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We consider three-dimensional convection of an incompressible fluid saturated in a parallelepiped with a porous medium. A mimetic finite-difference scheme for the Darcy convection problem in the primitive variables is developed. It consists…
We present experimental observations of the onset of flow (liquefaction) for horizontally vibrated granular materials. As the acceleration increases above certain value, the top layer of granular material liquefies, while the remainder of…
The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable…
A compressible laminar boundary layer developing over an isotropic porous substrate is investigated by asymptotic and numerical methods. The substrate is modeled as an array of cubes. The momentum and enthalpy balance equations are derived…
The influence of the thermal expansion of the Earth's atmosphere on the stability of vertical stratification of fluid density and temperature is studied. We show that such an influence leads to the instability of incompressible flows.…
Segregation patterns of size-bidisperse particle mixtures in a fully-three-dimensional flow produced by alternately rotating a spherical tumbler about two perpendicular axes are studied over a range of particle sizes and volume ratios using…
Mixing describes the process by which solutes evolve from an initial heterogeneous state to uniformity under the stirring action of a fluid flow. Fluid stretching forms thin scalar lamellae which coalesce due to molecular diffusion. Owing…
We discuss the crystallization process from the supersaturated melt in terms of its non-equilibrium properties. In particular, we quantify the amount of heat that is produced irreversibly when a suspension of hard spheres crystallizes. This…
The problem of disturbed flow in the laminar boundary layer is investigated when a heating element is located on the surface of the body. The flow is supposed to be laminar one. It is shown that the problem may be solved in terms of free…
Accurate prediction of self-pressurization in cryogenic tanks requires resolving the coupled effects of heat ingress, natural convection, and phase change. This work introduces a segregated numerical framework in which the liquid and vapor…
Motivated by the dynamics within terrestrial bodies, we consider a rotating, strongly thermally stratified fluid within a spherical shell subject to a prescribed laterally inhomogeneous heat-flux condition at the outer boundary. Using a…
Flow structure stability of a steady radial thermocapillary flow from the local heat source in cylindrical geometry has been studied numerically. The up boundary of the liquid was partially covered by the stationary film of an insoluble…
Convection in a thin layer of liquid (gas) with temperature dependent viscosity between poorly heat conducting boundaries is studied within framework of the Proctor-Sivashinsky model. This model is examined in order to study both the flow…
Instabilities at interface of two stream granular flows have been reported in recent experiment [1] that breaking waves can form at the interface between two streams of identical grains flowing on an inclined plane downstream of a splitter…
We present a realistic phenomenological description of liquid transport through defective, layered membranes. We derive general expressions based on conventional models of laminar flow and extend the formalism to accommodate slip flow. We…
We investigate numerically the dynamics and statistics of inertial particles transported by stratified turbulence, in the case of particle density intermediate in the average density profile of the fluid. In these conditions, particles tend…
The paper deals with the fundamental problem of a modeling of the physical, in particular, thermal hydraulic processes, in various media of fractal structure of the natural, technological and technical systems and devices. The examples of a…
We consider the homogenization of a model of reactive flows through periodic porous media involving a single solute which can be absorbed and desorbed on the pore boundaries. This is a system of two convection-diffusion equations, one in…
A class of nonlinear problems on the plane, described by nonlinear inhomogeneous $\bar{\partial}$-equations, is considered. It is shown that the corresponding dynamics, generated by deformations of inhomogeneous terms (sources) is described…
The dropwise condensation underneath a horizontal super-hydrophobic surface having unidirectional wettability gradient is modeled with implication to enhance the rate of condensation. The mathematical model includes nucleation, growth by…