Note: CD, capillary die attached to the extruder; CR, capillary rheometer; CDV, capillary die viscometer is capillary die with multiple transducers along its length; SDV, slit die viscometer is slit die with multiple transducers along its length.

Note: CD, capillary die attached to the extruder; CR, capillary rheometer; CDV, capillary die viscometer is capillary die with multiple transducers along its length; SDV, slit die viscometer is slit die with multiple transducers along its length.

To account for the shear history in the extruder, an equation was suggested of the form (73).

t]S{y, T,M,N) = tfy"-1 exp(JE/RT) exp(KM)N~a (5)

The flow curves obtained using a capillary rheometer (9) and slit-die viscometer were significantly different for food doughs (corn grits and potato flour), whereas for low-density polyethylene the flow curves were the same whether obtained using a capillary rheometer or slit-die viscometer. The flow behavior index was found to be affected by screw speed and temperature. This would indicate that shear history is varying, due to different screw speeds. Hence, the Bagley procedure for obtaining the viscosity during extrusion cooking is invalid because the fluid entering the die is Theologically not the same for each condition. A model has been developed that accounts for the thermal and mechanical energy imparted to the product (shear history) before the viscosity is measured (78).

In addition to these viscosity models, two recent models are worth mentioning. They present almost identical expression for starch and protein doughs based on reaction kinetics (79,80). The models are cumbersome because of the large number of constants (10 or more). One notable feature of these models is the inclusion of yield stress. Another study indicated that soy doughs exhibited yield stress (72). The magnitude of yield stress was found to be a function of temperature.

There are several drawbacks to the existing viscosity models. The model of Harper and co-workers (68) assumes that the decrease in viscosity is due to shear thinning only. Most plastic polymers are modeled by a network of mac-romolecular entanglements. Shear thinning flow is associated with the decrease of the entanglement density under the influence of deformation of the polymer (81). For food doughs the decrease in viscosity is due to the sum of shear thinning process history (screw configuration, residence time), and molecular degradation. A complete model that quantifies the effect of parameters other than product moisture and temperature on shear viscosity is still lacking. These effects are discussed in Ref. 82, though no attempt has been made to quantify them. Another drawback of these models are that the fluid is assumed to be inelastic, ie, normal stress effects are neglected. Because doughs are viscoelastic fluids, inelastic models are inadequate. Evidence has been presented that the pressure drop experienced at the entrance of the die is much greater than that predicted by shear viscosity alone, indicating that elasticity is important (79). As will be discussed later, elasticity is important in the manufacture of products at temperatures below 100°C.

Extruded starches are used as thickening agents or as ingredients in instant foods. The viscosity of powdered ex-trudate in solvent (water) has also received attention. Typically, shear thinning behavior is observed in all cases. Increasing the concentration of wheat starch from 5 to 9% in solution resulted in the shifting of flow behavior from almost Newtonian to shear thinning (83). For plastic polymers it is known that when the molecular weight is greater than a certain critical molecular weight, non-Newtonian flow behavior is observed (81). Extruded cornstarch in solution exhibited a constant viscosity at high and low shear rates (Fig. 6) (84). Increasing barrel temperature decreased the values of the constant viscosities, whereas increasing moisture content was found to increase the values of constant viscosity, ie, depended on the severity of the extrusion environment.

The effect of emulsifiers on dough viscosity has also been studied (70). The presence of sodium stearoyl-2-lactylate (SSL) was found to affect the viscosity, whereas diacetyltartaric acid ester of monoglyceride did not affect the viscosity. Fat did not affect the viscosity when SSL was present, but it was found to increase the viscosity in the absence of additives.

Normal Stress Difference

It is seen from equation 1 that when Nx and N2 are not equal to zero the normal stresses are unequal. The presence of unequal normal stresses can create some interesting phenomena (85). The reason for nonzero values of Nx and N2 can be attributed to the anisotropy of fluid microstructure in the flow field and is observed in elastic fluids (86). The ratio of primary normal stress difference to the wall shear stress is an indirect measure of the elasticity of the fluid, ie, the higher the ratio, the more elastic is the fluid.

Measurement of normal stress differences on-line has been a subject of intense research among polymer engi-

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