On self similarity and coarsening rate of a convecting bicontinuous phase separating mixture: effect of the viscosity contrast

TL;DR

This computational study investigates how viscosity contrast affects the self-similar coarsening and topology of bicontinuous microstructures in phase-separating mixtures, confirming the viscous growth regime and the role of effective viscosity.

Contribution

It demonstrates that self-similar morphological evolution occurs regardless of viscosity contrast and introduces the concept of effective viscosity as the geometric mean influencing coarsening rate.

Findings

Self similarity exists in both iso-viscous and variable viscosity systems.

Coarsening rate is inversely proportional to effective viscosity.

Distinct topological characteristics are observed between systems with different viscosities.

Abstract

We present a computational study of the hydrodynamic coarsening in 3D of a critical mixture using the Cahn-Hilliard/Navier-Stokes model. The topology of the resulting intricate bicontinuous microstructure is analyzed through the principal curvatures to prove self-similar morphological evolution. We find that the self similarity exists for both systems: iso-viscous and with variable viscosity. However the two system have distinct topological character. Our simulations confirm that the predicted viscous growth regime exists in both cases. Moreover the coarsening rate is inversely proportional to an \textit{effective viscosity} that is the geometrical average of the viscosities of the two phases.