Chromodynamic Lattice Boltzmann Method for the Simulation of Drops, Erythrocytes, and Other Vesicles (Communications in Computational Physics, 2023)
Recently, we have validated a three-dimensional, single framework multicomponent lattice Boltzmann method, modified to generate vesicles (rather than drops)[“Three-dimensional single framework multicomponent lattice Boltzmann equationmethod for vesicle hydrodynamics,” Phys. Fluids 33, 077110 (2021)]. This approachimplements an immersed boundary force distribution, characterised by bending rigidity, surface tension, preferred curvature and conserved membrane area, in which workwe successfully validated isolated vesicle flows against other methodologies and experiment. Like most immersed boundary algorithms, our method relies on numericalcomputation of high-order spatial derivatives and an intricate body force density. Thenext step is to verify that it has sufficient numerical stability to address the anticipatedapplication of high volume fraction flows of highly deformable objects in intimate interaction. It is this in silico verification – of both the class of fluid object attainable andthe stability of the later in strong, straining and shearing flows which is at issue, here.We extend our method to simulate multiple variously deflated vesicles and multipleliquid droplets still within a single framework, from which our fluid objects emerge asparticular parameterisations. We present data from simulations containing up to fourvesicles (five immiscible fluid species), which threshold verifies that simulations containing unlimited fluid objects are possible [“Modeling the flow of dense suspensionsof deformable particles in three dimensions,” Phys. Rev. E 75, 066707 (2007)]. These data also assure the ability of our immersed boundary forcing to preserve the character and integrity of fluid objects in interactions characterised by large local velocitygradients (intimate squeezing, shearing and elongational straining). Throughout, wetake interfacial or membrane area, $A,$ as a proxy for stability and physical veracity.
Keywords: Lattice Boltzmann; membranes; vesicles.