Theory for Shock Dynamics in Particle-Laden Thin Films

Junjie Zhou, B. Dupuy, A. L. Bertozzi, and A. E. Hosoi
Phys. Rev. Lett. 94, 117803 – Published 23 March 2005

Abstract

We present a theory to explain the emergence of a particle-rich ridge observed experimentally in a thin film particle-laden flow on an incline. We derive a lubrication theory for this system which is qualitatively compared to preliminary experimental data. The ridge formation arises from the creation of two shocks due to the differential transport rates of fluid and particles. This parallels recent findings of double shocks in thermal-gravity-driven flow [A. L. Bertozzi et al., Phys. Rev. Lett. 81, 5169 (1998); J. Sur et al., Phys. Rev. Lett. 90, 126105 (2003); A. Münch, Phys. Rev. Lett. 91, 016105 (2003)]. However, here the emergence of the shocks arises from a new mechanism involving the settling rates of the species.

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  • Received 20 July 2004

DOI:https://doi.org/10.1103/PhysRevLett.94.117803

©2005 American Physical Society

Authors & Affiliations

Junjie Zhou1, B. Dupuy1, A. L. Bertozzi2, and A. E. Hosoi1

  • 1Department of Mechanical Engineering, Hatsopoulos Microfluids Laboratory, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
  • 2UCLA Mathematics Department, Box 951555, Los Angeles, California 90095-1555, USA

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Issue

Vol. 94, Iss. 11 — 25 March 2005

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