential field. The electrical potential contours are shown in Fig. 3 for the treatment with ΔV = 200 v, on the symmetry plane as well as surfaces passing through the middle of electrodes. The potential gradient was significant close to the electrode faces, while a nearly uniform distribution was observed in the zones far from the end caps. As the current density and consequently the generated heat was proportional to the gradient of the electrical potential, the initiation of temperature rise near the regions with high gradient values of potential filed was predictable. Moreover, as the electrical conductivity of the liquid and gas phases was different, the isopotential lines pattern was dissimilar below and above the free surface (Marra, Zell, Lyng, Morgan, & Cronin, 2009). However, the electrical potential did not directly affect the generated heat; their effects were gradient (electrical field) and consequently the electrical current were responsible for the energy release in the ohmic heating process. Hence, the average value of the electrical field was calculated for various applied voltages. The average value of the
electrical field was calculated to be 346.23, 461.64 and 577.05 for an applied voltage of 150, 200 and 250 V. The averaged electrical field was increased linearly with increasing in the applied voltage. However, the temperature elevation due to the complex involving phenomena in heat and mass transfer was not linearly dependent to the applied voltage. The velocity magnitude contours at predefined planes are presented in Fig. 4 in several instances. To provide better visualization of the velocity field inside of the domain, the results are depicted at the symmetry plane as well as equally spaced circular planes. As the phases' densities were assumed to be temperature dependent (Boussinesq assumption) in the regions with elevated temperature the buoyancy force (due to the presence of low-density liquids) created an upward fluid motion (Krishnani & Basu, 2016). Hence, the initial temperature increase caused confined vortices above and below the electrodes' tips (Fig. 4a). For later instances during the simulation (Fig. 4b to d), the propagation of the generated thermal energy in addition to the emerged velocity vortices resulted in fluid motion throughout the computational zone. The velocity magnitudes were higher in the gas phase zone in comparison to the liquid phase zone due to the higher Rayleigh number. Moreover, in the conventional method, heat flux was passing through all of the peripheral container walls; the velocity vortices due to the buoyancy effect were absent. Therefore, the conventional heating process was more like uniform heating of a solid cylinder, so the common and predictable temperature field due to the conventional procedure isn't illustrated here to avoid text prolongation. 319
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(a)
(b)
(c) Fig. 6. Numerically and experimentally evaluated temperatures during inactivation process: a) ohmic heating for the middle thermocouple, b) conventional method for the middle thermocouple and c) 200 v ohmic heating for three thermocouples.
The temperature contours in addition to the velocity vectors are illustrated in Fig. 5 for various instances during the ohmic inactivation. At the early stages (Fig. 5a), the temperature enhancement was limited to the regions in the vicinity of the electrodes. As time passes (Fig. 5b), the heated fluid propagated throughout the domain via the natural convection heat transfer mechanism. However, regarding the lower thermal conductivity of the gas phase in comparison to the fluid phase
and the placement of electrodes in the liquid phase, the temperature in the lower part of the container was higher and more uniform. The velocity vectors pattern and their length (magnitude) measured the existed free convection mechanism. At final stages (Fig. 5c and d), strong velocity vortices were produced in both phases to balance the buoyancy force created as a result of density differences. These vortices in addition to the conduction heat transfer mechanism aid the creation 320
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(a)
(b)
(c)
(d)
(e)
(f)
Fig. 7. The inactivation curves for ohmic process at various implemented voltages: a) E. coli, b) S. aureus, c) S. enterica subsp. enterica serovar Paratyphi A, d) S. Typhi, e) S. dysenteriae, f) S. flexneri.
of a uniform temperature field in the container. The variations in the mixture temperature are presented in Fig. 6 for CFD simulation as well as the conducted experimental examination for the ohmic (part a) and conventional (part b) inactivation processes. Moreover, the container was supposedly divided into three sections, and the mixture temperature was measured using thermocouple probes at the center of each section. Therefore, the mixture temperature was measured uniformly at equal distances (Fig. 6c). The illustrated temperatures for the conventional method were measured based on the average container temperature. According to the obtained results, the numerically predicted temperatures were in good agreement with the
measured data. For low to moderate temperatures, the apparent error was below 2%, while for higher temperature magnitudes a maximum error of 5% can be observed. As the implemented potential difference was increased, the mixture temperature was elevated, however, for the initial 30 s period of time; the difference between various cases was negligible. It should be added that as the phase change process was not considered in the current CFD simulation, the numerical modeling was only performed for 110 s when the temperature was below the boiling point. Moreover, the continuity, momentum and energy equations for the natural convection issue were coupled (the buoyancy term in the 321
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Table 1 The evaluated statistical parameters for the kinetic models. Weibull model
E. coli S. aureus S. enterica subsp. enterica serovar Paratyphi A S. Typhi S. dysenteriae S. flexneri
150 v 200 v 250 v 150 v 200 v 250 v 150 v 200 v 250 v 150 v 200 v 250 v 150 v 200 v 250 v 150 v 200 v 250 v
Modified Gompertz 2
b
n
Adj_R
1.01E−8 0.83E−9 3.93E−9 8.84E−9 2.52E−9 8.60E−5 3.45E−7 4.34E−7 3.04E−7 5.80E−6 7.34E−8 3.16E−8 4.50E−7 2.79E−7 1.51E−6 1.41E−6 1.01E−6 1.81E−6
4.391 5.044 4.826 4.432 4.802 2.57 3.631 3.659 3.952 2.965 4.062 4.357 3.572 3.754 3.573 3.333 3.479 3.444
0.992 0.991 0.989 0.986 0.984 0.963 0.985 0.989 0.993 0.976 0.990 0.991 0.980 0.990 0.995 0.989 0.994 0.974
RSME
B
C
M
Adj_R2
RSME
0.1747 0.1758 0.2104 0.2516 2.449 0.4629 0.2565 0.2127 0.1661 0.3476 0.2129 0.191 0.301 0.2027 0.1334 0.2308 0.1596 0.3587
0.0194 0.0050 0.0096 0.0506 0.0136 0.0474 0.0299 0.0160 0.0053 0.0453 0.0304 0.0266 0.0596 0.0217 0.0121 0.0182 0.0086 0.0174
49.22 9.99E+05 3982 9.828 265.6 9.67 15.22 68.6 8.00E+05 8.068 20.3 30.06 7.517 32.68 443.4 30.41 712.5 68.91
138.2 586.4 274.2 84.69 187.9 60.67 97.6 145 534.1 80.6 95.29 98.4 76.21 114.3 190.3 124.8 268.4 129.3
0.996 0.994 0.989 0.998 0.983 0.972 0.995 0.989 0.996 0.995 0.992 0.982 0.997 0.990 0.997 0.996 0.995 0.972
0.1135 0.1442 0.2079 0.0737 0.2549 0.4043 0.1404 0.2155 0.1172 0.16 0.1899 0.2766 0.1127 0.1978 0.1119 0.134 0.1453 0.3735
and 5.044 for E. coli, and its lowest value occurred for S. flexneri in the range of 3.333 to 3.479. The higher value of n parameter indicated more abrupt behavior in the microbial inactivation. On the other hand, the b parameter as the pre-exponent coefficient represents the rate of inactivation. Considering the fact that the value of n is not the same for all of the applied voltages, the effect of implemented voltages can't be examined directly based on the value of the b parameter (Table 1). According to the modified Gompertz function, C parameter is the difference between the upper and lower asymptotes, B is the relative inactivation rate at M and M is the occurrence instance of the maximum death rate. Based on the obtained results the time required to reach the maximum inactivation rate (M) was increased by utilization of higher voltages. The inactivation curves for all of the examined pathogens at various implemented voltages of 150, 200 and 250 v are depicted in Fig. 7. According to the obtained results, as the applied voltage was increased, the required time for the inactivation process was decreased, e.g., the required inactivation time was reduced from 100 to 80 s for E. coli and from 100 to 70 for S. enterica subsp. enterica serovar Paratyphi A by increasing the electrodes voltage from 150 to 250 v. Moreover, the effect of increasing in the applied voltage was different for the various bacteria examined in the current study. For the initial 60-s time interval, the increasing in the utilized voltage from 150 to 250 v resulted in only 0.6-log CFU/mL reduction for E. coli while a significant reduction of 2.8-log CFU/mL was observed for S. aureus. Based on similar analysis, variation of implemented voltage had higher influence on E. coli, S. Typhi and S. flexneri at early stages (prior to 60s), while the other bacteria (S. aureus, S. enterica subsp. enterica serovar Paratyphi A and S. dysenteriae) showed higher inactivation rate after the first 60-s of experiment. Additionally, it should be stated that the variations in the required process time is a function of both applied voltage and the temperature of field inside the examined domain. Hence, any parameter of the study should be conducted by neutralizing the effect of other involving parameters. However, for the present simulation, these two variables were completely connected and changed accordingly. However, the variations in pathogens population were strongly associated with the temperature field, the produced temperature filed was in direct correlation with the applied apparatus voltage (the thermal source term was a direct function of applied voltage). Moreover, to make the results useful for applicable purposes, the main variable was selected to be the system voltage, and the temperature field was reported as a function of applied voltage.
momentum equation and the convective term in the energy equation are the links between these two equations). Therefore, it would be impossible to obtain accurate results for the temperature without computing the velocity field precisely by the aid of mathematically modeling. In other words, the validation of temperature field implicitly guarantees the accuracy of the calculated velocity field. Additionally, to improve the validation process, the temperature measurements at two more points are also illustrated in Fig. 6a. The temperatures at these three separate points can be used to validate the solution of energy equation as well as the capability of the numerical simulation to determine energy convective term due to the fluid velocity and vortices. The temperature elevation history for the conventional method is illustrated in Fig. 6b. The required time to elevate the mixture temperature for the conventional method was considerably higher than those corresponded with the ohmic process (e.g., the mixture temperature was increased to 70 °C in 65 s for ohmic heating while 27 min was required for the same temperature increase via conventional method). The different nature of the involving heat generation and transfer mechanisms were the reasons for the significant difference in temperature increasing durations. In the case of conventional method, the thermal energy was transferred from a heated fluid outside of the domain. Therefore, the thermal resistance of the outer fluid, as well as container wall, caused a reduction in the magnitude of the heat flux. Additionally, the natural convection heat transfer (which plays an important role in heat transfer of ohmic heating process via the creation of vortices) was weaker for conventional method due to the nearly uniform temperature elevation of lower and upper parts of the vessel. The mentioned important role of the natural convection referred to the role in circulating the fluid inside the container part and creating a uniform temperature field in comparison to the conventional method in which a gradually varying temperature filed (stratified) was created. In other words, for the conventional method, the heat flux was transferred through the system walls and gradually reached to the center of the container; however, for the ohmic heating process the global heat generation and the natural stirring due to the buoyancy effect produced a more uniform and more rapid temperature elevation. 3.2. Kinetic modeling The Weibull model main parameters are n and b which represent the shape factor of curves and the scale factor. The shape factor of curves was above unity which indicated a downward concave form for the curves (Fig. 7). The highest value of shape factor was between 4.391 322
Innovative Food Science and Emerging Technologies 52 (2019) 313–324
Log CFU/mL
S.M.B. Hashemi, R. Roohi
S. Typhi
Fig. 8. The logarithmic reduction of the microbes' quantity for ohmic inactivation at various implemented voltages after 60 s.
The inactivation value of all of the examined bacteria for implemented voltages of 150–250 after 60-s from the process initiation is shown in Fig. 8. The inactivation values are defined as the difference between the logarithmic number of pathogens after 60 s and at the initial instance. As stated previously, some of the pathogens were responded more quickly to the applied ohmic heating, 3.1, 3.2 and 3.4 reduction in the logarithmic number of the bacteria was observed for S. aureus, S. enterica subsp. enterica serovar Paratyphi A and S. dysenteriae, while a lower value of 1.2, 1.5 and 1.9-log CFU/mL was observed for E. coli, S. Typhi and S. flexneri, respectively. Besides, it can be concluded that the sensitivity of the bacteria to the implemented voltage was maximum for S. aureus by increasing the ohmic voltage from 150 to 250 v (the observed increase is defined as the relative increase of inactivation value due to 100 v increase of applied voltage from 150 to 250 v). The next highest inactivation sensitivity to the applied voltage belonged to S. dysenteriae, S. enterica subsp. enterica serovar Paratyphi A, S. Typhi, E. coli and S. flexneri with an increase of 680, 457, 375, 240 and 237% in the inactivation value by enhancement of the applied voltage from 150 to 250 v, respectively. Palaniappan and Sastry (1991) reported thermal effect is the main factor in the inactivation of microorganisms by ohmic heating. Additionally, an extra effect is electroporation in the microbial cell membrane. Electroporation is correlated to charge transfer resulting from differences between the internal and external potential of microorganisms subjected to ohmic heating. This event causes the creation of pores in the proteins and lipid bilayer of microbial cell membranes (Park & Kang, 2013). Lee, Sagong, Ryu, and Kang (2012) found the ohmic treatment of orange juice reduced E. coli O157: H7 more than 5-log after 60, 90 and180 s treatments with 40, 35 and 30 V cm−1 electric field strength, respectively. In tomato juice, ohmic treatment with 25 V cm−1 for 30 s resulted in a 5-log reduction in E. coli O157: H7. Similar results were observed in L. monocytogenes and S. Typhimurium. It was reported Alicyclobacillus acidoterrestris spores treated with ohmic heating had higher lethality compared to spores treated with conventional heating in orange juice. Conventional heating was ineffective for pasteurization of the juice; while the ohmic heating treatment applied at 30 V cm−1 was adequate to a 5-log reduction of A. acidoterrestris spores (Baysal & İçier, 2010).
confined vortices above and below the electrodes' tips, while for later instances, the propagation of the generated thermal energy in addition to the emerged velocity vortices resulted in fluid motion throughout the computational zone. As the applied voltage was increased, the required time for the inactivation process was decreased, e.g., the required inactivation time was reduced from 100 to 80 s for E. coli and from 100 to 70 for S. enterica subsp. enterica serovar Paratyphi A by increasing the electrodes voltage from 150 to 250 v. The sensitivity of the bacteria during ohmic heating was maximum for S. aureus, followed by E. coli, S. enterica subsp. enterica serovar Paratyphi A, S. Typhi, S. dysenteriae and S. flexneri. This study can be integrated into a multi-criteria optimization approach to improve the ohmic heating process and give desired results. References Baysal, A. H., & İçier, F. (2010). Inactivation kinetics of Alicyclobacillus acidoterrestris spores in orange juice by ohmic heating: Effects of voltage gradient and temperature on inactivation. Journal of Food Protection, 73(2), 299–304. Buzrul, S., Alpas, H., & Bozoglu, F. (2005). Use of Weibull frequency distribution model to describe the inactivation of Alicyclobacillus acidoterrestris by high pressure at different temperatures. Food Research International, 38(2), 151–157. Caccavale, P., De Bonis, M. V., & Ruocco, G. (2016). Conjugate heat and mass transfer in drying: A modeling review. Journal of Food Engineering, 176, 28–35. Chen, H., & Hoover, D. G. (2003). Modeling the combined effect of high hydrostatic pressure and mild heat on the inactivation kinetics of Listeria monocytogenes Scott A in whole milk. Innovative Food Science & Emerging Technologies, 4(1), 25–34. Churchill, S. W., & Chu, H. H. (1975). Correlating equations for laminar and turbulent free convection from a horizontal cylinder. International Journal of Heat and Mass Transfer, 18(9), 1049–1053. Crilly, J., & Fryer, P. (1993). New directions in food research: The role of mathematical models in food processing. IMA Journal of Management Mathematics, 5(1), 265–282. Davies, L. J., & Fryer, P. J. (2001). Modeling electrical resistance (“ohmic”) heating of foods. Food processing operations modeling (pp. 227–264). CRC Press. Diels, A. M., Wuytack, E. Y., & Michiels, C. W. (2003). Modelling inactivation of Staphylococcus aureus and Yersinia enterocolitica by high-pressure homogenisation at different temperatures. International Journal of Food Microbiology, 87(1–2), 55–62. Fryer, P. J., Knoerzer, K., & Juliano, P. (2011). The future of multiphysics modeling of innovative food processing technologies. Innovative food processing technologies: advances in multiphysics simulation (pp. 353–364). . Gally, T., Rouaud, O., Jury, V., & Le-Bail, A. (2016). Bread baking using ohmic heating technology; a comprehensive study based on experiments and modelling. Journal of Food Engineering, 190, 176–184. Ghiji, M., Goldsworthy, L., Brandner, P. A., Garaniya, V., & Hield, P. (2017). Analysis of diesel spray dynamics using a compressible Eulerian/VOF/LES model and microscopic shadow graphy. Fuel, 188, 352–366. Hashemi, S. M. B., Amininezhad, R., Shirzadinezhad, E., Farahani, M., & Yousefabad, S. H. A. (2016). The antimicrobial and antioxidant effects of Citrus aurantium L. flowers (Bahar narang) extract in traditional yoghurt stew during refrigerated storage. Journal of Food Safety, 36(2), 153–161. Hashemi, S. M. B., Mousavi Khaneghah, A., Fidelis, M., & Granato, D. (2018). Effects of pulsed thermosonication treatment on fungal growth and bioactive compounds of
4. Conclusion The numerically predicted temperatures were confirmed by the measured data. For low, to moderate temperatures, the apparent error was below 2%, while for higher temperature magnitudes a maximum error of 5% can be observed. The initial temperature increase caused 323
Innovative Food Science and Emerging Technologies 52 (2019) 313–324
S.M.B. Hashemi, R. Roohi Berberis vulgaris juice. International Journal of Food Science & Technology, 53, 1589–1596. Hashemi, S. M. B., Nikmaram, N., Esteghlal, S., Khaneghah, A. M., Niakousari, M., Barba, F. J., ... Koubaa, M. (2017). Efficiency of ohmic assisted hydrodistillation for the extraction of essential oil from oregano (Origanum vulgare subsp. viride) spices. Innovative Food Science & Emerging Technologies, 41, 172–178. Jun, S., & Sastry, S. (2005). Modeling and optimization of ohmic heating of foods inside a flexible package. Journal of Food Process Engineering, 28(4), 417–436. Kiani, H., Karimi, F., Labbafi, M., & Fathi, M. (2018). A novel inverse numerical modeling method for the estimation of water and salt mass transfer coefficients during ultrasonic assisted-osmotic dehydration of cucumber cubes. Ultrasonics Sonochemistry, 44, 171–176. Krishnani, M., & Basu, D. N. (2016). On the validity of Boussinesq approximation in transient simulation of single-phase natural circulation loops. International Journal of Thermal Sciences, 105, 224–232. Lee, S. Y., Sagong, H. G., Ryu, S., & Kang, D. H. (2012). Effect of continuous ohmic heating to inactivate Escherichia coli O157: H7, Salmonella Typhimurium and Listeria monocytogenes in orange juice and tomato juice. Journal of Applied Microbiology, 112(4), 723–731. Mafart, P., Couvert, O., Gaillard, S., & Leguérinel, I. (2002). On calculating sterility in thermal preservation methods: Application of the Weibull frequency distribution model. International Journal of Food Microbiology, 72(1–2), 107–113. Marra, F., Zell, M., Lyng, J. G., Morgan, D. J., & Cronin, D. A. (2009). Analysis of heat transfer during ohmic processing of a solid food. Journal of Food Engineering, 91(1), 56–63. Mirmasoumi, S., & Behzadmehr, A. (2008). Numerical study of laminar mixed convection of a nanofluid in a horizontal tube using two-phase mixture model. Applied Thermal Engineering, 28(7), 717–727. Norton, T., Tiwari, B., & Sun, D. W. (2013). Computational fluid dynamics in the design and analysis of thermal processes: A review of recent advances. Critical Reviews in Food Science and Nutrition, 53(3), 251–275.
Palaniappan, S., & Sastry, S. K. (1991). Electrical conductivity of selected juices: Influences of temperature, solids content, applied voltage, and particle size. Journal of Food Process Engineering, 14(4), 247–260. Park, I. K., & Kang, D. H. (2013). Effect of electropermeabilization by ohmic heating for inactivation of Escherichia coli O157: H7, Salmonella enterica serovar Typhimurium, and Listeria monocytogenes in buffered peptone water and apple juice. Applied and Environmental Microbiology, 79(23), 7122–7129. Pereira, R. N., & Vicente, A. A. (2010). Environmental impact of novel thermal and nonthermal technologies in food processing. Food Research International, 43(7), 1936–1943. Sastry, S. K., & Palaniappan, S. (1992). Mathematical modeling and experimental studies on ohmic heating of liquid-particle mixtures in a static heater. Journal of Food Process Engineering, 15(4), 241–261. Sastry, S. K., & Salengke, S. (1998). Ohmic heating of solid-liquid mixtures: A comparison of mathematical models under worst-case heating conditions. Journal of Food Process Engineering, 21(6), 441–458. Shim, J., Lee, S. H., & Jun, S. (2010). Modeling of ohmic heating patterns of multiphase food products using computational fluid dynamics codes. Journal of Food Engineering, 99(2), 136–141. Siguemoto, É. S., Gut, J. A. W., Martinez, A., & Rodrigo, D. (2018). Inactivation kinetics of Escherichia coli O157: H7 and Listeria monocytogenes in apple juice by microwave and conventional thermal processing. Innovative Food Science & Emerging Technologies, 45, 84–91. Tavakolpour, Y., Moosavi-Nasab, M., Niakousari, M., Haghighi-Manesh, S., Hashemi, S. M. B., & Mousavi Khaneghah, A. (2017). Comparison of four extraction methods for essential oil from Thymus daenensis subsp. Lancifolius and chemical analysis of extracted essential oil. Journal of Food Processing and Preservation, 41(4), e13046. Wang, J., Hu, X., & Wang, Z. (2010). Kinetics models for the inactivation of Alicyclobacillus acidiphilus DSM14558T and Alicyclobacillus acidoterrestris DSM 3922T in apple juice by ultrasound. International Journal of Food Microbiology, 139(3), 177–181.
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Innovative Food Science and Emerging Technologies journal homepage: www.elsevier.com/locate/ifset
Ohmic heating of blended citrus juice: Numerical modeling of process and bacterial inactivation kinetics
T
Seyed Mohammad Bagher Hashemia, , Reza Roohib ⁎
a b
Department of Food Science and Technology, College of Agriculture, Fasa University, Fasa, Iran Department of Mechanical Engineering, Fasa University, Fasa, Iran
ARTICLE INFO
ABSTRACT
Keywords: Foodborne bacteria Ohmic heating Weibull model Modified Gompertz model Inactivation
A comprehensive 3D, transient-free convection, and multiphase model was developed to determine the performance of ohmic heating (150, 200 and 250 V; 120 s; 99.4 °C) and conventional heating (90 °C; 15 min) for the inactivation of Escherichia coli, Staphylococcus aureus, Salmonella enterica subsp. enterica serovar Paratyphi A, Salmonella Typhi, Shigella dysenteriae, and Shigella flexneri in blended citrus juice (sweet lemon and orange). Results indicated the computed temperatures were in good agreement with the experimentally measured data (below 5% deviation). The examination of velocity and temperature patterns throughout the computational domain explained the reasons for significant differences between the conventional and ohmic heating process. The homogeneously distributed vortices in ohmic heating lead to a more uniform and rapid temperature rise in temperature (from 26 to 99.4 °C) while compared with the conventional method with a stratified flow pattern. Based on the evaluation of temperature rise, increasing in the applied voltage from 150 to 250 V was deducted to reduce the inactivation time about 20–30% for the investigated pathogens. The inactivation rate of pathogens during ohmic heating process was maximum for S. aureus, followed by E. coli, S. enterica subsp. enterica serovar Paratyphi A, S. Typhi, S. dysenteriae and S. flexneri. In conclusion, the developed numerical modeling can be conveniently applied to simulate and predict the ohmic heating for the inactivation of pathogenic bacteria. Industrial relevance: Several thermophysical phenomena affect the optimization and design of ohmic heating systems such as heat and mass transport as well as electrical field distribution. The implementation of the computational fluid dynamics (CFD) method is an efficient and economical technique that can provide valuable data for researchers. Moreover, the determination of off-design thermal spots, heat-loss magnitude and apparatus efficiency can be determined via numerical calculations.
1. Introduction Pasteurization as a thermal processing technique has been applied for inactivation of pathogenic and spoilage microorganisms to ensure safety and extend shelf-life of a diversity of foods. However, the novel thermal technologies compared to the traditional thermal treatments enhance retention of nutrients, texture, color and flavors of food products. Therefore, the development of novel thermal process technologies has attracted notable attention over last decades (Hashemi, Mousavi Khaneghah, Fidelis, & Granato, 2018; Pereira & Vicente, 2010). Ohmic heating can be used as an effective thermal processing for consistently heating of food products by the passage of electric currents through food matrices. Thus, ohmic heating can circumvent the limitations of conventional pasteurization by using electricity (Hashemi
⁎
et al., 2017; Tavakolpour et al., 2017). However, understanding of the ohmic heating process for pasteurization of food products is crucial in order to guarantee the safety and suitability of the process. In this context, a vast number of models have been applied to explain nonlinear microbial inactivation kinetics, such as the modified Gompertz equation, the Weibull distribution function and the log-logistic model (Siguemoto, Gut, Martinez, & Rodrigo, 2018; Wang, Hu, & Wang, 2010). For instance, the Weibull model has been used for the modeling of the inactivation of Alicyclobacillus acidiphilus treated with high hydrostatic pressure (Buzrul, Alpas, & Bozoglu, 2005). However, no model regarding kinetics of inactivation of pathogenic bacteria in citrus juice by ohmic heating is available. The numerical simulation of applied methods in food processing has gained considerable attention due to their accuracy and efficiency, as well as the economical aspects in comparison with experimental
Corresponding author. E-mail address: [email protected] (S.M.B. Hashemi).
https://doi.org/10.1016/j.ifset.2019.01.012 Received 4 December 2018; Received in revised form 10 January 2019; Accepted 22 January 2019 Available online 23 January 2019 1466-8564/ © 2019 Elsevier Ltd. All rights reserved.
Innovative Food Science and Emerging Technologies 52 (2019) 313–324
S.M.B. Hashemi, R. Roohi
examinations (Fryer, Knoerzer, & Juliano, 2011; Kiani, Karimi, Labbafi, & Fathi, 2018; Norton, Tiwari, & Sun, 2013). The implementation of computational fluid dynamics (CFD) as a simulation approach, can provide insights regarding the several mutually affecting mechanisms in food procedures such as heat and mass transfer, chemical reactions, and flow turbulence (Caccavale, De Bonis, & Ruocco, 2016; Crilly & Fryer, 1993). The numerical simulation and modeling of ohmic heating has been performed by several investigations to evaluate the major aspects of ohmic heating process such as the generated temperature field, the effect of mixture electrical conductivity, the role of electrodes' sizing and their position inside the sample (Sastry & Palaniappan, 1992; Sastry & Salengke, 1998; Jun & Sastry, 2005; Davies & Fryer, 2001; Shim, Lee, & Jun, 2010; Gally, Rouaud, Jury, & Le-Bail, 2016). However, to the best of our knowledge, simulation of heat and mass transfer through ohmic heating of citrus juice process has not been examined. Hence, in the present study, the ohmic heating and heating processes for inactivation of pathogenic bacteria were numerically simulated with a 3D, laminar, and transient model and the results were compared with those using a conventional approach. Moreover, the mixture model was utilized for the multiphase flow, and the ohmic heating generation was simulated based on the calculation of the potential electrical field. The variations of temperature and velocity fields during the process were determined and compared to experimental data for ohmic heating and conventional methods. Additionally, two mathematical models (Weibull and modified Gompertz) were applied to the experimentally captured data set and the effect of utilized voltages on the inactivation of pathogens was investigated.
Ohmic treatments were carried out in a 1000-mL capacity laboratory-scale reactor at three voltages (150, 200 and 250 V). The reactor part included a Teflon chamber in cylindrical form (7-cm internal diameter and 25-cm length) and was prepared with two titanium electrodes. The fully automated system for the control of current (0–16) A, voltage (0–300) V, and temperature, allowed recording data through the experiment. For all samples, 600 mL of citrus juice was poured into the chamber and treatments were carried out for 120 s. Each one of the treatments was carried out in triplicate. 2.3. Microbial enumeration For microbial enumeration, 1-mL aliquots of each samples were serially diluted in 0.1% peptone water and 0.1 mL of proper diluents were spread plated onto each appropriate medium. Sorbitol Mac Conkey agar (PO0232, Oxoid, UK) and Baird-parker Agar (PO0168, Oxoid, UK) were used as appropriate media for the enumeration of E. coli and S. aureus, respectively. Nutrient agar (CM0003, Oxoid, UK) was used for other pathogens. All the plates were incubated at 37 °C for 24–48 h, colonies were counted. All tests were duplicate-plated and replicated three times (Hashemi, Amininezhad, Shirzadinezhad, Farahani, & Yousefabad, 2016). 2.4. Governing equations Several approaches were proposed to simulate the behavior of multiphase flows, namely Eulerian, mixture and volume of fluid (VOF) model (Ghiji, Goldsworthy, Brandner, Garaniya, & Hield, 2017). According to the mixture model, the conservation equations including continuity, momentum, and energy as well as volume fraction equation (for secondary phases) were considered. In addition, an algebraic expression was implemented to calculation of relative velocity of phases. On the other hand, based on the VOF model, the dynamics of several immiscible phases can be determined via the solution of a single momentum equation while the continuity equation was considered separately for each phase. Based on the Eulerian method, to calculate the domain characteristics the governing equations (i.e., continuity, momentum and energy equations) should be solved separately for each phase; however, a single pressure equation was assigned to all of the phases. Moreover, the interaction between phases was simulated using the calculated drag and lift forces (Mirmasoumi & Behzadmehr, 2008). Each model offers benefits as well as computational complexities. In the present study, the mixture model was chosen based on its capability for simulation of nearly uniform flows with a relative velocity of phases. The transient form of the mass conservation equation for the mixture of n phases is:
2. Materials and methods 2.1. Chemicals and microorganisms Escherichia coli PTCC 1399, Staphylococcus aureus PTCC 1764, Salmonella enterica subsp. enterica serovar Paratyphi A PTCC 1230, Salmonella Typhi PTCC 160, Shigella dysenteriae PTCC 1188 and Shigella flexneri PTCC 1865 were obtained from the Iranian Research Organization for Science and Technology, Tehran, Iran. All strains were reactivated in Mueller Hinton broth (CM0405, Oxoid, UK) and incubated at 37 °C overnight. All chemicals were of analytical reagent grade and purchased from Sigma (ST. Louis, MO). 2.2. Sample and treatments Sweet lemon and orange were purchased from a local market in Fasa city (Autumn of 2017), Fars province, Iran. Samples were washed and manually peeled. The juices were prepared by a domestic juicer (Pars Khazar, VITAFRUIT model, Gilan, Iran) under aseptic conditions. After mixing the juices (50:50 (v/v) %; pH 4.04 and 14.7°Brix), the blended citrus juice was transferred into sealed glass tubes. Then, the tubes were submerged simultaneously into the water bath (Fan Azema Gostar, WB 22, Tehran, Iran), which was maintained at 90 °C for 15 min. After cooling the tubes, each strain of pathogenic bacteria was inoculated separately into blended juice. Following reactivation of each strain in Mueller Hinton broth, cells were collected by centrifugation at 4000 ×g for 15 min. The supernatant was removed and 10 mL of 0.2% peptone water was mixed with the pellet to wash cells. Cells were centrifuged and the washing step was repeated. Following the washing step, the pellets were resuspended in blended juice to get the desired concentration of cells (~6–6.2 log CFU/mL). Approximately 600 mL of the blended citrus juice was poured in 1000-mL sealed glass tubes for conventional heating. Four tubes per test were immersed in a water bath under control temperature (75 °C for 30 min). A digital thermometer (106 Model, Testo, Germany) fitted to a reference tube was applied to measure the blended citrus juice temperature during the thermal examination. After thermal treatment, the tubes were quickly cooled.
t
(
m)
+
·(
m Vm )
=0
(1)
where ρm and Vm represent the mixture averaged density and velocity, respectively. Assume φk, as the kth phase volume fraction, ρm and Vm can be calculated using Eqs. (2) and (3):
Vm =
n k=1
k k Vk
(2)
m
m
=
n k=1
k k
(3)
The momentum equation of the mixture model is derived based on the summation of the momentum equation of each phase as: 314
Innovative Food Science and Emerging Technologies 52 (2019) 313–324
S.M.B. Hashemi, R. Roohi
t
(
m Vm )
+
.(
m Vm Vm )
=
p+ + +
m mg
.
(
. [µm ( Vm + (T
diameter and outer fluid conductivity coefficient, respectively. Based on Eqs. (12) and (13) the convective heat transfer coefficient of the outer container walls is assumed to be a function of system geometrical and operational conditions. Additionally, RaD and Pr are the Rayleigh and Prandtl numbers defined as:
T
Vm )]
T0)
n k=1
k k Vdr , k Vdr , k
)
(4)
In Eq. (4), p, μm, T, and dr denote the pressure, mixture viscosity, matrix transpose and drift, respectively. βm is the volumetric expansion coefficient and can be calculated as: m
1
=
RaD =
k k
m
(5)
n
k µk
k=1
vdr , k = vk
(6) (7)
vm
The conservation of the energy equation has the following form:
t
(
n k=1
k k Ek
)+
n k=1
k vk ( k Ek
+ p) =
·(keff
T ) + Sohmi c (8)
where keff is the effective mixture conductivity, Ek is the kth phase energy and Sohmic is thermal heat source due to the ohmic heating. The ohmic heating is referring to the phenomena of heat generation due to the electrical passage through conductors with electrical resistivity (Davies & Fryer, 2001). It should be noted that the applied voltage can be altered, in this context; the electrical potential, current, and the generated power are time-dependent. The root means square value of these variables over time cycles were calculated and used in the energy equation. The electrical potential distribution is required to estimate the produced electrical current and consequently the generated thermal power as:
·(
To mathematically describe the variations of the pathogens' quantity as a function of time two commonly used models were selected.
where σ and Φ represent the electrical conductivity and potential, respectively. Hence, the current density (J) and the Sohmic can be estimated as:
1) The modified Gompertz model: The modified Gompertz model was acknowledged for its capability in the prediction of smooth curves (Chen & Hoover, 2003). This kinetic model has three tunable variables of C, B and M.
(10)
J= Sohmic =
J·J
(11)
log
2.5. Boundary conditions
h=
NuD ·k D
0.387RaD1/6 [1 + (0.559/ Pr )9/16]8/27
1012
C exp( exp( B × (t
M )))
(16)
The Weibull kinetic model is the general case of the linear model, in which the decreasing of the inspected parameter is assumed to have various rates during the process (Mafart, Couvert, Gaillard, & Leguérinel, 2002).
log
N = N0
bt n
(17)
where b and n are representatives of the scale and shape factor (the slope of the line in a probability plot), respectively.
2
, RaD
N = C exp( exp(B × M )) N0
2) The Weibull model:
To determine the flow and thermal fields, the governing equations should be solved accompanied by a proper set of boundary and initial conditions. For the momentum equation the no-slip condition was assigned to all of the domain wall boundaries. The wall boundaries were defined as the system surfaces where the fluid phase was in contact with the solid domain. Moreover, as the outer container walls were in contact with surrounding air (for ohmic heating) and water (for the conventional case), the appropriate convection heat transfer coefficient was applied as (Churchill & Chu, 1975):
NuD = 0.6 +
(15)
2.6. Statistical simulation of pathogens
(9)
)=0
(14)
In addition to the container's outer walls, the adiabatic (zero heat flux) boundary condition was set at other domain walls (i.e., the electrode's walls). It should be noted that regarding the insulation applied at the electrodes connection point to the containers caps, the adiabatic boundary condition is valid. For the electrical potential equation, constant values were assigned to the anode and cathode electrodes, while the zero gradient boundary condition was set for the other boundaries. It should be noted that constant voltage values were referred to the amplitude of the applied voltage and instantaneous apparatus voltage varied as a sinusoidal function during the time. The initial conditions were determined based on the system properties before the exposing to ohmic system. Hence, the field temperature was set to be 26 °C, phases were assumed to be stagnant (zero velocity) and the domain electrical potential was set to zero. The water level was also calculated and set based on the volume of the liquid initially placed in the container, while the rest of the container was filled with air. The governing equations were solved numerically using the open source code program of OpenFOAM. The numerical simulation was performed with the aid of a computer system with following characteristics: Intel Core i7 [email protected], 16 GB of DDR4 RAM. Each simulation was converged in about 16 h to the final results.
Due to the small values of velocity magnitude, the flow field is assumed to be laminar. Mixture viscosity (μm) and drift velocity (the difference between phase and averaged mixture velocity), vdr , k , can be obtained using:
µm =
TD3
Pr =
n k=1
g
2.7. Mathematical model accuracy evaluation
(12)
Two main measures were utilized to assess the accuracy of the fitted correlations, adjusted R2 and RMSE:
(13)
where in the above equations, h , NuD , D and k are the averaged convection heat transfer coefficient, averaged Nusselt number, cylinder
Adjusted R2 = 1
315
(n
i)(1 R2) n p
(18)
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(a)
(b)
(c)
(d)
Fig. 1. Schematic of geometry (a: ohmic heating, b: conventional method) and computational domain grids (c: overall grid's view and d: internal cell distribution via sectioned view).
where n indicates the number of the measured data, p is the number of parameters and i as the indicator variable with the value of 1 for happening of an intercept in the model and 0 for other situations (Diels, Wuytack, & Michiels, 2003). Moreover, RMSE is a measure of the average difference between the estimated and observed data as:
RMSE =
(observed predicted )2 n 1
To assure the sufficiency of the number of utilized cells, the grid independence test was carried out for three unstructured grids with the amount of 880,457, 930,876 and 1,102,635 computational cells. Based on the effect of cell numbers on the velocity profile at the center of the container and the computational cost, the grid with the medium number of cells (930,876) was selected, and the hereafter results were obtained based on the mentioned grid.
(19)
2.9. Solution method The governing equations including the conservation laws of mass, momentum, energy, electrical potential and drift velocity of phases were solved simultaneously to determine the flow and thermal fields' characteristics. To do so, a transient, laminar and multiphase CFD code was employed. The SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm was implemented for pressure-velocity coupling. Besides, the central and second-order upwind schemes were applied for the discretization of diffusive and convective terms, respectively. The convergence criteria for mass, momentum, energy and electrical potential equations were set to 10−4, 10−5, 10−6 and 10−8, respectively.
2.8. Geometry and computational grids The assumed geometry was based on the actual configuration of the inactivation apparatus. The container for both cases of ohmic inactivation and conventional method was a cylinder with an internal diameter of 7-cm and 25-cm in height. Besides, for the ohmic process, two electrode rods with diameter and length of 1 cm and 2.5 cm were added to the left and right sides of the container (Fig. 1a and b). The created geometry should be divided into several small control volumes (computational cells), and the discretized form of the governing equation was solved consequently. Thus, the quality and quantity of the utilized grids had a significant effect on the CFD simulation results accuracy and computational cost. In the present investigation, the grids density was increased near the zones with a higher gradient of variables, i.e., zones beside the walls, at the interface between phases and around the electrodes. Moreover, to determine the flow behavior inside the boundary layers near the walls, five layers of structured grids with gradually increasing height was implemented at the device walls (Fig. 1c and d).
3. Results and discussion The fact that the ohmic heating is better than conventional methods for the inactivation process was well demonstrated in several previous studies (Pereira & Vicente, 2010). However, the physical background of ohmic heating and conventional methods as well as the impact of operating conditions on the velocity and thermal fields were listed as the main goals of the current study. In other words, the pathogens 316
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(a)
(b)
(c)
(d)
Fig. 2. The velocity (a) and temperature (b–d) contours: a) t = 30 min, b) t = 10 min s, c) t = 20 min s and d = 30 min for conventional method.
Fig. 3. The electrical potential distribution at various planes for ΔV = 200 v for ohmic heating process. 317
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(a)
(b)
(c)
(d)
Fig. 4. The velocity magnitude contours at various time instances: a) t = 25 s, b) t = 45 s, c) t = 60 s and d = 90 s for ohmic heating process.
inactivation is due to increase in temperature and the numerical simulation was dealing with the determination of temperature throughout the domain. Therefore, the temperature field was the common link between the simulation and the inactivation process. The numerical modeling was used to describe the reasons of establishment of a more rapid and uniform temperature rise during ohmic heating in comparison to the conventional method. Moreover, developing numerical models for heating and inactivation processes (which both were done in the present study in addition to the experimental data) with high accuracy, aids to determine the inactivation process outputs using merely theoretical simulations.
and ohmic inactivation experiments. The results of the conventional modeling are illustrated in Fig. 2. The container with a specified amount of liquid was placed inside a Bain-marie bath and heat was transferred to the mixture from the surrounding walls due to the temperature difference between the fluids on both sides of the container walls. As the temperature in the container liquid zone (the lower part) was slightly higher near the walls, the upward liquid stream was observed due to the density reduction and the buoyancy force (Fig. 2a). The time history of temperature variations is depicted in Fig. 2b to d at some internal planes. According to the lower value of the specific heat capacity of the gas phase (upper zone) in comparison to the liquid phase (lower zone), the temperature level was more elevated in the gas containing zone. The gas phase (evaporated liquid) formation was initiated in hot spots where the temperature was above the saturation temperature at the local pressure. Additionally, it should be stated that
3.1. Numerical simulation The numerical simulation was performed for both of conventional 318
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(a)
(b)
(c)
(d)
Fig. 5. The temperature contours and velocity vectors at various time instances: a) t = 25 s, b) t = 45 s, c) t = 60 s and d = 90 s for ohmic heating process.
as the heat from all of the peripheral boundaries was transferred to the container, the fluid circulation due to the natural convection was substantially decreased. Therefore, the required time for the liquid to reach the desired point was increased significantly in comparison to the other examined heating method (ca. 30 min for the conventional method and 120 s for the ohmic heating). For the ohmic inactivation process, the generated heat due to the passage of the electrical current was strongly related to the distribution of the electrical potential field. The electrical potential contours are shown in Fig. 3 for the treatment with ΔV = 200 v, on the symmetry plane as well as surfaces passing through the middle of electrodes. The potential gradient was significant close to the electrode faces, while a nearly uniform distribution was observed in the zones far from the end caps. As the current density and consequently the generated heat was proportional to the gradient of the electrical potential, the initiation of temperature rise near the regions with high gradient values of potential filed was predictable. Moreover, as the electrical conductivity of the liquid and gas phases was different, the isopotential lines pattern was dissimilar below and above the free surface (Marra, Zell, Lyng, Morgan, & Cronin, 2009). However, the electrical potential did not directly affect the generated heat; their effects were gradient (electrical field) and consequently the electrical current were responsible for the energy release in the ohmic heating process. Hence, the average value of the electrical field was calculated for various applied voltages. The average value of the
electrical field was calculated to be 346.23, 461.64 and 577.05 for an applied voltage of 150, 200 and 250 V. The averaged electrical field was increased linearly with increasing in the applied voltage. However, the temperature elevation due to the complex involving phenomena in heat and mass transfer was not linearly dependent to the applied voltage. The velocity magnitude contours at predefined planes are presented in Fig. 4 in several instances. To provide better visualization of the velocity field inside of the domain, the results are depicted at the symmetry plane as well as equally spaced circular planes. As the phases' densities were assumed to be temperature dependent (Boussinesq assumption) in the regions with elevated temperature the buoyancy force (due to the presence of low-density liquids) created an upward fluid motion (Krishnani & Basu, 2016). Hence, the initial temperature increase caused confined vortices above and below the electrodes' tips (Fig. 4a). For later instances during the simulation (Fig. 4b to d), the propagation of the generated thermal energy in addition to the emerged velocity vortices resulted in fluid motion throughout the computational zone. The velocity magnitudes were higher in the gas phase zone in comparison to the liquid phase zone due to the higher Rayleigh number. Moreover, in the conventional method, heat flux was passing through all of the peripheral container walls; the velocity vortices due to the buoyancy effect were absent. Therefore, the conventional heating process was more like uniform heating of a solid cylinder, so the common and predictable temperature field due to the conventional procedure isn't illustrated here to avoid text prolongation. 319
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(a)
(b)
(c) Fig. 6. Numerically and experimentally evaluated temperatures during inactivation process: a) ohmic heating for the middle thermocouple, b) conventional method for the middle thermocouple and c) 200 v ohmic heating for three thermocouples.
The temperature contours in addition to the velocity vectors are illustrated in Fig. 5 for various instances during the ohmic inactivation. At the early stages (Fig. 5a), the temperature enhancement was limited to the regions in the vicinity of the electrodes. As time passes (Fig. 5b), the heated fluid propagated throughout the domain via the natural convection heat transfer mechanism. However, regarding the lower thermal conductivity of the gas phase in comparison to the fluid phase
and the placement of electrodes in the liquid phase, the temperature in the lower part of the container was higher and more uniform. The velocity vectors pattern and their length (magnitude) measured the existed free convection mechanism. At final stages (Fig. 5c and d), strong velocity vortices were produced in both phases to balance the buoyancy force created as a result of density differences. These vortices in addition to the conduction heat transfer mechanism aid the creation 320
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(a)
(b)
(c)
(d)
(e)
(f)
Fig. 7. The inactivation curves for ohmic process at various implemented voltages: a) E. coli, b) S. aureus, c) S. enterica subsp. enterica serovar Paratyphi A, d) S. Typhi, e) S. dysenteriae, f) S. flexneri.
of a uniform temperature field in the container. The variations in the mixture temperature are presented in Fig. 6 for CFD simulation as well as the conducted experimental examination for the ohmic (part a) and conventional (part b) inactivation processes. Moreover, the container was supposedly divided into three sections, and the mixture temperature was measured using thermocouple probes at the center of each section. Therefore, the mixture temperature was measured uniformly at equal distances (Fig. 6c). The illustrated temperatures for the conventional method were measured based on the average container temperature. According to the obtained results, the numerically predicted temperatures were in good agreement with the
measured data. For low to moderate temperatures, the apparent error was below 2%, while for higher temperature magnitudes a maximum error of 5% can be observed. As the implemented potential difference was increased, the mixture temperature was elevated, however, for the initial 30 s period of time; the difference between various cases was negligible. It should be added that as the phase change process was not considered in the current CFD simulation, the numerical modeling was only performed for 110 s when the temperature was below the boiling point. Moreover, the continuity, momentum and energy equations for the natural convection issue were coupled (the buoyancy term in the 321
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Table 1 The evaluated statistical parameters for the kinetic models. Weibull model
E. coli S. aureus S. enterica subsp. enterica serovar Paratyphi A S. Typhi S. dysenteriae S. flexneri
150 v 200 v 250 v 150 v 200 v 250 v 150 v 200 v 250 v 150 v 200 v 250 v 150 v 200 v 250 v 150 v 200 v 250 v
Modified Gompertz 2
b
n
Adj_R
1.01E−8 0.83E−9 3.93E−9 8.84E−9 2.52E−9 8.60E−5 3.45E−7 4.34E−7 3.04E−7 5.80E−6 7.34E−8 3.16E−8 4.50E−7 2.79E−7 1.51E−6 1.41E−6 1.01E−6 1.81E−6
4.391 5.044 4.826 4.432 4.802 2.57 3.631 3.659 3.952 2.965 4.062 4.357 3.572 3.754 3.573 3.333 3.479 3.444
0.992 0.991 0.989 0.986 0.984 0.963 0.985 0.989 0.993 0.976 0.990 0.991 0.980 0.990 0.995 0.989 0.994 0.974
RSME
B
C
M
Adj_R2
RSME
0.1747 0.1758 0.2104 0.2516 2.449 0.4629 0.2565 0.2127 0.1661 0.3476 0.2129 0.191 0.301 0.2027 0.1334 0.2308 0.1596 0.3587
0.0194 0.0050 0.0096 0.0506 0.0136 0.0474 0.0299 0.0160 0.0053 0.0453 0.0304 0.0266 0.0596 0.0217 0.0121 0.0182 0.0086 0.0174
49.22 9.99E+05 3982 9.828 265.6 9.67 15.22 68.6 8.00E+05 8.068 20.3 30.06 7.517 32.68 443.4 30.41 712.5 68.91
138.2 586.4 274.2 84.69 187.9 60.67 97.6 145 534.1 80.6 95.29 98.4 76.21 114.3 190.3 124.8 268.4 129.3
0.996 0.994 0.989 0.998 0.983 0.972 0.995 0.989 0.996 0.995 0.992 0.982 0.997 0.990 0.997 0.996 0.995 0.972
0.1135 0.1442 0.2079 0.0737 0.2549 0.4043 0.1404 0.2155 0.1172 0.16 0.1899 0.2766 0.1127 0.1978 0.1119 0.134 0.1453 0.3735
and 5.044 for E. coli, and its lowest value occurred for S. flexneri in the range of 3.333 to 3.479. The higher value of n parameter indicated more abrupt behavior in the microbial inactivation. On the other hand, the b parameter as the pre-exponent coefficient represents the rate of inactivation. Considering the fact that the value of n is not the same for all of the applied voltages, the effect of implemented voltages can't be examined directly based on the value of the b parameter (Table 1). According to the modified Gompertz function, C parameter is the difference between the upper and lower asymptotes, B is the relative inactivation rate at M and M is the occurrence instance of the maximum death rate. Based on the obtained results the time required to reach the maximum inactivation rate (M) was increased by utilization of higher voltages. The inactivation curves for all of the examined pathogens at various implemented voltages of 150, 200 and 250 v are depicted in Fig. 7. According to the obtained results, as the applied voltage was increased, the required time for the inactivation process was decreased, e.g., the required inactivation time was reduced from 100 to 80 s for E. coli and from 100 to 70 for S. enterica subsp. enterica serovar Paratyphi A by increasing the electrodes voltage from 150 to 250 v. Moreover, the effect of increasing in the applied voltage was different for the various bacteria examined in the current study. For the initial 60-s time interval, the increasing in the utilized voltage from 150 to 250 v resulted in only 0.6-log CFU/mL reduction for E. coli while a significant reduction of 2.8-log CFU/mL was observed for S. aureus. Based on similar analysis, variation of implemented voltage had higher influence on E. coli, S. Typhi and S. flexneri at early stages (prior to 60s), while the other bacteria (S. aureus, S. enterica subsp. enterica serovar Paratyphi A and S. dysenteriae) showed higher inactivation rate after the first 60-s of experiment. Additionally, it should be stated that the variations in the required process time is a function of both applied voltage and the temperature of field inside the examined domain. Hence, any parameter of the study should be conducted by neutralizing the effect of other involving parameters. However, for the present simulation, these two variables were completely connected and changed accordingly. However, the variations in pathogens population were strongly associated with the temperature field, the produced temperature filed was in direct correlation with the applied apparatus voltage (the thermal source term was a direct function of applied voltage). Moreover, to make the results useful for applicable purposes, the main variable was selected to be the system voltage, and the temperature field was reported as a function of applied voltage.
momentum equation and the convective term in the energy equation are the links between these two equations). Therefore, it would be impossible to obtain accurate results for the temperature without computing the velocity field precisely by the aid of mathematically modeling. In other words, the validation of temperature field implicitly guarantees the accuracy of the calculated velocity field. Additionally, to improve the validation process, the temperature measurements at two more points are also illustrated in Fig. 6a. The temperatures at these three separate points can be used to validate the solution of energy equation as well as the capability of the numerical simulation to determine energy convective term due to the fluid velocity and vortices. The temperature elevation history for the conventional method is illustrated in Fig. 6b. The required time to elevate the mixture temperature for the conventional method was considerably higher than those corresponded with the ohmic process (e.g., the mixture temperature was increased to 70 °C in 65 s for ohmic heating while 27 min was required for the same temperature increase via conventional method). The different nature of the involving heat generation and transfer mechanisms were the reasons for the significant difference in temperature increasing durations. In the case of conventional method, the thermal energy was transferred from a heated fluid outside of the domain. Therefore, the thermal resistance of the outer fluid, as well as container wall, caused a reduction in the magnitude of the heat flux. Additionally, the natural convection heat transfer (which plays an important role in heat transfer of ohmic heating process via the creation of vortices) was weaker for conventional method due to the nearly uniform temperature elevation of lower and upper parts of the vessel. The mentioned important role of the natural convection referred to the role in circulating the fluid inside the container part and creating a uniform temperature field in comparison to the conventional method in which a gradually varying temperature filed (stratified) was created. In other words, for the conventional method, the heat flux was transferred through the system walls and gradually reached to the center of the container; however, for the ohmic heating process the global heat generation and the natural stirring due to the buoyancy effect produced a more uniform and more rapid temperature elevation. 3.2. Kinetic modeling The Weibull model main parameters are n and b which represent the shape factor of curves and the scale factor. The shape factor of curves was above unity which indicated a downward concave form for the curves (Fig. 7). The highest value of shape factor was between 4.391 322
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Log CFU/mL
S.M.B. Hashemi, R. Roohi
S. Typhi
Fig. 8. The logarithmic reduction of the microbes' quantity for ohmic inactivation at various implemented voltages after 60 s.
The inactivation value of all of the examined bacteria for implemented voltages of 150–250 after 60-s from the process initiation is shown in Fig. 8. The inactivation values are defined as the difference between the logarithmic number of pathogens after 60 s and at the initial instance. As stated previously, some of the pathogens were responded more quickly to the applied ohmic heating, 3.1, 3.2 and 3.4 reduction in the logarithmic number of the bacteria was observed for S. aureus, S. enterica subsp. enterica serovar Paratyphi A and S. dysenteriae, while a lower value of 1.2, 1.5 and 1.9-log CFU/mL was observed for E. coli, S. Typhi and S. flexneri, respectively. Besides, it can be concluded that the sensitivity of the bacteria to the implemented voltage was maximum for S. aureus by increasing the ohmic voltage from 150 to 250 v (the observed increase is defined as the relative increase of inactivation value due to 100 v increase of applied voltage from 150 to 250 v). The next highest inactivation sensitivity to the applied voltage belonged to S. dysenteriae, S. enterica subsp. enterica serovar Paratyphi A, S. Typhi, E. coli and S. flexneri with an increase of 680, 457, 375, 240 and 237% in the inactivation value by enhancement of the applied voltage from 150 to 250 v, respectively. Palaniappan and Sastry (1991) reported thermal effect is the main factor in the inactivation of microorganisms by ohmic heating. Additionally, an extra effect is electroporation in the microbial cell membrane. Electroporation is correlated to charge transfer resulting from differences between the internal and external potential of microorganisms subjected to ohmic heating. This event causes the creation of pores in the proteins and lipid bilayer of microbial cell membranes (Park & Kang, 2013). Lee, Sagong, Ryu, and Kang (2012) found the ohmic treatment of orange juice reduced E. coli O157: H7 more than 5-log after 60, 90 and180 s treatments with 40, 35 and 30 V cm−1 electric field strength, respectively. In tomato juice, ohmic treatment with 25 V cm−1 for 30 s resulted in a 5-log reduction in E. coli O157: H7. Similar results were observed in L. monocytogenes and S. Typhimurium. It was reported Alicyclobacillus acidoterrestris spores treated with ohmic heating had higher lethality compared to spores treated with conventional heating in orange juice. Conventional heating was ineffective for pasteurization of the juice; while the ohmic heating treatment applied at 30 V cm−1 was adequate to a 5-log reduction of A. acidoterrestris spores (Baysal & İçier, 2010).
confined vortices above and below the electrodes' tips, while for later instances, the propagation of the generated thermal energy in addition to the emerged velocity vortices resulted in fluid motion throughout the computational zone. As the applied voltage was increased, the required time for the inactivation process was decreased, e.g., the required inactivation time was reduced from 100 to 80 s for E. coli and from 100 to 70 for S. enterica subsp. enterica serovar Paratyphi A by increasing the electrodes voltage from 150 to 250 v. The sensitivity of the bacteria during ohmic heating was maximum for S. aureus, followed by E. coli, S. enterica subsp. enterica serovar Paratyphi A, S. Typhi, S. dysenteriae and S. flexneri. This study can be integrated into a multi-criteria optimization approach to improve the ohmic heating process and give desired results. References Baysal, A. H., & İçier, F. (2010). Inactivation kinetics of Alicyclobacillus acidoterrestris spores in orange juice by ohmic heating: Effects of voltage gradient and temperature on inactivation. Journal of Food Protection, 73(2), 299–304. Buzrul, S., Alpas, H., & Bozoglu, F. (2005). Use of Weibull frequency distribution model to describe the inactivation of Alicyclobacillus acidoterrestris by high pressure at different temperatures. Food Research International, 38(2), 151–157. Caccavale, P., De Bonis, M. V., & Ruocco, G. (2016). Conjugate heat and mass transfer in drying: A modeling review. Journal of Food Engineering, 176, 28–35. Chen, H., & Hoover, D. G. (2003). Modeling the combined effect of high hydrostatic pressure and mild heat on the inactivation kinetics of Listeria monocytogenes Scott A in whole milk. Innovative Food Science & Emerging Technologies, 4(1), 25–34. Churchill, S. W., & Chu, H. H. (1975). Correlating equations for laminar and turbulent free convection from a horizontal cylinder. International Journal of Heat and Mass Transfer, 18(9), 1049–1053. Crilly, J., & Fryer, P. (1993). New directions in food research: The role of mathematical models in food processing. IMA Journal of Management Mathematics, 5(1), 265–282. Davies, L. J., & Fryer, P. J. (2001). Modeling electrical resistance (“ohmic”) heating of foods. Food processing operations modeling (pp. 227–264). CRC Press. Diels, A. M., Wuytack, E. Y., & Michiels, C. W. (2003). Modelling inactivation of Staphylococcus aureus and Yersinia enterocolitica by high-pressure homogenisation at different temperatures. International Journal of Food Microbiology, 87(1–2), 55–62. Fryer, P. J., Knoerzer, K., & Juliano, P. (2011). The future of multiphysics modeling of innovative food processing technologies. Innovative food processing technologies: advances in multiphysics simulation (pp. 353–364). . Gally, T., Rouaud, O., Jury, V., & Le-Bail, A. (2016). Bread baking using ohmic heating technology; a comprehensive study based on experiments and modelling. Journal of Food Engineering, 190, 176–184. Ghiji, M., Goldsworthy, L., Brandner, P. A., Garaniya, V., & Hield, P. (2017). Analysis of diesel spray dynamics using a compressible Eulerian/VOF/LES model and microscopic shadow graphy. Fuel, 188, 352–366. Hashemi, S. M. B., Amininezhad, R., Shirzadinezhad, E., Farahani, M., & Yousefabad, S. H. A. (2016). The antimicrobial and antioxidant effects of Citrus aurantium L. flowers (Bahar narang) extract in traditional yoghurt stew during refrigerated storage. Journal of Food Safety, 36(2), 153–161. Hashemi, S. M. B., Mousavi Khaneghah, A., Fidelis, M., & Granato, D. (2018). Effects of pulsed thermosonication treatment on fungal growth and bioactive compounds of
4. Conclusion The numerically predicted temperatures were confirmed by the measured data. For low, to moderate temperatures, the apparent error was below 2%, while for higher temperature magnitudes a maximum error of 5% can be observed. The initial temperature increase caused 323
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