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 properties