A deformable elastic membrane embedded in a lattice Boltzmann fluid

TL;DR

This paper introduces a novel computational method for simulating deformable elastic membranes within a lattice Boltzmann fluid, enabling realistic modeling of biological and soft matter systems.

Contribution

It presents a new approach to embed deformable membranes in lattice Boltzmann simulations using a free energy functional, validated in 2D with various physical constraints.

Findings

Successfully recovers equilibrium membrane shapes.

Accurately models membrane deformation under shear flow.

Applicable to biological cell simulations.

Abstract

A method is described for embedding a deformable, elastic, membrane within a lattice Boltzmann fluid. The membrane is represented by a set of massless points which advect with the fluid and which impose forces on the fluid which are derived from a free energy functional with a value which is dependent upon the geometric properties of the membrane. The method is validated in two dimensions with a free energy functional which imposes the constraint of constant membrane length, constant enclosed area, a bending rigidity and a preferred curvature. The method is shown to recover the expected equilibrium shape in the absence of flow and deformation in the presence of an applied shear flow. The method may have applications in a number of mesoscopic simulations, including discrete models of blood cells.