Conference Record of the 1996 IEEE International Symposium on Electrical Insulation, Montreal, Quebec, Canada, June 16-19,1996

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Space Charge Near Microbes During Pulsed Electric Field Pasteurization of Liquid Foods

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R. E. Bruhn , P. D. Pedrow, and R. G. Olsen School of Electrical Engineering and Computer Science

B. G. Swanson Department of Food Science and Human Nutrition

Abstract: Inactivation of microbes by the application of pulsed electric fields could result in low temperature pasteurization of liquid foods. Advantages over conventional heat pasteurization include longer shelf life, better flavor, and less enzyme damage. In this work, fields as high as 40kVkm have been applied to milk, apple juice, and electrolyte that was inoculated with microorganisms. Modeling of the microbes during exposure to these intense electric fields is described. Suspension solution and liquid protoplasm are modeled with a relative pemittivity of 81 and each contains two species of ionic charge carriers (one species plus and one species minus). The microbe membrane is modeled with a relative permittivity of 2 and zero conductivity. The continuity equation has been solved numerically in 1 dimension for low ion concentration to investigate the transient behavior of space charge sheaths near the microbes. Free surface charge density, which accumulates on both sides of the cell membrane is also described by this model. Mesh size and simulation time step were adjusted to resolve space charge sheath dynamics near the microbes.

INTRODUCTION Pasteurization of liquid foods by pulsed electric fields

has been studied as an alternate to conventional thermal pasteurization [ 1,2,3,4,5]. Microbe mortality may be caused by electroporation which is the creation of pores in the cell membrane when voltage drop across the membrane exceeds about 1 volt [6]. Electric fields on the order of 40 kV/cm have been applied to a variety of microbes that have included Escherichia coli, Staphylococcus aureus, Bacillus subtilis, Saccharomyces cerevisiae, Yersinia enterocolitica, Listeria monocytogenes, and Candida albicans. Liquid suspensions have included milk, apple juice, NaCl solution, and a simulated milk solution (described in [SI). Depending on parameters, these pulsed electric fields have produced

survival fractions smaller than lo-* . Since this inactivation of microorganisms takes place at temperatures substantially lower than for conventional heat pasteurization, improved flavor, longer shelf life, and reduced enzyme damage are possible improvements in the final product [7,8].

Previous work, which was cited above, focused on microbial and high voltage engineering issues such as culture techniques and dielectric breakdown of the test chamber. Electrical modeling of the space charge sheaths that form within the liquid suspension near the liquidelectrode interfaces has been described [9]. Response of

G. V. Barbosa-Canovas Department of Biological Systems Engineering

Washington State University Pullman, WA 99164

microorganisms to electric fields has been investigated by others who were studying electroporation [6] and cell fusion [10,11]. In that work, cell inactivation usually was not the objective as it is in the present work.

In its simplest form, the cell membrane is composed of a lipid bilayer with the hydrophobic ends of the molecules being shielded from the suspending liquid (and from the protoplasm of the microbe) by the hydrophilic ends of the molecules [6]. In reality, cell membranes are quite complex [ 12,131.

In this work, we have used numerical techniques to simulate the cell membrane of a microorganism exposed to large electric fields. During early model development, the membrane has been represented by a shell of lossless dielectric encasing a region of lossy dielectric (the protoplasm) with the entire system immersed in a third lossy dielectric (the suspension liquid). Each of these three regions have been assumed linear, homogeneous, and isotropic.

We have assumed planar geometry and that the space charge sheaths are too weak to have significant influence upon the externally applied electric field. More realistic assumptions (to be used in future work) are described below in the Discussion section.

PLANAR MODEL Assumptions

Figure 1 shows the five regions being modeled and Table 1 describes parameters used to characterize each region. Initially all interfaces are assumed to have zero free surface charge density but free surface charge accumulates at the interfaces as the simulation progresses.

Suspenslor Liquid

Figure 1. Five regions being considered in the planar model.

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I Table 1. I

For each ion species a we can write the continuity equation as

-+V.(n, i ia) h a = 0 at

where n, and Ea are concentration and fluid velocity,

respectively, for ion species a. We assume there are no volume sources nor volume sinks of ions; however, ions can impinge on and exist as free surface charge density at interfaces. Ion mobility can be used to write -

ii, = p,E (2)

where p a is mobility of species a and is electric field.

Ion diffusion and motion of the suspension liquid have been ignored. Using a vector identity, Eqs. (1) and (2) can be combined to give

(3)

The third term is assumed small enough to be neglected (this will be valid only for small volume charge density) giving

(4)

Numerical Algorithm The numerical simulation begins at t=O by assuming a

step increase in the D field (throughout all 5 regions) from zero to some value Do . Evolving volume charge density in sheaths and surface charge density at interfaces are assumed small enough that D is not significantly modified from its externally applied value, Do . 'Thus we have

Dl = D2 = D3 = D4 = D5 = Do ( 5 )

and

Since D is uniform throughout the five regions, E will be uniform within each region and so Eq. (4) applies. It can be represented [ 141 by the numerical algorithm

At

where i and j are indices that represent the i" spatial grid point and the j" time step, respectively. This is a time centered algorithm, characterized by a high order of accuracy [ 141. For convenience, we form the dimensionless quantity

which is proportional to the fraction of a grid spacing traversed during a time step by an element of the ion fluid traveling at the speed p , E . Substituting Eq. (8) into (7) and placing known densities on the right hand side and unknown densities on the left hand side gives

This yields a set of simultaneous linear equations at each time step for each ion species. Solution to these is obtained by inverting a tridiagonal matrix. Volume space charge density is found from ( 1 . 6 ~ )( n+-n. ) and surface charge density at interfaces is found from the net flux of ions to the interface. Results are shown in the next section.

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Results For the parameters shown in Table 2 the numerical

simulation showed the development of volume space charge

Figure2.

in response to the applied electric field. In addition to the volume charge density shown in Figure 2, the magnitude of the free surface charge density on the four membrane

size of the protoplasm (4 pm) is consistent with real microbes, membrane thicknesses are known to be [12,13] in

Space charge sheaths result from uncompensated charge the range to 2o nm rather than the pm here. A thicker membrane was used for illustrative Purposes.

sheaths on both sides of the cell membrane as shown in Surfaces reached about 1.7~10-~ C/m2 at t = 5pS. While the

that is born when charge of the opposite sign vacates a region

Volume Charge Density Versus z and t

- 0

E 0,

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> I 0 s -0

z(um) igure 2. Volume space charge density as a function of position and time.

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DISCUSSION For more dense ion fluids, volume charge density in

the sheaths and free surface charge density at interfaces will significantly modify the D field so that it will no longer be equal to the externally imposed value Do . For that condition, the more complicated model described in Eq. (3) will be used. Following that, the model will be extended to two dimensions.

ACKNOWLEDGMENT

Office Grant #DAAH04-94-G-0113. This work was supported in part by U. S . Army Research

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[ll] M. Kiyomota and H. Shirai, “Reconstruction of Starfish Eggs by Electric Cell Fusion: A New Method of Detecting the Cytoplasmic Determinant for Archenteron Formation”, Develop. Growth & Differ., Vol. 35 , pp 107-114, 1993.

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[13] F. S . Barnes and C. J. Hu, “Nonlinear Interactions of Electromagnetic Waves with Biological Materials,” in Nonlinear Electromagnetics, edited by P. Uslenghi, N Y Academic Press, pp. 391-426, 1980.

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[ 101 L.Y. Song, et al., “Divalent Cations, Phospholipid Asymmetry and Osmotic Swelling in Electrically-Induced Lysis, Cell

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