The method of regularized Stokeslets is a Lagrangian method for computing Stokes flow driven by forces distributed at material points in a fluid. It is based on the superposition of exact solutions of the Stokes equations when forces are given by a cutoff function. We present this method in three dimensions, along with an analysis of its accuracy and performance on the model problems of flow past a sphere and the steady state rotation of rigid helical tubes. Predicted swimming speeds for various helical geometries are compared with experimental data for motile spirochetes. In addition, the regularized Stokeslet method is readily implemented in conjunction with an immersed boundary representation of an elastic helix that incorporates passive elastic properties as well as mechanisms of internal force generation.

Mammalian fertilization requires the coordinated activity of motile spermatozoa, muscular contractions of the uterus and oviduct, as well as ciliary beating. These elastic structures generate forces that drive fluid motion, but their configurations are, in turn, determined by the fluid dynamics. We review the basic fluid mechanical aspects of reproduction, including flagellar/ciliary beating and peristalsis. We report on recent biological studies that have shed light on the relative importance of the mechanical ingredients of reproduction. In particular, we examine sperm motility in the reproductive tract, ovum pickup and transport in the oviduct, as well as sperm-egg interactions. We review recent advances in understanding the internal mechanics of cilia and flagella, flagellar surface interaction, sperm motility in complex fluids, and the role of fluid dynamics in embryo transfer. We outline promising computational fluid dynamics frameworks that may be used to investigate these complex, fluid-structure interactions.

Animal movements result from a complex balance of many different forces. Muscles produce force to move the body; the body has inertial, elastic, and damping properties that may aid or oppose the muscle force; and the environment produces reaction forces back on the body. The actual motion is an emergent property of these interactions. To examine the roles of body stiffness, muscle activation, and fluid environment for swimming animals, a computational model of a lamprey was developed. The model uses an immersed boundary framework that fully couples the Navier–Stokes equations of fluid dynamics with an actuated, elastic body model. This is the first model at a Reynolds number appropriate for a swimming fish that captures the complete fluid-structure interaction, in which the body deforms according to both internal muscular forces and external fluid forces. Results indicate that identical muscle activation patterns can produce different kinematics depending on body stiffness, and the optimal value of stiffness for maximum acceleration is different from that for maximum steady swimming speed. Additionally, negative muscle work, observed in many fishes, emerges at higher tail beat frequencies without sensory input and may contribute to energy efficiency. Swimming fishes that can tune their body stiffness by appropriately timed muscle contractions may therefore be able to optimize the passive dynamics of their bodies to maximize peak acceleration or swimming speed.

Microorganisms navigate through complex environments such as biofilms and mucosal tissues and tracts. To understand the effect of a complex medium upon their locomotion, we investigate numerically the effect of fluid viscoelasticity on the dynamics of an undulating swimming sheet. First, we recover recent small-amplitude results for infinite sheets that suggest that viscoelasticity impedes locomotion. We find the opposite result when simulating free swimmers with large tail undulations, with both velocity and mechanical efficiency peaking for Deborah numbers near one. We associate this with regions of highly stressed fluid aft of the undulating tail.