  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.
