Wn hH n1 U

and the extensional component for the pressure drop is:

These equations have been derived assuming a power law behavior in both shear and extensional flow. Expressions for sudden contraction in cylindrical and rectangular flow can also be found in Cogswell's paper. Several other expressions have been suggested using differing assumptions (118,119). There is no significant difference from the values of strain rate obtained from these expression for low die angles (<30°). A spherical coordinates system was assumed to arrive at a slightly modified expressions for equations 8 and 9 (120). An alternative analysis for determining the extensional viscosity in planar and uniaxial extension has been proposed from entrance pressure-drop data (121123).

Studies on extensional viscosity of food doughs are scarce. A stretch-thinning behavior for corn grits using a capillary rheometer has been reported (124). Similar be havior for corn grits has been noted during extrusion cooking (76). Using Gibson's analysis, these authors found that the extensional viscosity decreased with increasing moisture content. The shear component of the entrance pressure was less than 5%. The Trouton ratio for the doughs ranged from 80-100. Not all materials exhibit shear thinning and stretch-thinning behavior. Several polymeric liquids exhibit stretch-thickening behavior while displaying shear thinning behavior in shear flows.

The entrance pressure-drop method for obtaining extensional viscosity has not been universally accepted. The shear viscosity parameters (B and n in eq. 8) are assumed to be known a priori. These parameters can be calculated from the pressure profile and flow-rate data in the die. At large die entrance angles, poor data fit is observed. The assumption used in the calculation of the shear component of the entrance pressure drop can lead to error. However, the magnitude of this error is expected to be small because extensional flow dominates. Also, only average quantities are computed, whereas in reality the stress and the rate of strain will change with position. It should be noted that this method gives only qualitative comparisons and not definitive data. Hence it is important that a comparison be made between the magnitude of the extensional viscosity obtained from entrance pressure calculations with those obtained by other methods. Such a comparison has been made for polymers, and the values obtained were reported to be of the same order of magnitude (125,126).

Dynamic Oscillatory Flow

The dynamic properties of rice dough have been studied using an on-line rheometer (127). Storage and loss moduli increased with increasing frequency and decreasing moisture content. However, these authors reported significant problems with the equipment and recommended several modifications.

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