Swimming in a confined liquid crystal


Microscopic lifeforms rarely locomote in an unconfined liquid. Solid boundaries representing biological membranes, other swimmers, or filaments much larger than the swimmer can represent elements of confinement. Due to the long range of hydrodynamic forces at this scale, the boundaries often have a dominant impact on the physics of locomotion. Here we extend previous work on locomotion of a swimmer with a prescribed stroke in confined isotropic fluids to anisotropic fluids, using the model of a nematic liquid crystal. The competition between elasticity, hydrodynamics, and anchoring conditions leads to a complex locomotion problem with unique transport properties. We examine this problem analytically and numerically for a model swimmer near a bounding wall which can itself also be elastic. For strong planar anchoring at a rigid wall, we find that the swimming speed goes to the isotropic Newtonian limit as the swimmer gets close to the wall, although the power required to maintain the swimmer’s speed depends on liquid crystal properties. We also report new findings on the swimming speed due to large-amplitude waveforms in unbounded liquid crystals.

Madison S. Krieger, Saverio E. Spagnolie and Thomas R. Powers, “Swimming in a confined liquid crystal”, arXiv, PDF


Microscale locomotion in a nematic liquid crystal


Microorganisms often encounter anisotropy, for example in mucus and biofilms. We study how anisotropy and elasticity of the ambient fluid affects the speed of a swimming microorganism with a prescribed stroke. Motivated by recent experiments on swimming bacteria in anisotropic environments, we extend a classical model for swimming microorganisms, the Taylor swimming sheet, actuated by small-amplitude traveling waves in a three-dimensional nematic liquid crystal without twist. We calculate the swimming speed and entrained volumetric flux as a function of the swimmer’s stroke properties as well as the elastic and rheological properties of the liquid crystal. These results are then compared to previous results on an analogous swimmer in a hexatic liquid crystal, indicating large differences in the cases of small Ericksen number and in a nematic fluid when the tumbling parameter is near the transition to a shear-aligning nematic. We also propose a novel method of swimming in a nematic fluid by passing a traveling wave of director oscillation along a rigid wall.

Madison S. Krieger, Saverio E. Spagnolie and Thomas R. Powers, “Microscale locomotion in a nematic liquid crystal”, Soft Matter, 2015, 11, 9115 – 9125, arXiv, PDF

Minimal model for transient swimming in a liquid crystal


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.

Madison S. Krieger, Marcelo A. Dias and Thomas R. Powers, “Transient swimming in a hexatic liquid crystal”,  Eur. Phys. J. E. 38, 94, arXiv, PDF

Locomotion and Transport in a Hexatic Liquid Crystal



The swimming behavior of bacteria and other microorganisms is sensitive to the physical properties of the fluid in which they swim. Mucus, biofilms, and artificial liquid-crystalline solutions are all examples of fluids with some degree of anisotropy that are also commonly encountered by bacteria. In this article, we study how liquid-crystalline order affects the swimming behavior of a model swimmer. The swimmer is a one-dimensional version of G. I. Taylor’s swimming sheet: an infinite line undulating with small-amplitude transverse or longitudinal traveling waves. The fluid is a two-dimensional hexatic liquid-crystalline film. We calculate the power dissipated, swimming speed, and flux of fluid entrained as a function of the swimmer’s waveform as well as properties of the hexatic film, such as the rotational and shear viscosity, the Frank elastic constant, and the anchoring strength. The departure from isotropic behavior is greatest for large rotational viscosity and weak anchoring boundary conditions on the orientational order at the swimmer surface. We even find that if the rotational viscosity is large enough, the transverse-wave swimmer moves in the opposite direction relative to a swimmer in an isotropic fluid.

Madison S. Krieger, Saverio E. Spagnolie and Thomas R. Powers, “Locomotion and transport in a hexatic liquid crystal”, Phys. Rev. E 90, 052503, arXiv, PDF

Tunable wrinkling of thin liquid crystal elastomer membranes


We study the formation of wrinkles due to compressive stress of a thin nematic liquid crystal elastomer atop an elastic or fluid substrate. Using a Foppl-von Karman-like plate theory for the nematic elastomer, we find the scaling of wrinkle wavelength and amplitude in terms of material parameters and the applied compression. The result is that unlike in thin isotropic elastomer films, the number of wrinkles is a non-monotonic function of strain and material parameters. Furthermore, there are multiple ways to suppress wrinkling by tuning the nematic-rubber coupling parameters.

Madison S. Krieger, Marcelo A. Dias and Thomas R. Powers, “Tunable wrinkling of thin liquid crystal elastomer membranes”,  —,