Mixing by random stirring in confined mixtures

Abstract

International audienceWe study the relaxation of initially segregated scalar mixtures in randomly stirred media, aiming to describe the overall concentration distribution of the mixture, its shape and rate of deformation as it evolves towards uniformity. A stirred scalar mixture can be viewed as a collection of stretched sheets, possibly interacting with each other. We consider a situation in which the interaction between the sheets is enforced by confinement and is the key factor ruling its evolution. It consists of following a mixture relaxing towards uniformity around a fixed average concentration while flowing along a constant cross-section channel. The interaction between the sheets is found to be of a random addition nature in concentration space, leading to concentration distributions that are stable by self-convolution. The resulting scalar field is naturally coarsened at a scale much larger than the dissipation scale. Consequences on the mixture entropy and scalar rate of dissipation are also examined

Following the Cosmic Evolution of Pristine Gas. I. Implications for Milky Way Halo Stars

“…The models of Curl (1963) and Venaille & Sommeria (2007) correspond to n = 1 and n → ∞, respectively. By integrating Φ(Z; t) from a finite but extremely small value up to the critical metallicity, the Duplat & Villermaux (2008) model can be used to derive a very simple equation for the evolution of the Z < Z crit pristine fraction:…”

Modeling the Pollution of Pristine Gas in the Early Universe

“…The continuous-convolution model essentially assumes that the convolution occurs everywhere in the flow at any given time, but in an infinitesimal time, the number of convolutions is infinitesimal and equal to (Duplat & Villermaux 2008). The assumption can be represented by Ψ(ζ ; t + δt) = Ψ(ζ /(1 + ); t) (1+ ) .…”

“…Fortunately, for the problem of pristine gas pollution, the model provides a useful prediction that works immediately from the initial time (PSS). A more general extension of the self-convolution model in Laplace space was given in Duplat & Villermaux (2008),…”

Rate of chaotic mixing in localized flows

“…The stretching and folding of fluid filaments results in an exponential separation of neighboring particles with time, and in a fast mixing rate compared to diffusion alone, as characterized for example by the decay of concentration fluctuations [2][3][4][5][6][7]. Fluctuations decrease when concentration heterogeneities are stretched into thin filaments, down to an equilibrium diffusion scale at which molecular diffusion blurs filaments together [6].…”

“…However, relating quantitatively kinematic flow parameters to the distribution of stretching factors, or its statistics, is hard to achieve. No such attempt has yet been made in the mixing literature for a realistic mixing flow, with the noteworthy exception of flows for which successive stretching factors are uncorrelated enough that stochastic models of random convolution account well for mixing rates as well as concentration distributions [5][6][7]12]. Such cases include flow in porous media [13] or turbulent flows [5] In this work, we consider an experimental mixing device in which the shearing and stretching of fluid particles is strongly localized around mobile obstacles, so that the distribution of stretching is simple enough that two zones can be defined: one close to the moving cylinders where the shear is high and the other part which experiences only small shear.…”