2003/12/08 by Rama Govindarajan, Govindarajan, Rama, Prabhu R. Nott +4
Chemical Engineering · Engineering · Physics and Astronomy · #Fluid Dynamics and Thin Films #Fluid Dynamics and Turbulent Flows #Rheology and Fluid Dynamics Studies #cond-mat.soft
paper · pdf · doi:10.48550/arxiv.cond-mat/0312189
28 pages, 6 .eps figures, submitted to Phys Fluids
arxiv created 2003/12/08 · arxiv updated 2009/12/01
Starting from the equations of Stokes flow and the mass conservation of particles as determined by shear-induced diffusion, we derive the coupled equations for the dynamics of particle concentration and film thickness for the free-surface flow of a fluid film pulled up by a tilted wall rising from a pool of neutrally buoyant, non-Brownian suspension. We find an instability of the film with respect to axial undulations of film thickness and modulations of particle concentration, and the instability growth-rate increases as a certain combination of the two dimensionless shear induced diffusivities (which determine the particle flux driven by concentration and shear rate gradients) falls below a critical value. This reinforces the conclusions of \it Phys. Fluids \bf 13 (12), p. 3517 (2001), suggesting an explanation of the experiments of Tirumkudulu \it et al., Phys. Fluids \bf 11, 507-509 (1999); \it ibid. \bf 12, 1615 (2000). In addition, we predict a ``pile-up'' instability in which perturbations that vary in the direction of the wall velocity are amplified; this instability is not driven by shear-induced migration, but is a result of the dependence of the suspension viscosity on the particle concentration.