Related papers: Diffusion of a passive scalar by convective flows …
Lateral diffusion of molecules on surfaces plays a very important role in various biological processes, including lipid transport across the cell membrane, synaptic transmission and other phenomena such as exo- and endocytosis, signal…
Anomalous diffusion is the fundamental ansatz of phenomenological theories of passive scalar turbulence, and has been confirmed numerically and experimentally to an extraordinary extent. The purpose of this survey is to discuss our recent…
We investigate horizontal dispersion of a passive scalar in a porous stratum with Rayleigh-Darcy convection initiated by a geothermal gradient. While increasing Rayleigh number ($Ra$) keeps enhancing convection, the horizontal dispersion…
In this paper we present a mathematical model and a numerical workflow for the simulation of a thermal single-phase flow with reactive transport in porous media, in the presence of fractures. The latter are thin regions which might behave…
Large-scale electrical and thermal currents in ordinary metals are well approximated by effective medium theory: global transport properties are governed by the solution to homogenized coupled diffusion equations. In some metals, including…
In this paper we study the heat transfer with a general fractional diffusion term of an incompressible fluid in a porous medium governed by Darcy's law. We show formation of singularities with infinite energy and for finite energy we obtain…
In this paper we present a complete framework for the energy-stable simulation of stratified incompressible flow in channels, using the one-dimensional two-fluid model. Building on earlier energy-conserving work on the basic two-fluid…
We show existence and uniqueness of strong solutions to a Navier-Stokes/Cahn-Hilliard type system on a given two-dimensional evolving surface in the case of different densities and a singular (logarithmic) potential. The system describes a…
We show that the Turing patterns in reaction systems with subdiffusion can be replicated in an effective system with Markovian cross-diffusion. The effective system has the same Turing instability as the original system, and the same…
Diffusion of colored dye on water saturated paper substrates has been traditionally exploited with great skill by renowned water color artists. The same physics finds more recent practical applications in paper based diagnostic devices…
The diffusive properties in velocity fields whose small scales are parameterized by non $\delta$-correlated noise is investigated using multiscale technique. The analytical expression of the eddy diffusivity tensor is found for a 2D steady…
L\'evy-type walks with correlated jumps, induced by the topology of the medium, are studied on a class of one-dimensional deterministic graphs built from generalized Cantor and Smith-Volterra-Cantor sets. The particle performs a standard…
We study the transport properties of particles draining from a silo using imaging and direct particle tracking. The particle displacements show a universal transition from super-diffusion to normal diffusion, as a function of the distance…
Turbulent thermals emerge in a wide variety of geophysical and industrial flows, such as atmospheric cumulus convection and pollutant dispersal in oceans and lakes. When a buoyant fluid mass rises, or sinks, heat and mass transfers occur by…
We consider evolution of a passive scalar (concentration of pollutants or temperature) in a chaotic (turbulent) flow. A universal asymptotic behavior of the passive scalar decay (homogenization) related to peripheral regions (near walls) is…
We study non-isothermal diffusive transport of a weakly-soluble two-component substance in a liquid-saturated porous medium being in contact with the reservoir of this substance. Particular attention is given to the example case of…
A practical application of universal wall scalings is near-wall turbulence modeling. In this paper, we exploit temperature's semi-local scaling [Patel, Boersma, and Pecnik, {Scalar statistics in variable property turbulent channel flows},…
Channels are fundamental building blocks from biophysics to soft robotics, often used to transport or separate solutes. As solute particles inevitably transverse between streamlines along the channel by molecular diffusion, the effective…
In this contribution we prove the existence of weak solutions to degenerate parabolic systems arising from the coupled moisture movement, transport of dissolved species and heat transfer through partially saturated porous materials.…
Poroelastic materials, consisting of a permeable solid matrix infiltrated with fluid, are ubiquitous in natural and engineering contexts. In poroelastic polymer solids, the elastic matrix swells to equilibrium when immersed in a solvent…