Mixing by random stirring in confined mixtures
Résumé
We 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.