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A boundary element analysis for transient viscoelastic blade coating flow. (English) Zbl 0964.76056

Summary: First, we describe a one-dimensional plane Couette flow for a large class of Oldroyd fluids with added viscosity, which typically represent polymer solutions composed of a Newtonian solvent and a polymeric solute. Next, the determined channel velocity profile is used as the boundary condition at the channel exit for the blade coating flow. The free-surface evolution of the flow at the channel exit is simulated using the boundary element method. It is argued that the free surface flow can be assumed to be Newtonian. For the channel flow, the problem is reduced to a nonlinear dynamical system using the Galerkin projection method. Stability analysis indicates that the velocity profile at the inlet may be linear or nonlinear depending on the range of the Weissenberg number.

MSC:

76M15 Boundary element methods applied to problems in fluid mechanics
76A10 Viscoelastic fluids
76E05 Parallel shear flows in hydrodynamic stability
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