Modeling the flow of dense suspensions of deformable particles in three dimensions

Abstract

We describe here a rigorous and accurate model for the simulation of three-dimensional deformable particles (DPs). The method is very versatile, easily simulating various types of deformable particles such as vesicles, capsules, and biological cells. Each DP is resolved explicitly and advects within the surrounding Newtonian fluid. The DPs have a preferred rest shape (e.g., spherical for vesicles, or biconcave for red blood cells). The model uses a classic hybrid system: an Eulerian approach is used for the Navier-Stokes solver (the lattice Boltzmann method) and a Lagrangian approach for the evolution of the DP mesh. Coupling is accomplished through the lattice Boltzmann velocity field, which transmits force to the membranes of the DPs. The novelty of this method resides in its ability (by design) to simulate a large number of DPs within the bounds of current computational limitations: our simple and efficient approach is to (i) use the lattice Boltzmann method because of its acknowledged efficiency at low Reynolds number and its ease of parallelization, and (ii) model the DP dynamics using a coarse mesh (approximately 500 nodes) and a spring model constraining (if necessary) local area, total area, cell volume, local curvature, and local primary stresses. We show that this approach is comparable to the more common-yet numerically expensive-approach of membrane potential function, through a series of quantitative comparisons. To demonstrate the capabilities of the model, we simulate the flow of 200 densely packed red blood cells-a computationally challenging task. The model is very efficient, requiring of the order of minutes for a single DP in a 50 μm×40 μm×40 μm simulation domain and only hours for 200 DPs in 80 μm×30 μm×30 μm. Moreover, the model is highly scalable and efficient compared to other models of blood cells in flow, making it an ideal and unique tool for studying blood flow in microvessels or vesicle or capsule flow (or a mixture of different particles). In addition to directly predicting fluid dynamics in complex suspension in any geometry, the model allows determination of accurate, empirical rules which may improve existing macroscopic, continuum models.

Two-dimensional vesicle dynamics under shear flow: Effect of confinement

“…The main issue of the work presented in Ref. [14] is to accomplish simulations with a large number of particles while using a small number of nodes to reduce the computational time and the required memory. This has been achieved by using ad hoc membrane forces that penalize any deviation from the equilibrium configuration.…”

“…Advantages of the LB method are its relative ease of implementation together with its versatile adaptability to quite arbitrary geometries. The LB method has been already adapted and used to perform simulations of deformable particles such as capsules [13], vesicles, and red blood cells [14] under flow. The main issue of the work presented in Ref.…”

Multi-scale interaction of particulate flow and the artery wall

“…Lattice Boltzmann equation (50) method (LBE) is a meso-scale technique, which is based on a particle distribution function description, which answers all these needs. In particular, when appropriately optimised, LBE has been shown to be able to simulate Lagrangian particulate flow systems over a range of particle volume fractions, in geometries of complexity comparable with that under consideration and on widely available computational platforms (51,52). Figure 6 shows an instantaneous WSS distribution over the boundary of a rectangular cross-section duct at Re = 10, obtained from a pressure-driven, suspension flow of inelastic spherical "erythrocytes", at hematocrit concentration (40%), in what would be, in the continuum hemodynamic approximation, the steady state.…”

Investigation of membrane mechanics using spring networks: Application to red-blood-cell modelling

“…Discrete membrane models became popular in the late 1990s [10,11] due to their simplicity and similarity to the cytoskeleton. A number of discrete RBC models yield a good representation of the cell mechanics [12] and capture the characteristics of the cell's response in flow [13][14][15][16]. However, discrete RBC models have been criticised for their anisotropic membrane properties [17,18], i.e.…”