Enhanced chromodynamic multi-component lattice boltzmann method for drop and vesicle modelling

Multi-component fluid flows are frequently seen in both nature and industry, such as gas-liquid flows (air-water) and liquid-liquid flows (oil-water). The accurate simulation of such fluid flows requires models to: (i) solve the governing fluid dynamics equations; (ii) reproduce known boundary behaviour at the free surface between the fluids; (iii) embed known surface physics representative of that of the target fluid object, i.e., surface tension when simulating drops. Here, meso-scale modelling techniques offer attractive options for simulating such flows, where due to working at a smaller scale than macro-scale approaches, one can investigate more detailed interactions and phenomena, whilst also recovering the continuum fluid dynamics equations. The development of the lattice Boltzmann method (LBM), a bottom-up kinetic scale Navier-Stokes solver, furnishes the ability to model such macro-scale properties whilst allowing for the inclusion of meso-scale physics. The chromodynamic multicomponent extension of this (cMCLBM) treats the fluids as separate species, with a diffused interfacial region (de facto surface), where discrete immersed interface forces can be applied to embed known physics of the fluid object. Theoretically, such a modelling approach should be capable of simulating a range of fluid objects, for example: liquid drops, vesicles (erythrocytes), and capsules, by manipulating the treatment of the interface. This work explores extensions to the cMCLBM, with a final objective of modelling vesicles (tailored towards erythrocytes) using this essential approach. Before this, however, it is sensible to confirm the fundamental foundations of the model, i.e., the model’s kinematics and dynamics. As such, work first focuses on the simulation of less complex fluid objects (drops), investigating the utility of the model when applied to fluid flows with a density contrast, where stability is strained. Here, the kinematics and dynamics of the model are assessed in detail through both mathematical analysis and simulation data, to quantify its compliance with known continuum hydrodynamic conditions such as: mutual impenetrability, the no-slip condition, and stress balance across the interface. Following the enhanced understanding of the cMCLBM gained from this work, the simulation of vesicles is targeted. The primary outcome of this work is the development of a single framework approach to modelling vesicle hydrodynamics, with promising possibilities for future applications within haemorheology and microfluidics.