COATING FLOWS AND PROCESSING OF VISCOELASTIC LIQUIDS: FLUID MECHANICS, RHEOLOGY, AND COMPUTER-AIDED ANALYSIS (SPINNING, DIE-SWELL, FINITE-ELEMENT)

Viscoelastic liquids possess memory. Unlike Newtonian liquids, the local state of stress in flowing viscoelastic liquids depends on the upstream kinematics and deformation. Coating flows are small-scale laminar free surface flows by which a liquid film is deposited on a moving substrate. Coating flows of viscoelastic liquids provide highly instructive case studies to advance fundamental understanding of the physics of confined and free surface viscoelastic flows and to develop methods of theoretical and experimental analysis of such flows.;Predictions of the theory compare well with experiments. These experiments include rheological measurements in shear and extensional deformations with the Rheometrics System Four; measurements of free surface profiles of free falling and drawn curtains of viscoelastic liquids; and data from spinning of fibers of viscoelastic liquids and from bubble collapse in baths of viscoelastic liquids.;The combination of nonlinear integral constitutive equation, streamlined finite element discretization, and Newton iteration lead to accurate predictions of viscoelastic flow at high Weissenberg numbers (rate of deformation times average relaxation time): beyond 60 for lubrication and average flows, beyond 20 for two-dimensional channel and free surface flows, and beyond 1 for free surface flows with contact lines. The theory suggests ways and provides the means to extend the predictions at higher Weissenberg numbers when free surface flows with contact lines are encountered. The latter is nowadays feasible with the appearance and fast evolution of the new generation of supercomputers.;The theory rests on modern nonlinear integral constitutive equations and comprehensive Galerkin/finite element methods for the computer-aided analysis of steady, two-dimensional viscoelastic flow. New developments include an integral constitutive equation designed to account for shear deformation, extensional deformation, and mixtures of the two; a modern streamlined finite element method that provides the means for accurate and cost-effective tracking of particles along streamlines; and the application of Newton iteration to sets of integrodifferential equations that involve line-integrals along streamlines that are unknown a priori. Analyses of one-dimensional lubrication and averaged flows as well as of two-dimensional channel and free surface flows demonstrate the power of these methods.