Shock solutions for high concentration particle-laden thin films

Li Wang, Andrea L. Bertozzi

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We study the shock dynamics for a recently proposed system of conservation laws (Murisic et al. [J. Fluid Mech., 17 (2013), pp. 203-231]) describing gravity-driven thin-film flow of a suspension of negatively buoyant particles down an incline. When the particle concentration is above a critical value, singular shock solutions can occur. We analyze the Hugoniot topology associated with the Riemann problem for this system, describing in detail how the transition from a double shock to a singular shock happens. We also derive the singular shock speed based on a key observation that the particles pile up at the maximum packing fraction near the contact line.

Original languageEnglish (US)
Pages (from-to)322-344
Number of pages23
JournalSIAM Journal on Applied Mathematics
Volume74
Issue number2
DOIs
StatePublished - 2014
Externally publishedYes

Keywords

  • Conservation laws
  • Riemann problem
  • Singular shock
  • Thin film

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