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Hydromechanics of low-Reynolds-number flow. Part 1. Rotation of axisymmetric prolate bodies

Chwang, A and Wu, T. Yao-Tsu (1974) Hydromechanics of low-Reynolds-number flow. Part 1. Rotation of axisymmetric prolate bodies. Journal of Fluid Mechanics, 63 (3). pp. 607-622. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:CHWjfm74

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Abstract

The present series of studies is concerned with low-Reynolds-number flow in general; the main objective is to develop an effective method of solution for arbitrary body shapes. In this first part, consideration is given to the viscous flow generated by pure rotation of an axisymmetric body having an arbitrary prolate form, the inertia forces being assumed to have a negligible effect on the flow. The method of solution explored here is based on a spatial distribution of singular torques, called rotlets, by which the rotational motion of a given body can be represented. Exact solutions are determined in closed form for a number of body shapes, including the dumbbell profile, elongated rods and some prolate forms. In the special case of prolate spheroids, the present exact solution agrees with that of Jeffery (1922), this being one of very few cases where previous exact solutions are available for comparison. The velocity field and the total torque are derived, and their salient features discussed for several representative and limiting cases. The moment coefficient C[sub]M = M/(8[pi][mu][omega sub 0]ab^2) (M being the torque of an axisymmetric body of length 2a and maximum radius b rotating at angular velocity [omega], about its axis in a fluid of viscosity [mu]) of various body shapes so far investigated is found to lie between 2/3 and 1, usually very near unity for not extremely slender bodies. For slender bodies, an asymptotic relationship is found between the nose curvature and the rotlet strength near the end of its axial distribution. It is also found that the theory, when applied to slender bodies, remains valid at higher Reynolds numbers than was originally intended, so long as they are small compared with the (large) aspect ratio of the body, before the inertia effects become significant.


Item Type:Article
Additional Information:"Reprinted with the permission of Cambridge University Press." (Received 1 May 1973). This work was partially sponsored by the National Science Foundation, under Grant GK31161X, and by the Office of Naval Research, under Contract N00014-67-A-0094-0012.
Record Number:CaltechAUTHORS:CHWjfm74
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:CHWjfm74
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:338
Collection:CaltechAUTHORS
Deposited By: Theodore Yao-tsu Wu
Deposited On:03 Jun 2005
Last Modified:26 Dec 2012 08:39

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