Dynamics of particle-laden thin films [DELETED]

Dynamics of particle-laden thin films [DELETED]

###### CNCS Seminar

#### Jeffrey Wong (Duke University, Mathematics)

**Tuesday, April 24, 2018 -3:00pm to 4:00pm**

Under shear, particles suspended in a viscous fluid migrate due to the induced stresses, leading to dispersion of the particle phase. For a film flowing down an incline, particles are driven towards the free surface, which can lead to accumulation of particles at the leading front, even when the particles are negatively buoyant. We consider these dynamics in the lubrication limit for suspensions of moderate to dense concentrations, accounting for the non-uniform distribution of particles in the bulk of the fluid. Assuming a separation of time scales between the fast normal migration of particles and slower flow down the incline, the lubrication model yields a system of PDEs for the depth-integrated flow coupled to a diffusion equation for the particle equilibration in the normal direction. Depending on the distribution of particles, the mixture may either separate into distinct fronts or accumulate at a single particle-rich ridge. We explore how the particle distribution determines this behavior, and how shock solutions of the depth-integrated system can be used to describe the downstream dynamics. Of particular interest are singular shock solutions due to the accumulation of particles towards the maximum packing fraction, which introduces a degeneracy into the equation. The saturated ridge at high concentrations is considered in detail with the addition of surface tension, which regularizes the degeneracy.