A mathematical treatment of the bump structure of particle-laden flows with particle features

In this study, we consider particle-laden flows on an inclined plane under the effect of gravity. Previous experimental works have noted that a particle-rich ridge is generated near the contact line. We investigate the bump structure observed in particle-rich ridges in terms of Lax’s shock waves in the mathematical theory of conservation laws, explicitly considering the effect of particles with nontrivial radii on morphology of particle-laden flows. We also extract the dependence of radius and concentration of particles on the bump structure.