Title Geometric pumping induced by shear flow in dilute liquid
crystalline polymer solutions. Author(s) Yabunaka, Shunsuka; Hayakawa, Hisao Citation The Journal of chemical physics (2015), 142(5) Issue Date 2015-02-04 URL http://hdl.handle.net/2433/197278 Right © 2015 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. Type Journal Article Textversion publisher
Tumbling of a rigid rod in a shear flow
The tumbling of a rigid rod in a shear flow is analyzed in the high viscosity limit. Following Burgers, the Master Equation is derived for the probability distribution of the orientation of the rod. The equation contains one dimensionless number, the Weissenberg number, which is the ratio of the shear rate and the orientational diffusion constant. The equation is solved for the stationary state distribution for arbitrary Weissenberg numbers, in particular for the limit of high Weissenberg numbers. The stationary state gives an interesting flow pattern for the orientation of the rod, showing the interplay between flow due to the driving shear force and diffusion due to the random thermal forces of the fluid. The average tumbling time and tumbling frequency is calculated as a function of the Weissenberg number. A simple crossover function is proposed which covers the whole regime from small to large Weissenberg numbers.
Fluctuations, dynamics, and the stretch-coil transition of single actin filaments in extensional flows.
Semiflexible polymers subject to hydrodynamic forcing play an important role in cytoskeletal motions in the cell, particularly when filaments guide molecular motors whose motions create flows. Near hyperbolic stagnation points, filaments experience a competition between bending elasticity and tension and are predicted to display suppressed thermal fluctuations in the extensional regime and a buckling instability under compression. Using a microfluidic cross-flow geometry, we verify these predictions in detail, including a fluctuation-rounded stretch-coil transition of actin filaments.