Linear stability of shear-thinning fluid down an inclined plane

Unsteady granular flows down an inclined plane.

The continuum description of granular flows is still a challenge despite their importance in many geophysical and industrial applications. We extend previous works, which have explored steady flow properties, by focusing on unsteady flows accelerating or decelerating down an inclined plane in the simple shear configuration. We solve the flow kinematics analytically, including predictions of evo...

Liquid Drops sliding down an inclined plane

We investigate a one-dimensional model describing the motion of liquid drops sliding down an inclined plane (the so-called quasi-static approximation model). We prove existence and uniqueness of a solution and investigate its long time behavior for both homogeneous and inhomogeneous medium (i.e. constant and non-constant contact angle). We also obtain some homogenization results.

Nonparallel spatial stability of shallow water flow down an inclined plane of arbitrary slope

Roll waves are known to occur in the frictional flow of a thin layer of water down an inclined solid surface. For a layer of constant depth, the formation of these waves on a solid plane with small slope angle have been explained as a hydrodynamic instability occurring above a critical Froude number by analyzing the temporal stability of the constant velocity flow. Here we analyze the linear, s...

Film flow of a suspension down an inclined plane.

A method is developed for simulating the film flow of a suspension of rigid particles with arbitrary shapes down an inclined plane in the limit of vanishing Reynolds number. The problem is formulated in terms of a system of integral equations of the first and second kind for the free-surface velocity and the traction distribution along the particle surfaces involving the a priori unknown partic...

Wave celerity on a shear-thinning fluid film flowing down an incline