Effective diffusion coefficient including the Marangoni effect

TL;DR

This paper derives an analytical expression for the effective diffusion coefficient caused by Marangoni convection, validated by numerical simulations and experimental measurements, advancing understanding of surface-active molecule transport.

Contribution

It introduces a new analytical model for the effective diffusion coefficient including Marangoni effects, validated by simulations and experiments.

Findings

Analytical formula matches numerical results

Effective diffusion coefficient increases with Marangoni flow

Experimental measurements confirm theoretical predictions

Abstract

Surface-active molecules supplied from a particle fixed at the water surface create a spatial gradient of the molecule concentration, resulting in Marangoni convection. Convective flow transports the molecules far from the particle, enhancing diffusion. We analytically derive the effective diffusion coefficient associated with the Marangoni convection rolls. The resulting estimated effective diffusion coefficient is consistent with our numerical results and the apparent diffusion coefficient measured in experiments.