Date of Award
Doctor of Engineering Science in Chemical Engineering
Chemical Engineering and Chemistry
Ernest N. Bart
John E. McCormick
Roy A. Plastock
The creeping motion equation has been solved for the case of planar arrays of spheres settling under the influence of gravity in a viscous fluid. The solution is a general solution which applies to an arbitrary number of spheres. All particles will lie at the corners of a regular polygon. Thus, two particles side by side, three particles in an equilateral triangular array, or four spheres in a square array will be special cases of the general solution.
The solution has been obtained by a unique application of the method of reflections. Only a first correction to the drag has been obtained which puts an additional constraint on the solution since the higher order terms have been neglected. As a result, the solution is most accurate when the spheres are far apart.
In order to verify the general solution for the case of two spheres, the result has been compared with the literature value which exists for the case of two spheres falling perpendicular to their line of centers. The solution obtained in this work for two spheres is in exact agreement with the literature solution for the two sphere case. The results of the general solution indicate that as the number of spheres in the array is increased, the terminal settling velocity increases rapidly.
Bixon, Eric Robert, "The settling of an arbitrary number of spherical particles arranged on the corners of a regular polygon in a viscous fluid" (1983). Dissertations. 1280.