Particle-laden filaments from a draining suspension

Abstract

We investigate the drainage of a suspension of non-colloidal particles from an air-filled vertical Hele-Shaw cell. When the channel gap thickness is comparable to the particle size, the suspended particles move slower than the draining fluid and cause interfacial deformations as they push against the receding oil-air interface. Distinct from the classic viscous fingering, the resultant patterns comprise thin particle-laden filaments that grow normal to an otherwise flat receding interface. When we further increase the drainage rates, we recover the classic Saffman-Taylor instability that is enhanced by the effective viscosity of the suspension. To rationalize the onset of this particle-scale instability, we derive a simple scaling law based on the force balance on a single particle entrained in a draining fluid, in reasonable agreement with our experimental data. We demonstrate that the resultant instability indeed comes from the dynamics of individual particles by reproducing it with a single particle for a narrower range of experimental parameters.