Minimal model for transient swimming in a liquid crystal

StartUp When a microorganism begins swimming from rest in a Newtonian fluid such as water, it rapidly attains its steady-state swimming speed since changes in the velocity field spread quickly when the Reynolds number is small.  However, swimming microorganisms are commonly found or studied in complex fluids. Because these fluids have long relaxation times, the time to attain the steady-state swimming speed can also be long. In this article we study the swimming startup problem in the simplest liquid crystalline fluid: a two-dimensional hexatic liquid crystal film. We study the dependence of startup time on anchoring strength and Ericksen number, which is the ratio of viscous to elastic stresses. For strong anchoring, the fluid flow starts up immediately but the liquid crystal field and swimming velocity attain their sinusoidal steady-state values after a time proportional to the relaxation time of the liquid crystal. When the Ericksen number is high, the behavior is the same as in the strong anchoring case for any anchoring strength. We also find that the startup time increases with the ratio of the rotational viscosity to the shear viscosity, and then ultimately saturates once the rotational viscosity is much greater than the shear viscosity.

M. S. Krieger, M. A. Dias, and T. R. Powers,  EPJE  (2015). Arxiv and Journal

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Swimming near Deformable Membranes at Low Reynolds Number

Microorganisms are rarely found in Nature swimming freely in an unbounded fluid. Instead, they typically encounter other organisms, hard walls, or deformable boundaries such as free interfaces or membranes. Hydrodynamic interactions between the swimmer and nearby objects lead to many interesting phenomena, such as changes in swimming speed, tendencies to accumulate or turn, and coordinated flagellar beating. Inspired by this class of problems, we investigate locomotion of microorganisms near deformable boundaries. We calculate the speed of an infinitely long swimmer close to a flexible surface separating two fluids; we also calculate the deformation and swimming speed of the flexible surface. When the viscosities on either side of the flexible interface differ, we find that fluid is pumped along or against the swimming direction, depending on which viscosity is greater.ModelInterface

M. A. Dias and T. R. Powers PoF (2013) Arxiv and Journal.