Mixing by shear, dilation, swap, and diffusion

Abstract

This paper presents a theory of poroviscosity for binary solutions. Subject to mechanical forces and connected to reservoirs of molecules, a binary solution evolves by concurrent flow and diffusion. Our theory generalizes the classical theory of interdiffusion by decoupling the molecular processes for flow and diffusion. We further remove the assumption of local chemical equilibrium, so that the insertion of molecular into a material element, accompanied by a change in volume, is treated as nonequilibrium process and is put on the same footing as the process of shear deformation by viscous flow. The theory of poroviscosity has an intrinsic length scale, called the poroviscous length, below which the homogenization of a composition heterogeneity is limited by viscous flow, rather than by diffusion. The theory has implications for the analysis of interdiffusion in systems that display a decoupling between flow and diffusion, such as supercooled liquids, glasses, and physical gels. We illustrate the theory with numerical examples of a layered structure and a spherical particle. We discuss the results for feature sizes below and above the poroviscous length.

Cutting and shuffling with diffusion: Evidence for cut-offs in interval exchange maps

“…Finally, we note in passing that a recently introduced thermodynamic approach by Brassart et al [60,61] to molecular mixing makes use of the same basic concepts as in the continuum theories of the mixing of fluids: shear, dilation, diffusion and "swap." Brassart et al [60,61] define "swap" as "preserv[ing] the shape and the volume, but chang[ing] the ratio of the two species of molecules" in a piece of material [60, p. 50]. Indeed, this definition coincides with the notion of cutting and shuffling discussed herein if we consider how the color changes with iterations on an arbitrary finite piece of the original line segment.…”

The impact of magnesium content on lithium-magnesium alloy electrode performance with argyrodite solid electrolyte

“…8-10 and Supplementary Note 3)), building on the continuum theory presented in ref. 51. According to the model, the stripping of lithium near the interface induces volume contraction of the host alloy, which must be accommodated by creep due to lateral geometric constraints.…”