The Fluid Dynamics of Swimming Microorganisms and Cells

Abstract

In this review, we describe the fluid mechanics of swimming microorganisms, with an emphasis on recent developments. We begin with the mechanics of individual swimmers, and describe the requirement for a non-reciprocal cyclic swimming stroke for net displacement in the absence of inertia. We discuss Purcell's three-link swimmer and other artificial models as simple pedagogical examples. Thereafter, we consider the swimming of real microorganisms, which may be classified into ciliates and the flagellates. In addition to the stroke kinematics, we examine the nature of the fluid velocity field around a swimmer, which governs the hydrodynamic interactions between swimmers. We then consider the large-scale hydrodynamics in a suspension of swimmers, our efforts motivated primarily by experimental observations of coherent motion. The theoretical analyses fall into two categories: the first considers coherent motion that arises from the coupling of gravity with the density difference between the swimmer and the suspending fluid. The second category is more recent, and examines the smaller-scale coherent motion, in the absence of buoyancy forces, that is driven by the anisotropic orientation distribution of the swimmer force-dipoles. We then describe a variety of discrete simulation methods, wherein the motion of every swimmer is tracked in time. The continuum theories and simulations reveal fundamental differences in the collective dynamics between suspensions of pushers, pullers and squirmers; only suspensions of pushers, for instance, are predicted to be linearly unstable. Despite the successes of the theoretical and computational methods, significant issues remain unexplained, some of which are highlighted towards the end of the review.