Instabilities in Shear Flow of Viscoelastic Fluids with Fading Memory
Abstract
For certain models of viscoelastic fluids with fading memory, classical steady channel flow does not exist beyond a maximal wall shear stress. This occurs when the shear stress for steady flow decreases with strain. For generalized Newtonian models of viscoelastic flow, such a decrease implies that the flow is unstable. Because of this example, a constitutive relation that exhibits a maximal wall shear stress in regarded as defective. The author reports on work showing that, contrary to this intuition, such models correctly describe the experimentally observed spurt phenomenon: exceeding this critical stress results in large increase in volumetric flow rate. The transition to spurt flow is analogous to a dynamically generated phase transition. To analyze this phenomenon, we derive a system of conservation laws that govern the flow; these equations take the form of gas dynamics with relaxation terms. We solve the Riemann problem for this non-strictly-hyperbolic system, and incorporate this solution into the random choice method. Numerical simulation of channel flow, with the maximal wall shear stress exceeded, shows that a discontinuity forms at the wall, allowing the fluid to slip; no steady state exists. However, when a small Newtonian viscosity is included in the model, a slip layer forms and the flow approaches a discontinuous steady state.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1988
- Accession Number
- ADA203735
Entities
People
- Bradley J. Plohr
Organizations
- University of Wisconsin–Madison