Hydrodynamics of Suspensions of Passive and Active Rigid Particles: A Rigid Multiblob Approach

We develop a rigid multiblob method for numerically solving the mobility problem for suspensions of passive and active rigid particles of complex shape in Stokes flow in unconfined, partially confined, and fully confined geometries. As in a number of existing methods, we discretize rigid bodies using a collection of minimally-resolved spherical blobs constrained to move as a rigid body, to arrive at a potentially large linear system of equations for the unknown Lagrange multipliers and rigid-body motions. Here we develop a block-diagonal preconditioner for this linear system and show that a standard Krylov solver converges in a modest number of iterations that is essentially independent of the number of particles. For unbounded suspensions and suspensions sedimented against a single no-slip boundary, we rely on existing analytical expressions for the Rotne-Prager tensor combined with a fast multipole method or a direct summation on a Graphical Processing Unit to obtain an simple yet efficient and scalable implementation. For fully confined domains, such as periodic suspensions or suspensions confined in slit and square channels, we extend a recently-developed rigid-body immersed boundary method to suspensions of freely-moving passive or active rigid particles at zero Reynolds number. We demonstrate that the iterative solver for the coupled fluid and rigid body equations converges in a bounded number of iterations regardless of the system size. We optimize a number of parameters in the iterative solvers and apply our method to a variety of benchmark problems to carefully assess the accuracy of the rigid multiblob approach as a function of the resolution. We also model the dynamics of colloidal particles studied in recent experiments, such as passive boomerangs in a slit channel, as well as a pair of non-Brownian active nanorods sedimented against a wall.Comment: Under revision in CAMCOS, Nov 201

Numerical simulation of destabilizing heterogeneous suspensions at vanishing Reynolds numbers

This work deals with the numerical investigation of destabilizing suspensions, which are governed by two basic processes: Clustering and sedimentation. After laying the foundation to an efficient numerical simulation based on the Stokesian Dynamics method, hydrodynamic clustering and clustering due to non-hydrodynamic interactions are investigated. It is shown that multi-particle simulations need parallelization and an efficient post-processing to yield reliable results within a reasonable time

On the bulk viscosity of suspensions

The bulk viscosity of a suspension relates the deviation of the trace of the macroscopic or averaged stress from its equilibrium value to the average rate of expansion. For a suspension the equilibrium macroscopic stress is the sum of the fluid pressure and the osmotic pressure of the suspended particles. An average rate of expansion drives the suspension microstructure out of equilibrium and is resisted by the thermal motion of the particles. Expressions are given to compute the bulk viscosity for all concentrations and all expansion rates and shown to be completely analogous to the well-known formulae for the deviatoric macroscopic stress, which are used, for example, to compute the shear viscosity. The effect of rigid spherical particles on the bulk viscosity is determined to second order in volume fraction and to leading order in the Péclet number, which is defined as the expansion rate made dimensionless with the Brownian time scale. A repulsive hard-sphere-like interparticle force reduces the hydrodynamic interactions between particles and decreases the bulk viscosity

Suspensions of prolate spheroids in Stokes flow. Part 1. Dynamics of a finite number of particles in an unbounded fluid

A new simulation method is presented for low-Reynolds-number flow problems involving elongated particles in an unbounded fluid. The technique extends the principles of Stokesian dynamics, a multipole moment expansion method, to ellipsoidal particle shapes. The methodology is applied to prolate spheroids in particular, and shown to be efficient and accurate by comparison with other numerical methods for Stokes flow. The importance of hydrodynamic interactions is illustrated by examples on sedimenting spheroids and particles in a simple shear flow

Numerical methods for simulations and optimization of vesicle flows in microfluidic devices

Vesicles are highly deformable particles that are filled with a Newtonian fluid. They resemble biological cells without a nucleus such as red blood cells (RBCs). Vesicle flow simulations can be used to design microfluidic devices for medical diagnoses and drug delivery systems. This dissertation focuses on efficient numerical methods for simulations and optimization of vesicle flows in two dimensions. We consider flows with very low Reynolds numbers and inextensible vesicle membranes that resist bending. Our numerical scheme is based on a boundary integral formulation which is known to be efficient for such flows. This formulation leads to a set of nonlinear integro-differential equations for the vesicle dynamics. Complex interplay between the nonlocal hydrodynamic forces and the membranes’ elasticity determines the vesicles’ motion. Many state-of-the-art numerical schemes can resolve these complex flows. However, simulations remain computationally expensive since high-resolution discretization is needed. The high computational cost limits the use of the simulations for practical purposes such as optimization. Our first attempt to reduce the cost is to use low-resolution discretization. We present a scheme that systematically integrates several correction algorithms that are necessary for stable and accurate low-resolution simulations. We compare the low-resolution simulations with their high-fidelity counterparts. We observe that our scheme enables both fast and statistically accurate simulations. We accelerate vesicle flow simulations further by replacing expensive parts of the numerical scheme with low-cost function approximations. We propose a machine-learning-augmented reduced model that uses several multilayer perceptrons to model different aspects of the flows. Although we train the perceptrons with high-fidelity single-particle simulations for one time step, our method enables us to conduct long-horizon simulations of suspensions with several particles in confined geometries. It is faster than a state-of-the-art numerical scheme having the same number of degrees of freedom and can reproduce several features of the flow accurately. It generalizes as is to other particles like deformable capsules, drops, filaments and rigid bodies. Moreover, we investigate deformability-based sorting of RBCs using a microfluidic device that enables medical diagnoses of diseases such as malaria. Using our numerical scheme we solve a design optimization problem to find optimal designs of the device that provide efficient sorting of cells with arbitrary mechanical propertiesMechanical Engineerin