A pseudo-viscoelastic approach for transient polymeric flow exiting a channel

The influence of elasticity of a fluid exiting a channel is examined on transient coating downstream. A hybrid spectral/boundary element approach is proposed to solve the problem. The flow inside the channel is assumed to be fully developed. A viscoelastic instability of one-dimensional plane Couette flow is first determined for a large class of Oldroyd fluids with added viscosity, which typically represent polymer solutions composed of a Newtonian solvent and a polymeric solute. The Johnson-Segalman equation is used as the constitutive model. The velocity profile inside the channel is taken as the exit profile for the emerging free-surface flow. The flow is assumed to be Newtonian as it emerges from the channel. An estimate of the magnitude of the rate-of-strain tensor components in the free-surface region reveals that they are generally smaller than the shear rate inside the channel. The evolution of the flow front is simulated using the boundary element method. For the channel flow, the problem is reduced to a nonlinear dynamical system using the Galerkin projection method. Stability analysis indicates that the channel velocity may be linear or non-linear depending on the range of the Weissenberg number. The evolution of the coating flow at the exit is examined for steady as well as transient (monotonic and oscillatory) channel flow. It is found that adverse flow can exist as a result of fluid elasticity, which can hinder the process of blade coating. Copyright (C) 2003 John Wiley Sons, Ltd.