A Study of Spherical and Sessile Droplet Dynamics by Fluctuating Hydrodynamics

TL;DR

This paper investigates the mesoscopic dynamics of nanometer-scale droplets using fluctuating hydrodynamics, comparing spherical and sessile droplets, and analyzing their mobility and diffusion properties through deterministic and stochastic simulations.

Contribution

It introduces a combined Cahn-Hilliard and fluctuating hydrodynamics model to simulate droplet behavior, including contact angles and boundary effects, at nanoscales.

Findings

Deterministic and stochastic methods generally agree on diffusion coefficients.

Discrepancies occur for droplets near slip walls or with large contact angles.

The model captures the influence of solid boundaries on droplet dynamics.

Abstract

We simulate the mesoscopic dynamics of droplets formed by phase separated fluids at nanometer scales where thermal fluctuations are significant. Both spherical droplets fully immersed in a second fluid and sessile droplets which are also in contact with a solid surface are studied. Our model combines a Cahn-Hillard formulation with incompressible fluctuating hydrodynamics; for sessile droplets the fluid-solid contact angle is specified as a boundary condition. Deterministic simulations with an applied body force are used to measure the droplets' mobility from which a diffusion coefficient is obtained using the Einstein relation. Stochastic simulations are independently used to obtain a diffusion coefficient from a linear fit of the variance of a droplet's position with time. In some scenarios these two measurements give the same value but not in the case of a spherical droplet initialized near a slip wall or in the case of sessile droplets with large contact angles (greater than 90 degrees) on both slip and no-slip surfaces.