Related papers: Diffusion-limited mixing by incompressible flows
We consider coupled diffusions in $n$-dimensional space and on a compact manifold and the resulting effective advective-diffusive motion on large scales in space. The effective drift (advection) and effective diffusion are determined as a…
We study the mixing in the presence of convective flow in a porous medium. Convection is characterized by the formation of vortices and stagnation points, where the fluid interface is stretched and compressed enhancing mixing. We analyze…
We study the mixing properties of a passive scalar advected by an incompressible flow. We consider a class of cellular flows (more general than the class in [Crippa-Schulze M3AS 2017]) and show that, under the constraint that the…
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…
Motivated in part by the work of Vanneste and Byatt-Smith, we study mixing and enhanced dissipation for the advection-diffusion equation with velocity field $\mathbf{u}(x,y,t)=(\sin(y-ct),0)$, a shear flow whose profile translates rigidly…
We investigate diffusion in supersonic, turbulent, compressible flows. Supersonic turbulence can be characterized as network of interacting shocks. We consider flows with different rms Mach numbers and where energy necessary to maintain…
Discrete element method simulations of confined bidisperse granular shear flows elucidate the balance between diffusion and segregation that can lead to either mixed or segregated states, depending on confining pressure. Results indicate…
Transport and mixing properties of passive particles advected by an array of vortices are investigated. Starting from the integrable case, it is shown that a special class of perturbations allows one to preserve separatrices which act as…
In this paper we characterize the mixing properties in the advection of passive tracers by exploiting the extreme value theory for dynamical systems. With respect to classical techniques directly related to the Poincar\'e recurrences…
We consider a model for mixing binary viscous fluids under an incompressible flow. We proof the impossibility of perfect mixing in finite time for flows with finite viscous dissipation. As measures of mixedness we consider a…
We propose a seamless multiscale method which approximates the macroscopic behavior of the passive advection-diffusion equations with steady incompressible velocity fields with multi-spatial scales. The method uses decompositions of the…
Diffusion describes the motion of microscopic entities from regions of high concentration to regions of low concentration. In multiplex networks, flows can occur both within and across layers, and super-diffusion, a regime where the time…
We formulate a scaling theory for the long-time diffusive motion in a space occluded by a high density of moving obstacles in dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in time, before reaching a diffusive…
We consider the nonlinear optimisation of irreversible mixing induced by an initial finite amplitude perturbation of a statically stable density-stratified fluid. A constant pressure gradient is imposed in a plane two-dimensional channel.…
We consider pressure-driven flows in wide microchannels, and discuss how a transverse shear, generated by misaligned superhydrophobic walls, impacts cross-sectional spreading of Brownian particles. We show that such a transverse shear can…
Diffusion Bridge and Flow Matching have both demonstrated compelling empirical performance in transformation between arbitrary distributions. However, there remains confusion about which approach is generally preferable, and the substantial…
We study diffusive mixing in the presence of thermal fluctuations under the assumption of large Schmidt number. In this regime we obtain a limiting equation that contains a diffusive thermal drift term with diffusion coefficient obeying a…
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…
Understanding particle motion in narrow channels is essential to guide progress in numerous applications, from filtration to vascular transport. Thermal or active fluctuations of channel walls for fluid-filled channels can slow down or…
Mixing in fluids is a rapidly developing field of fluid mechanics \cite{Sreen,Shr,War}, being an important industrial and environmental problem. The mixing of liquids at low Reynolds numbers is usually quite weak in simple flows, and it…