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

  • Author(s): Wang, L
  • Mavromoustaki, A
  • Bertozzi, AL
  • Urdaneta, G
  • Huang, K
  • et al.

Published Web Location

https://doi.org/10.1063/1.4913851
Abstract

© 2015 AIP Publishing LLC. 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.

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