Related papers: Maximal mixing by incompressible fluid flows
The microscopic approach to the description of the phase behaviour and critical phenomena in binary fluid mixtures is proposed. It is based on the method of collective variables with a reference system. The physical nature of the order…
In this paper, we are interested in the dynamics of charged particles interacting with the incompressible viscous flow. More precisely, we consider the Vlasov-Poisson or Vlasov-Poisson-Fokker-Planck equation coupled with the incompressible…
We study the time evolution of a viscous incompressible fluid with axial symmetry without swirl, when the initial vorticity is very concentrated in $N$ disjoint rings. We show that in a suitable joint limit, in which both the thickness of…
In this paper we give a new proof of the homogenization result for an immiscible incompressible two-phase flow in double porosity media obtained earlier in the pioneer work by A. Bourgeat, S. Luckhaus, A. Mikeli\'c (1996) and in the paper…
We study the properties of `infinite-volume mixing' for two classes of intermittent maps: expanding maps $[0,1] \longrightarrow [0,1]$ with an indifferent fixed point at 0 preserving an infinite, absolutely continuous measure, and expanding…
The present paper is dedicated to the global large solutions and incompressible limit for the compressible flow of liquid crystals under the assumption on almost constant density and large volume viscosity. The result is based on Fourier…
Versatile mixed finite element methods were originally developed by Chen and Williams for isothermal incompressible flows in "Versatile mixed methods for the incompressible Navier-Stokes equations," Computers & Mathematics with…
This paper is concerned with the inhomogeneous incompressible Euler system. We establish a Duchon--Robert type approximation theorem for the distribution describing the local energy flux of bounded solutions. The velocity field is assumed…
We consider a Navier-Stokes-Fick-Onsager-Fourier system of PDEs describing mass, energy and momentum balance in a Newtonian fluid with composite molecular structure. For the resulting parabolic-hyperbolic system, we introduce the notion of…
We study the system of equations which describes barotropic (isentropic) flows of viscous compressible multi-fluids (mixtures of fluids). We study the relations between pressure, densities, concentrations, viscosities and other parameters…
We investigate the dynamics of viscous fingering (VF) in miscible slices in homogeneous, isotropic porous media. The fluid flow is governed by incompressible Darcy's law, whereas the solute transport is described using an…
We formulate a finite-particle method of mass transport that accounts for general mixed boundary conditions. The particle method couples a geometrically-exact treatment of advection; Wasserstein gradient-flow dynamics; and a…
A computer simulation model is used to study the density profile and flow of a miscible gaseous fluid mixture consisting of differing constituent masses ($m_A = m_B/3$) through an open matrix. The density profile is found to decay with the…
In this paper we study the dynamics of a small rigid body in a viscous incompressible fluid in dimension two and three. More precisely we investigate the trajectory of the rigid body in the limit when the its mass and its size tend to zero.…
We consider the advection-diffusion equation on $\mathbb{T}^2$ with a Lipschitz and time-periodic velocity field that alternates between two piecewise linear shear flows. We prove enhanced dissipation on the timescale $|\log \nu|$, where…
The majority of available numerical algorithms for interfacial two-phase flows either treat both fluid phases as incompressible (constant density) or treat both phases as compressible (variable density). This presents a limitation for the…
We consider the mixing behaviour of the solutions of the continuity equation associated with a divergence-free velocity field. In this announcement we sketch two explicit examples of exponential decay of the mixing scale of the solution, in…
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…
We theoretically study the critical speed for superfluid flow of a two-dimensional miscible binary superfluid of light past a polarization-sensitive optical obstacle. This speed corresponds to the maximum mean flow velocity below which…
The connection between the compressible flow of liquid crystals with low Mach number and the incompressible flow of liquid crystals is studied in a bounded domain. In particular, the convergence of weak solutions of the compressible flow of…