Drag Coefficient in Near-Critical Binary Mixtures: Solving Hydrodynamic Fields with Improved Numerics

TL;DR

This paper develops an improved numerical method to calculate the drag coefficient of particles in near-critical binary mixtures, enabling better comparison with experiments by overcoming previous computational challenges.

Contribution

It introduces a reformulation of hydrodynamic equations as ODEs with a compactified coordinate, allowing stable calculations over larger correlation lengths.

Findings

Successfully computed drag coefficients for a wider range of correlation lengths.

Achieved stable numerical solutions by reformulating equations as ODEs.

Provided theoretical predictions that align with experimental data.

Abstract

We calculate the drag coefficient of a spherical particle suspended in a near-critical binary fluid mixture. To capture the scaling behavior associated with critical adsorption in the strong adsorption regime, we employ the framework of local renormalized functional theory. Previous theoretical studies encountered numerical difficulties when attempting to solve the coupled hydrodynamic and chemical potential equations, expressed as integral equations, for systems with large bulk correlation lengths. These difficulties limited direct comparison with experimental results. In this study, we overcome those limitations by reformulating the hydrodynamic equations as a set of ordinary differential equations using a compactified radial coordinate. This approach enables more stable numerical computation and facilitates the implementation of appropriate boundary conditions at large distances from the particle. As a result, we successfully compute the drag coefficient over a broader range of bulk correlation lengths than in previous works and compare our theoretical predictions with available experimental data.