Rarefaction-singular shock dynamics for conserved volume gravity driven particle-laden thin film

L. Wang, A. Mavromoustaki, A. L. Bertozzi, G. Urdaneta, K. Huang

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We employ a recently proposed model [Murisic et al., "Dynamics of particle settling and resuspension in viscous liquids," J. Fluid. Mech. 717, 203-231 (2013)] to study a finite-volume, particle-laden thin film flowing under gravity on an incline. For negatively buoyant particles with concentration above a critical value and buoyant particles, the particles accumulate at the front of the flow forming a particle-rich ridge, whose similarity solution is of the rarefaction-singular shock type. We investigate the structure in detail and find that the particle/fluid front advances linearly to the leading order with time to the one-third power as predicted by the Huppert solution [H. E. Huppert, "Flow and instability of a viscous current down a slope," Nature 300, 427-419 (1982)] for clear fluid (i.e., in the absence of particles). We also explore a deviation from this law when the particle concentration is high. Several experiments are carried out with both buoyant and negatively buoyant particles whose results qualitatively agree with the theoretics.

Original languageEnglish (US)
Article number033301
JournalPhysics of Fluids
Issue number3
StatePublished - Mar 9 2015
Externally publishedYes

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