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.
Theoretical studies of a suspension of rigid particles affected by Brownian couples
This paper describes the work carried out to investigate the pore pressures occurring in secondary consolidation. A theoretical approach and an experimental technique was developed in order to conduct the study. By considering compression to occur only due to water leaving the soil it was possible to derive an ex(Received October 27, 1972) pression for the dissipation of pore pressure in the secondary phase• By further simplified assumptions which are based on experimental observations, the above general solution was reduced to a simple formula which predicted the observed behaviour of pore water pressures during secondary consolidation. A P P E N D I X Errata Since it has been very difficult receiving the many proofs of the papers of the Proceedings of the VIth International Congress of Rheology in time for printing, some proofs reached the editors, publishers and printers too late. So some mistakes or errors could not be eliminated before printing. The main errors now are corrected by the following Appendix. The page numbers quoted mean the bold type page numbers of the complete special issue of the proceedings shown at the bottom of each page.t Further remark: In this Appendix there are published mainly corrections of misleading mistakes in equations, of wrong values, ratios or numbers etc. but no merely stylistic or linguistic corrections of the text passages and of smaller misprints respectionly and easy to correct when reading. Theoretical studies of a suspension of rigid particles affected by Brownian couples By L. G. Leal ( Pasadena, Cal([i ) and E. J. Hinch ( Cambridqe) Rheol. Acta 12, 43-48 (1973) p. 43, Introduction, first paragraph, second sentence: read correctly: The particles are rigid, axially symmetric, free of external couples or forces, and sufficiently small so that they and their disturbance flow are inertialess. p. 43, after eq. [1] read correctly: where r is the aspect ratio... p. 43, Eq. [3], second line read correctly: B[Qp_p)=E + =E. (pp) ] p. 44, right column, fifth line read correctly: • .flows, ]lEll/~o ~ 0, leads to the linear viscoelast ic . . . Last sentence of the same paragraph read correctly: ù . t ion in the limit (r 2 1)/(r 2 + 1) ~ 0. p. 48, add the following Summary: We consider the rheology of a dilute suspension of rigid, axially symmetric particles which is undergoing a general time-dependent linear bulk flow. The particle orientation is determined as a balance between random Brownian rotations and the motion induced by flow of the suspending fluid. After outlining various approximate solutions of the resulting Fokker-Planck equation for the orientation distribution function, we consider the rheological behavior of the suspension for three specific bulk flows; steady axially symmetric extensional motion, steady simple shear flow, and start-up of a simple shear flow from rest.