Rheology of Batters Used in Frying
237
ω R
h
FIGURE 10.15 Plate–plate geometry.
where σ is the shear stress in Pa, Md is the torque in N·m and R is the external radius of the plate in m. In the case of non-Newtonian fluids that obey the power law, the shear stress is corrected by the following expression: σ = Md
2 ⎛⎜ 3 + n ⎞⎟ ⎟ ⎜ πR 3 ⎜⎝ 4 ⎟⎠
(10.17)
where n is the power index.
10.6
MODELLING THE NON-NEWTONIAN BEHAVIOR OF BATTERS
A system can respond to a particular shear stress in various ways. To describe these behavior patterns, several equations or mathematical models that relate shear stress to shear rate or viscosity to shear rate have been proposed.
10.6.1 OSTWALD –DE WAELE MODEL For fluids without yield stress, the simplest model is the Ostwald–de Waele model or power law: σ = k ⋅ γ n
(10.18)
where k and n are the rheological parameters of the model. The k parameter is known as the consistency index and n as the flow index. Because for n = 1 the expression reduces to Newton’s law with μ = k, the difference between n and 1 measures the deviation from Newtonian behavior. If n < 1, a rheogram that represents a pseudoplastic fluid is obtained. If n > 1, however, the characteristic rheogram is the one that represents a dilatant fluid. Bearing in mind that apparent viscosity is defined by the quotient of shear stress and shear rate, the Ostwald–de Waele model can be expressed as: η( γ ) = kγ n−1
55585_C010.indd 237
(10.19)
11/6/08 10:32:37 AM