Elastohydrodynamic collision of wet particles

The dynamics of small elastic particles coated with thin liquid layers has many applications in the chemical and pharmaceutical industries, including wet granular flows, dispersion filtering, particle agglomeration, slurry transport, spray coating, and pneumatic transport. Here, we extend the hard-sphere model of Davis & Sitison, Phys. Rev. Fluid. 2020, to a soft-sphere model with dynamic particle deformation. We combine lubrication theory and Hertz contact theory of linear elasticity to model the elastohydrodynamic deformation during a collision of two wet spheres. The problem is governed by an interplay between the Stokes number, elasticity parameter, and dimensionless thickness of the fluid film, which determine whether or not the particles will rebound after collision. We develop an asymptotic theory for head-on collisions in the regime of small deformations. For larger deformations (i.e., comparable to the gap size), the pressure due to squeezing lubrication in the fluid-filled gap between the particles leads to elastic deformation, which allows the particles to rebound without touching each other. Particle deformation causes a decrease in relative velocity during the approaching phase, resulting in longer collision times. For small particle inertia, agglomeration occurs, while for small elasticity numbers, the hard-sphere limit is approached.