Viscous fingering of a draining suspension

The liquid drainage is a commonplace process that affects a wide array of industrial applications ranging from medical procedures and manufacturing processes to food processing. While many drainage-related applications involve the complex fluids comprising solid particles, the effects of suspended particles on the liquid drainage have not been considered, leaving simple fundamental questions on the suspension drainage unanswered. In this paper, we experimentally investigate the effects of particles on drainage by withdrawing suspensions from an air-filled Hele-Shaw cell in a radial sink flow. As expected, viscous fingering arises as air invades a draining viscous suspension. Despite numerous studies on viscous fingering, only a few have studied this "inward" viscous fingering for pure liquids and none for suspensions. We find that, while the overall behavior of fingering remains unchanged from the pure liquid case, suspended particles are shown to delay the onset of fingering but also to accelerate its growth rate. This surprising dual effect of particles results in the increase of the total drainage time and in the amount of drained suspension as a function of particle concentrations. In addition, the particle entrainment into the thin film of wetting oil causes particles with select sizes to remain on the channel walls instead of draining, which closely follows our simple theoretical prediction.