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On the settling speed of dilute arrays of spheres


Mazaika, Paul K. (1974) On the settling speed of dilute arrays of spheres. Dissertation (Ph.D.), California Institute of Technology.


A method is developed to calculate the settling speed of dilute arrays of spheres for the three cases of: I, a random array of freely moving particles; II, a random array of rigidly held particles; and III, a cubic array of particles. The basic idea of the technique is to give a formal representation for the solution and then manipulate this representation in a straightforward manner to obtain the result. For infinite arrays of spheres, our results agree with the results previously found by other authors, and the analysis here appears to be simpler. This method is able to obtain more terms in the answer than was possible by Saffman's unified treatment for point particles. Some results for arbitrary two sphere distributions are presented, and an analysis of the wall effect for particles settling in a tube is given. It is expected that the method presented here can be generalized to solve other types of problems.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Applied Mathematics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Saffman, Philip G.
Thesis Committee:
  • Unknown, Unknown
Defense Date:22 May 1974
Record Number:CaltechTHESIS:03292013-090528899
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7562
Deposited By: Dan Anguka
Deposited On:29 Mar 2013 16:19
Last Modified:29 Mar 2013 16:19

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