A simulation method for the wetting dynamics of liquid droplets on deformable membranes

TL;DR

This paper introduces a novel numerical simulation method combining phase-field and ALE techniques to study the complex wetting dynamics of liquid droplets on deformable biological membranes, relevant for understanding cellular processes.

Contribution

It presents the first thermodynamically consistent numerical model for simulating droplet-membrane interactions involving elasticity and wetting phenomena.

Findings

Validated against theoretical shape equations for single droplets.

Demonstrated in 2D and 3D axisymmetric simulations.

Shows capability to simulate complex biological membrane interactions.

Abstract

Biological cells utilize membranes and liquid-like droplets, known as biomolecular condensates, to structure their interior. The interaction of droplets and membranes, despite being involved in several key biological processes, is so far little understood. Here, we present a first numerical method to simulate the continuum dynamics of droplets interacting with deformable membranes via wetting. The method combines the advantages of the phase-field method for multi-phase flow simulation and the arbitrary Lagrangian-Eulerian (ALE) method for an explicit description of the elastic surface. The model is thermodynamically consistent, coupling bulk hydrodynamics with capillary forces, as well as bending, tension, and stretching of a thin membrane. The method is validated by comparing simulations for single droplets to theoretical results of shape equations, and its capabilities are illustrated in 2D and 3D axisymmetric scenarios.