Effect of pressure-dependent slip on flow curve multiplicity |
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Authors: | K Arun Kumar M D Graham |
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Institution: | (1) Department of Chemical Engineering and Rheology Research Center University of Wisconsin-Madison Madison, WI 53706-1691 USA E-mail: graham@engr.wisc.edu, US |
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Abstract: | Various microstructural pictures for slip at polymer/solid interfaces lead to relations which have a region where multiple
values of slip velocity are predicted for the same shear stress. This leads to the expectation of multivalued flow curves,
which has been verified in specific cases by numerous researchers. We study the effect of pressure dependence on flow curve
multiplicity using a simple multivalued slip relation to model the phenomena of hysteresis and spurt flow in polymer extrusion.
A continuation technique is used to trace out the boundaries of the region of flow curve multiplicity as pressure drop and
die length to diameter (L/D) ratio are changed. Results for Newtonian, shear thinning and viscoelastic constitutive equations show that, despite the
multivalued nature of the slip model, multiplicity (and thus hysteresis) is absent at high L/D. For the sake of completeness, we also carry out time-dependent simulations at constant piston speed taking fluid compressibility
into account. These simulations show that oscillations in the pressure drop and exit volumetric flow rate result only if the
system is operated in the multiplicity region of the steady state flow curve, in agreement with the results of similar simulations
by researchers using various multivalued slip models without pressure dependence. The results demonstrate that a multivalued
slip model does not guarantee multiplicity in the flow curve for the constant pressure drop operation, nor oscillations for
constant piston speed operation.
Received: 18 August 1997 Accepted: 30 March 1998 |
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Keywords: | Extrusion multiplicity slip bifurcation analysis pressure effects |
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