Solutions to a two-phase mass flow model with generalized drag

Drag plays a dominant role in the interfacial momentum exchange in mixture mass flows. In this study, we examine a general two-phase mass flow model formulated by Pudasaini [1], which incorporates drag. This model describes the mass flow comprising a mixture of solid particles and viscous fluid moving downhill under the influence of gravity. We construct explicit, analytical, and numerical solutions to the model using the Lie symmetry method. These new solutions disclose the role of generalized drag in the dynamics of both solid particles and viscous fluid. The solutions show that solid and fluid phases undergo nonlinear evolution in a coupled manner. Additionally, the solutions demonstrate that increased drag results in a tighter binding between solid and fluid components. We also analyze the role of pressure gradients. The solutions reveal that when solid pressure dominates fluid pressure, solid velocity increases faster than fluid velocity. These findings align with our expectations, emphasizing the importance of analytical solution techniques in understanding the complex process of mixture mass transport in mountain slopes and valleys, thereby enhancing our understanding.