Thermal Food Processing

Ohmic Heating for Food Processing 439
concentration increases, they will increasingly block the conduction paths, forcing
a greater proportion of the total current to flow through them, thus showing higher
heat generation rates than those of the fluid. This means that the particles’ σ, although
lower than the fluid’s σ at low temperatures, will increase faster (Figure 14.6b),
overtaking the latter for higher temperatures and therefore justifying the shape of
the heating curves in Figure 14.6a.
Attempts have been made to determine the (overall) σ eff of particle–fluid
mixtures, which is a function of the conductivity and solids fraction of the component
phases. The first relation was determined by Maxwell, as quoted by Fryer
and Li 20 and is valid for a dilute dispersion of spheres with a volume fraction ε p
and electrical conductivity σ p immersed in a fluid with electrical conductivity σ f:
f p
where Φ= .
(14.18)
Modifications of this equation have been proposed, and there are a number of
different models for σ eff. 26 However, the main problem persists because σ eff will
vary with the position and orientation of the particles in the mixture. Kopelman 17
proposed the following model:
where
C ε p
σ −σ
2⋅σ
f −σp
(14.19)
These models (of which Equation 14.19 is an example) can be of use if they
are representative of the conditions under which they are to be applied. If this is
the case, then it is possible to use σ eff to estimate the temperature increase of a
mixture when it is subjected to OH by a very simple calculation.
14.2.4 MODELS
σ p ( σ f )
2
= 3 ⋅ 1 − .
1−2⋅Φ⋅εp σeff = σ f ⋅
1+
Φ ⋅ε
σ
eff
σ f ⋅( 1−C)
=
( 1−C) ⋅ 1−ε
The models described in the following sections are either the ones that are most
quoted in the literature or those that, in our opinion, constitute important landmarks
in the modeling effort in OH. Generally speaking, all assume that the
physical properties of the phases present in a food are constant with respect to
the temperature, with the obvious exception being electrical conductivity. Considering
the coexistence of several solid particles immersed in a fluid, it is also
generally assumed that the particles have short interaction times with the surrounding
particles and with the walls of the heater.
p
1
3 ( p )