Local membrane length conservation in two-dimensional vesicle simulation using a multicomponent lattice Boltzmann equation method

We present a method for applying a class of velocity-dependant forces within a multi-component lattice Boltzmann equation simulation which is designed to recover continuum regime incompressible hydrodynamics. This method is applied to the problem, in two dimensions, of constraining to uniformity the tangential velocity of a vesicle membrane implemented within a recent multi-component lattice Boltzmann simulation method, which avoids the use of Lagrangian boundary tracers. The constraint of uniform tangential velocity is carried by an additional contribution to an immersed boundary force, which we derive here from physical arguments. The result of this enhanced immersed boundary force is to apply a physically appropriate boundary condition at the interface between separated lattice fluids, defined as that region over which the phase-field varies most rapidly. Data from this enhanced vesicle boundary method are in agreement with other data obtained using related methods (e.g. T. Kruger, S, Frijters, F. Gunther, B. Kaoui and J. Harting, Eur. Phys. J. 222, 177 (2013)) ) and underscore the importance of a correct vesicle membrane condition.