Steady Free Surface Flow of a Fluid-Solid Mixture Down an Inclined Plane

The present work is an extension of the investigations performed by Massoudi and Anand (2001). The free surface flow problem is studied here. Numerical solutions for steady free surface flow of a solid-fluid mixture down an inclined plane are presented. The problem is formulated using the mixture theory framework. The resulting set of three coupled nonlinear differential equations is nondimensionalized. A parametric study is conducted to understand the influence of the dimensionless numbers on the velocity and volume fraction. The maximum fluid velocity is found to decrease with increase in the ratio of the drag force to the viscous forces within the fluid phase (D₁). The fluid phase velocity was found to decrease with increase in the ratio of the drag force to viscous force within the solid component (D₂), and the corresponding solid phase velocity was found to increase.