Abstract A numerical model is investigated representing counter-current spontaneous imbibition of water to displace oil or gas from a core plug. The based on mass and momentum conservation equations in the framework theory mixtures. We extend previous that included fluid–rock friction fluid–fluid drag interaction (viscous coupling) by including fluid compressibility Brinkman viscous terms. Gas ...

Ependymal cilia line the ventricular system moving cerebral spinal fluid close to the brain surface. They may be exposed to fluid of increasing viscosity in certain pathological conditions such as bacterial meningitis. Our aim was to determine the effect of increasing viscosity on ciliary function. Ciliated ependyma was exposed to solutions of different viscosities (1-60cP) and ciliary function...

We report theoretical and numerical studies of the flow behaviour when a fluid is injected into a confined porous medium saturated with another fluid of different density and viscosity. For a two-dimensional configuration with point source injection, a nonlinear convection–diffusion equation is derived to describe the time evolution of the fluid–fluid interface. In the early time period, the fl...

Potential flows u = ∇φ are solutions of the Navier–Stokes equations for viscous incompressible fluids for which the vorticity is identically zero. The viscous term μ∇u = μ∇∇φ vanishes, but the viscous contribution to the stress in an incompressible fluid (Stokes 1850) does not vanish in general. Here, we show how the viscosity of a viscous fluid in potential flow away from the boundary layers e...

The purpose of this paper is to derive rigorously the so called viscous shallow water equations given for instance page 958-959 in [A. Oron, S.H. Davis, S.G. Bankoff, Rev. Mod. Phys, 69 (1997), 931–980]. Such a system of equations is similar to compressible Navier-Stokes equations for a barotropic fluid with a non-constant viscosity. To do that, we consider a layer of incompressible and Newtoni...

Particles suspended in a viscous fluid circle in optical vortices generated by holographic optical-tweezer techniques [Curtis J E and Grier D G 2003 Phys. Rev. Lett. 9