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 language | English (US) |
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Pages (from-to) | 322-344 |
Number of pages | 23 |
Journal | SIAM Journal on Applied Mathematics |
Volume | 74 |
Issue number | 2 |
DOIs | |
State | Published - 2014 |
Externally published | Yes |
Keywords
- Conservation laws
- Riemann problem
- Singular shock
- Thin film