Dynamics of cylindrical droplets on flat substrate: Lattice Boltzmann modeling versus simple analytic models

TL;DR

This study compares lattice Boltzmann simulations and simple analytical models to understand the steady motion and deformation of cylindrical droplets on flat surfaces under external forces, revealing linear and non-linear behaviors and dissipation mechanisms.

Contribution

It introduces a simple analytical model that accurately reproduces the observed droplet dynamics and deformation behaviors under external forces.

Findings

Center-of-mass velocity scales linearly with force density and droplet size squared.

Deformation occurs at high external forcing, affecting velocity behavior.

Viscous dissipation mainly occurs near the substrate and contact line.

Abstract

The steady state motion of cylindrical droplets under the action of external body force is investigated both theoretically and via lattice Boltzmann simulation. As long as the shape-invariance of droplet is maintained, the droplet's center-of-mass velocity linearly scales with both the force density and the square of droplet radius. However, a non-linear behavior appears as the droplet deformation becomes significant. This deformation is associated with the drop elongation occurring at sufficiently high external forcing. Yet, independent of either the force density or the droplet size, the center-of-mass velocity is found to be linear in terms of the inverse of dynamic viscosity. In addition, it is shown that the energy is mainly dissipated in a region near the substrate particularly close to the three phase contact line. The total viscous dissipation is found to be proportional to both the square of force density and the inverse of dynamic viscosity. Moreover, the dependence of the center-of-mass velocity on the equilibrium contact angle is investigated. A simple analytic model is provided reproducing the observed behavior.