Thermal Food Processing

Ohmic Heating for Food Processing 429
where σ is the electrical conductivity, and is the voltage gradient. This
equation has been obtained combining Ohm’s law with the continuity equation
for electric current, 13 ∇V
and differs from the usual form of Laplace’s equation:
(14.2)
because σ is a function of both position and temperature.
In order to solve Equation 14.1, boundary conditions specific for each case
must be established. The solution has been obtained by de Alwis and Fryer 1 for
a static ohmic heater containing a single particle, using as boundary conditions:
(1) a uniform voltage on the electrodes, or (2) no current flux across the boundary
elsewhere. For a more general case of many different particles flowing in a fluid
composed of several liquid phases (e.g., vegetable soup, where different vegetable
solid pieces are dipped in a fluid broth with at least an aqueous and a lipid phase),
the mathematical solution for Equation 14.1 is, to our knowledge, still unknown.
In these cases, the prediction of the electric field has been based on semiempirical
models (see, for example, Sastry and Palaniappan 14 or Sastry 15 ).
The determination of the electric field is one of the most challenging subjects
of the modeling effort in OH technology.
14.2.1.2 Heat Generation
∇ 2V = 0
In order to ohmically heat a food, it is necessary to pass electrical current through
it. The heat generated in the food by that current ( ̇Q ) is proportional to the square
of its intensity (I), the proportionality constant being the electrical resistance (R),
thus yielding
̇Q= R⋅I2 Alternatively, if both electrical conductivity (σ) and voltage gradient
are known, it is possible to write
̇Q = | ∇V| ⋅ 2 σ
(14.3)
( ∇V )
(14.4)
where σ is a function of position and temperature. The dependence of position
is because foods are not necessarily homogeneous materials, the limiting scenarios
being foods containing particles (e.g., vegetables soup) and that of a reasonably
homogeneous liquid (e.g., orange juice). The relation of σ with temperature
is usually well described by a straight line of the type 5
σ = σ ⋅ [ 1+
m⋅( T −T
)]
T ref ref
(14.5)
where σ T is the electrical conductivity at temperature T, σ ref is the electrical
conductivity at a reference temperature, T ref, and m is the temperature coefficient.