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.
Statistics of tumbling of a single polymer molecule in shear flow.
We present experimental results on statistics of polymer orientation angles relative to the shear plane and tumbling times in shear flow with thermal noise. The strong deviation of the probability distribution functions (PDFs) of the orientation angles from Gaussian PDFs was observed in good accord with theory. A universal exponential PDF tail for the tumbling times and its predicted scaling with Wi (that is, the dimensionless shear rate normalized by the polymer relaxation time) are also tested experimentally against numerics. The scaling relations of PDF widths for both angles as a function of Wi are verified and compared with numerics.