Related papers: Surface permeability, capillary transport and the …
We develop a theory of existence and uniqueness for the following porous medium equation with fractional diffusion, $$ \{ll} \dfrac{\partial u}{\partial t} + (-\Delta)^{\sigma/2} (|u|^{m-1}u)=0, & \qquad x\in\mathbb{R}^N,\; t>0, [8pt]…
Light diffusion is usually associated with thick, opaque media. Indeed, multiple scattering is necessary for the onset of the diffusive regime and such condition is generally not met in almost transparent media. Nonetheless, at long enough…
Transport of liquid mixtures through porous membranes is central to processes such as desalination, chemical separations and energy harvesting, with ultrathin membranes made from novel 2D nanomaterials showing exceptional promise. Here we…
In this paper we establish in the fast diffusion range the higher integrability of the spatial gradient of weak solutions to porous medium systems. The result comes along with an explicit reverse H\"older inequality for the gradient. The…
In the study of packed granular materials, the performance of a sample (e.g., the detonation of a high-energy explosive) often correlates to measurements of a fluid flowing through it. The "effective surface area," the surface area…
We study a one dimensional model for two-phase flows in heterogeneous media, in which the capillary pressure functions can be discontinuous with respect to space. We first give a model, leading to a system of degenerated non-linear…
We present a systematic, quantitative assessment of the impact of pore size disorder and its interplay with flow rates and wettability on immiscible displacement of a viscous fluid. Pore-scale simulations and micromodel experiments show…
A lattice-gas model with heterogeneity is developed for the description of fluid condensation in finite sized one-dimensional pores of arbitrary shape. An exact solution of the model is presented for zero-temperature that reproduces the…
We explore an optimal partition problem on surfaces using a computational approach. The problem is to minimise the sum of the first Dirichlet Laplace--Beltrami operator eigenvalues over a given number of partitions of a surface. We consider…
This paper proposes two contributions to the calculation of free surface flows using the particle finite element method (PFEM). The PFEM is based on a Lagrangian approach: a set of particles defines the fluid. Then, unlike a pure Lagrangian…
We present a theoretical study of capillary condensation of fluids adsorbed in mesoporous disordered media. Combining mean-field density functional theory with a coarse-grained description in terms of a lattice-gas model allows us to…
Energy transmission over long distances by waves is a key mechanism for many natural processes. This possibility arises when an inhomogeneous medium is arranged in such a manner that it enables a certain type of wave to propagate with…
When a suspension dries, the suspending fluid evaporates, leaving behind a dry film composed of the suspended particles. During the final stages of drying, the height of the fluid film on the substrate drops below the particle size,…
In 1977 Berg & Purcell published a landmark paper entitled "Physics of Chemoreception" which examined how a bacterium can sense a chemical attractant in the fluid surrounding it. At small scales the attractant molecules move by Brownian…
We derive error estimates for the piecewise linear finite element approximation of the Laplace--Beltrami operator on a bounded, orientable, $C^3$, surface without boundary on general shape regular meshes. As an application, we consider a…
In this paper we develop a simple finite element method for simulation of embedded layers of high permeability in a matrix of lower permeability using a basic model of Darcy flow in embedded cracks. The cracks are allowed to cut through the…
We use the hyperbolic subdiffusion equation with fractional time derivatives (the generalized Cattaneo equation) to study the transport process of electrolytes in media where subdiffusion occurs. In this model the flux is delayed in a…
A simple manner to describe the diffusive relaxation of a colloidal fluid adsorbed in a porous medium is to model the porous medium as a set of spherical particles fixed in space at random positions with prescribed statistical structural…
In this letter, we describe the capillary sorting of particles by size based on dip coating. A substrate withdrawn from a liquid bath entrains a coating whose thickness depends on the withdrawal speed and the liquid properties. If the…
In this paper, we study the stability and convergence of a decoupled and linearized mixed finite element method (FEM) for incompressible miscible displacement in a porous media whose permeability and porosity are discontinuous across some…