Related papers: Axisymmetric viscous gravity currents flowing over…

This paper investigates density driven flow in porous media, focusing on the roles of viscosity contrast, density contrast, and linear adsorption. In this setup, the fluid on top is heavier and more viscous than the fluid below. Under the…

The problem of reconstructing non-harmonic internal gravity wave packets generated by a source moving in a stratified ocean is considered. The uniform asymptotic form of the internal gravity waves field generated by a source moving above…

Mathematical modeling of fluid flow in a porous medium is usually described by a continuity equation and a chosen constitutive law. The latter, depending on the problem at hand, may be a nonlinear relation between the fluid's pressure…

Fractured porous media or double porosity media are common in nature. At the same time, accurate modeling remains a significant challenge due to bi-modal pore size distribution, anisotropy, multi-field coupling, and various flow patterns.…

We report an experimental study of particle kinematics in a 3-dimensional system of inelastic spheres fluidized by intense vibration. The motion of particles in the interior of the medium is tracked by high speed video imaging, yielding a…

We introduce a system of shallow water-type equations to model laboratory experiments of particle-laden flows. We explore homogeneous liquid-solid suspensions of fine, non-cohesive, monodisperse glass beads which propagate as an equivalent…

We analyze both numerically and experimentally the stability of the steady jetting tip streaming produced by focusing a liquid stream with another liquid current when they coflow through the orifice of an axisymmetric nozzle. We calculate…

Unified geometric approach to describing kinematics of elastic and plastic deformations of continuous media is suggested. On the base of this approach we study mechanical deformations, viscous flow, and heat transport in glassy plastic…

This paper reviews theories, experimental data, and modeling methods for pre-Darcy flow in low-permeability porous media, where Darcy velocity shows nonlinear dependence on pressure gradients at sufficiently low pressures, a deviation from…

Polymer solutions are often injected in porous media for applications such as oil recovery and groundwater remediation. As the fluid navigates the tortuous pore space, elastic stresses build up, causing the flow to become unstable at…

We study a class of initial value problems (IVPs) involving perturbations on a density stratified, quiescent, viscous liquid layer with a free-surface. The geometry is a two-dimensional, rectangular configuration taking into account…

We analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space…

Particles moving along curved trajectories will diffuse if the curvature fluctuates sufficiently in either magnitude or orientation. We consider particles moving at a constant speed with either a fixed or with a Gaussian distributed…

This paper considers two-dimensional gravity solitary waves moving through a body of density stratified water lying below vacuum. The fluid domain is assumed to lie above an impenetrable flat ocean bed, while the interface between the water…

The dispersing equation was derived from system of the hydrodynamic equations that take into account the gravity, and from boundary conditions of shock front. The dispersing equation made it possible to study unstable stability of front not…

Flows within porous media play important roles in many scientific and industrial systems. However, the case wherein such flows become turbulent has not been completely understood, particularly, from a mathematical viewpoint. In this study,…

Many natural and engineering systems involve the mixing of two fluid streams, in which the effects of density and viscosity gradients play important roles in determining flow stability. We perform linear stability calculations for a jet…

We investigate the lateral dynamics in a purely viscous lipid membrane surrounded by viscoelastic media such as polymeric solutions. We first obtain the generalized frequency-dependent mobility tensor and focus on the case when the solvent…

A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the velocity vector is orthogonal to the gradient of the…

In the papers (Shvidler, 1985 and 1993, and Shvidler and Karasaki, 1999, 2001, 2005, and 2008) we developed an approach for finding the exactly averaged equations of flow and transport in porous media. We studied for steady state flow with…