Filaments (slender, microscopic elastic bodies) are prevalent in biological and industrial settings. In the biological case, the filaments are often active, in that they are driven internally by motor proteins, with the prime examples being cilia and flagella. For cilia in particular, which can appear in dense arrays, their resulting motions are coupled through the surrounding fluid, as well as through surfaces to which they are attached. In this talk, I present numerical simulations exploring the coordinated motion of active filaments and how it depends on the driving force, density of filaments, as well as the attached surface. In particular, we find that when the surface is spherical, its topology introduces local defects in coordinated motion which can then feedback and alter the global state. This is particularly true when the surface is not held fixed and is free to move in the surrounding fluid. These simulations take advantage of a computational framework we developed for fully 3D filament motion that combines unit quaternions, implicit geometric time integration, quasi-Newton methods, and fast, matrix-free methods for hydrodynamic interactions and it will also be presented.

Microorganisms can swim in a variety of environments, interacting with chemicals and other proteins in the fluid. In this talk, we will highlight recent computational methods and results for swimming efficiency and hydrodynamic interactions of swimmers in different fluid environments. Sperm are modeled via a centerline representation where forces are solved for using elastic rod theory. The method of regularized Stokeslets is used to solve the fluid-structure interaction where emergent swimming speeds can be compared to asymptotic analysis. In the case of fluids with extra proteins or cells that may act as friction, swimming speeds may be enhanced, and attraction may not occur. We will also highlight how parameter estimation techniques can be utilized to infer fluid and/or swimmer properties.

Understanding the transport of microorganisms and self-propelled particles in porous media has important consequences in human health as well as for microbial ecology. In this work, we explore models for the dispersion of active particles in both periodic and random porous media. In a first problem, we analyze the long-time transport properties in a dilute system of active Brownian particles swimming in a periodic lattice in the presence of an external flow. Using generalized Taylor dispersion theory, we calculate the mean transport velocity and dispersion dyadic and explain their dependence on flow strength, swimming activity and geometry. In a second approach, we address the case of run-and-tumble particles swimming through unstructured porous media composed of randomly distributed circular pillars. There, we show that the long-time dispersion is described by a universal hindrance function that depends on the medium porosity and ratio of the swimmer run length to the pillar size. An asymptotic expression for the hindrance function is derived in dilute media, and its extension to semi-dilute and dense media is obtained using stochastic simulations. We conclude by discussing the role of hydrodynamic interactions and swimmer concentration effects.