In enhanced oil recovery by chemical flooding within tertiary oil recovery, it is often necessary to choose optimal viscous profiles of the injected displacing fluids that reduce growth rates of hydrodynamic instabilities the most thereby substantially reducing the well-known fingering problem...

We consider the linear stability of three-layer Hele-Shaw flows with each layer having constant viscosity and viscosity increasing in the direction of a basic uniform flow. While the upper bound results on the growth rate of long waves are well known from our earlier works, lower bound results...

The Stokes flow involving a hybrid droplet submerged in an immiscible liquid is considered. The droplet has a two-sphere geometry with the two spherical surfaces intersecting orthogonally. The types of hybrid droplet considered here include (i) vapor–solid; (ii) vapor–vapor; and (iii)...

We study the singularly perturbed (sixth-order) Boussinesq equation recently introduced by Daripa and Hua [Appl. Math. Comput. 101 (1999) 159]. This equation describes the bi-directional propagation of small amplitude and long capillary-gravity waves on the surface of shallow water for bond...

Two-dimensional Stokes flows generated by line singularities inside a circular cylinder are studied in the presence of stick-slip boundary conditions. For simplicity, line singularities are assumed to be parallel to the cylinder axis, all axes in the same plane. The interior boundary value...