Effect of pressure-dependent slip on flow curve multiplicity

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.