Lattice Boltzmann simulation of deformable fluid-filled bodies: progress and perspectives.

With the rapid development of studies involving droplet microfluidics, drug delivery, cell detection, and microparticle synthesis, among others, many scientists have invested significant efforts to model the flow of these fluid-filled bodies. Motivated by the intricate coupling between hydrodynamics and the interactions of fluid-filled bodies, several methods have been developed. The objective of this review is to present a compact foundation of the methods used in the literature in the context of lattice Boltzmann methods. For hydrodynamics, we focus on the lattice Boltzmann method due to its specific ability to treat time- and spatial-dependent boundary conditions and to incorporate new physical models in a computationally efficient way. We split the existing methods into two groups with regard to the interfacial boundary: fluid-structure and fluid-fluid methods. The fluid-structure methods are characterised by the coupling between fluid dynamics and mechanics of the flowing body, often used in applications involving membranes and similar flexible solid boundaries. We further divide fluid-structure-based methods into two subcategories, those which treat the fluid-structure boundary as a continuum medium and those that treat it as a discrete collection of individual springs and particles. Next, we discuss the fluid-fluid methods, particularly useful for the simulations of fluid-fluid interfaces. We focus on models for immiscible droplets and their interaction in a suspending fluid and describe benchmark tests to validate the models for fluid-filled bodies.

Effect of droplet deformability on shear thinning in a cylindrical channel.

Droplets suspended in fluids flowing through microchannels are often encountered in different contexts and scales, from oil extraction down to microfluidics. They are usually flexible and deform as a product of the interplay between flexibility, hydrodynamics, and interaction with confining walls. Deformability adds distinct characteristics to the nature of the flow of these droplets. We simulate deformable droplets suspended in a fluid at a high volume fraction flowing through a cylindrical wetting channel. We find a discontinuous shear thinning transition, which depends on the droplet deformability. The capillary number is the main dimensionless parameter that controls the transition. Previous results have focused on two-dimensional configurations. Here we show that, in three dimensions, even the velocity profile is different. To perform this study, we improve and extend to three dimensions a multicomponent lattice Boltzmann method which prevents the coalescence between the droplets.