Field strength distribution, local

Fig. 3. Heat production is an important consideration for devices using electric fields in the liquid near cells. This figure shows the theoretical distribution of heat production in and around a spherical cell at the centre of a quadrupole electrode chamber in a solution of low electrical conductivity (top) and high conductivity (bottom). The heat production is given by gE2 where g is the conductivity of the solution or cell component and E is the (local) electric field strength. The contour interval is 7% of the maximum in each case. The cell is modelled as an electrically conductive sphere enveloped by an insulating but capacitive membrane.

Poisson-Boltzmann Equation A fundamental equation describing the distribution of electric potential around a charged species or surface. The local variation in electric-field strength at any distance from the surface is given by the Poisson equation, and the local concentration of ions corresponding to the electric-field strength at each position in an electric double layer is given by the Boltzmann equation. The Poisson-Boltzmann equation can be combined with Debye-Hiickel theory to yield a simplified, and much used, relation between potential and distance into the diffuse double layer. 

The study of the spatial electron relaxation in uniform fields has demonstrated its complexity and its sensitive dependence on the field strength. In these relaxation studies, a local disturbance at z = 0 has been initiated by the choice of the boundary value/j(L/) for the anisotropic distribution according to Eq. (59), and the succeeding spatial relaxation in a uniform electric field has been analyzed. 

F and n are local quantities. Only when the charge carriers are homogeneously distributed within the solid is the internal field determined by F = V/d, i.e. uniquely by the applied voltage V between plane-parallel electrodes at a spacing d (Fig. 8.1). And only when n and /x are both constant, and thus not dependent on the field strength F, does Ohm s law hold. 

Not only cell size but also tissue structure may affect the PEF performance, as the efficacy of cell damage is determined by the local electric field near the cell. The distribution of the local electric field strength inside the inhomogeneous material is a complex function of electrical properties, tissue porosity, and structure (Sahimi, 1994). Differences in porosity exist between various types of raw material, or even within the same food material, which may then cause a gradient of electrical conductivity inside the sample and lead to differences in permeabilization effectiveness. 

---