Rubinow-Keller theory

Denson provides a quantitative theoretical analysis which adequately accounts for these phenomena. Agreement is quite good, especially in the range Rep < 40. No adjustable parameters appear in the treatment. The unsteady-state analysis depends critically upon the applicability of the Rubinow-Keller theory to the instantaneous particle motion, and the observed agreement is construed by Denson as evidence of its applicability for RCp < 40. (See, however, the remarks in the last paragraph of Section III,E,3.)... 

Upon comparing Eqs. (265) and (267) with Eqs. (254)-(255) using the experimentally measured angular and axial slip velocities, Jeffrey concludes that the radial velocities predicted by the Rubinow-Keller theory are too small by an order of magnitude, except at the larger values of l> where their theory yields results too small by a factor of only about 1.5-3. 

As Rep 0 this ratio becomes infinite, showing that the restriction required by Eq. (274) is indeed met. Thus, at least in the neutrally buoyant case, the Rubinow-Keller theory is wholly inapplicable to Poiseuille flows. It should not be surmised, however, that Saffman s results themselves have any direct application to such flows for Saffman s calculations take no account of either the nonconstancy of the local shear rate or of the presence of boundaries constraining the flow. And either of these effects may result in the appearance of contributions to the lift force more dominant than Saffman s, at least for some ranges of the many independent variables. 

As mentioned previously, Repetti and Leonard (R4a) attempted an explanation of this phenomenon on the basis of a questionable modification of the Rubinow-Keller theory. It is now clear, however, that their proposal cannot be correct. 

With regard to the interpretation of available experimental data, the only outstanding point seemingly in need of further discussion is the observation by Denson (D4b) that the Rubinow-Keller theory agrees well with his... 

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