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.
Arabia's Frontiers: The Story of Britain's Boundary Drawing in the Desert
List of maps Prologue Convention Abbreviations PART I GEOPOLITICAL SETTING Chapter 1. The Regional Powers: Saudi Arabia, Yemen and Britain Chapter 2. The Gulf PART 11 THE BLUE LINE Chapter 1. The 1913 Anglo-Ottoman Convention Chapter 2. The Violet Line PART III SUCCESSOR STATE Chapter 5. Britain's Relations with lbn Saud up to the End of World War 1 Chapter 6. Post-War Relations Chapter 7. Conflict with Yemen PART IV PRE-WORLD WAR 11 NEGOTIATIONS Chapter 8. Oil: The Casoc and Qatar Concession Boundaries Chapter 9. Negotiations Chapter 10. Aftermath: 1936-9 PART V A NEW CLAIM Chapter 11. Procrastination Chapter 12. The Oman Problem Chapter 13. Final Negotiations