Related papers: Convergent flow in a two-layer system and mountain…
In the present contribution we review basic mathematical results for three physical systems involving self-organising solid or liquid films at solid surfaces. The films may undergo a structuring process by dewetting,…
The formation of liquid bridges between a planar and conical substrates is analyzed macroscopically taking into account the line tension. Depending on the value of the line tension coefficient \tau and geometric parameters of the system one…
The dissolution of solids has created spectacular geomorphologies ranging from centimeter-scale cave scallops to the kilometer-scale "stone forests" of China and Madagascar. Mathematically, dissolution processes are modeled by a Stefan…
We investigate the bulk rheology of dense granular flow down a rough slope, where the density profile has been found to show a plateau except for the boundary layers in simulations [Silbert {\it et al.}, Phys. Rev. E {\bf 64}, 051302…
In this paper we study the behavior of an incompressible viscous fluid moving between two very close surfaces also in motion. Using the asymptotic expansion method we formally justify two models, a lubrication model and a shallow water…
Granular material on an inclined plane will flow like a fluid if the angle $\theta$ the plane makes with the horizontal is large enough. We employ a modification of a hydrodynamic model introduced previously to describe Couette flow…
We use novel, fast 4D Synchrotron X-ray imaging with large field-of-view to reveal pore- and macro-scale drainage dynamics during gas-brine flow through a layered sandstone rock sample. We show that a single centimetre-scale layer, similar…
Liquid drops slide more slowly over soft, deformable substrates than over rigid solids. This phenomenon can be attributed to the viscoelastic dissipation induced by the moving wetting ridge, which inhibits a rapid motion, and is called…
Wrinkling instabilities of thin elastic sheets can be used to generate periodic structures over a wide range of length scales. Viscosity of the thin elastic sheet or its surrounding medium has been shown to be responsible for dynamic…
The rate of melting of a solid and the rate of deformation of the resulting melt due to capillary forces are comparable in additive manufacturing applications. This dynamic structural change of a melting solid is extremely challenging to…
Many technological processes include preparing some special materials adhering to a product surface. For example, this problem is important for the magnetic tape producing, wire adhering, etc. For a surface withdrawn from the molten metal…
We consider a coupled model for fluid flow and transport in a domain consisting of two bulk regions separated by a thin porous layer. The thickness of the layer is of order $\varepsilon$ and the microscopic structure of the layer is…
We investigate the flow of spherical, bulk granular particles down an inclined plane mixed with small-sized spherical lubricant particles using discrete element method simulations. Predefined cohesive interaction is implemented between…
We describe a comprehensive model for the formation and morphological development of atmospheric ice crystals growing from water vapor, also known as snow crystals. Our model derives in part from empirical measurements of the intrinsic ice…
We theoretically and numerically investigate the steady flow of two-dimensional granular materials in a rotating drum using the discrete element method and a continuum model with the $\mu(I)$-rheology. The velocity fields obtained from both…
We explore the fundamental flow structure of inclined gravity currents with direct numerical simulations. A velocity maximum naturally divides the current into inner and outer shear layers, which are weakly coupled by exchange of momentum…
The integral method can be used to model accurately flows down an inclined plane. Such a method consists in projecting the full 3D equations on a lower dimensional representation. The vertical velocity profiles have their functional form…
We assess experimentally the scaling laws that characterize the mixing region produced by the Rayleigh-Taylor instability in a confined porous medium. In particular, we wish to assess experimentally the existence of a superlinear scaling…
A steady-state analytical solution is given describing the temperature distribution in a homogeneous massif perturbed by cold water flow through a discrete vertical fracture. A relation is derived to express the flow rate in the fracture as…
In this paper, we analyze the dynamics of two layers of immiscible, inviscid, incompressible, and irrotational fluids through a full nonlinear system. Our goal is to establish a virial theorem and prove the polynomial growth of slope and…