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The effect of fluid motions on the absorption of molecules by suspended particles

Published online by Cambridge University Press:  12 April 2006

Edward M. Purcell
Edward M. Purcell
Affiliation:
Lyman Laboratory, Harvard University, Cambridge, Massachusetts 02138
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Abstract

The rate at which a particle in suspension can capture diffusing solute molecules can be increased by stirring the fluid. It is shown that the increase is closely related to the total power expended, per unit volume of fluid, by the stirring device. The increase in diffusion current to a particle is related to the local rate of deformation of the fluid Ω (which, in turn, determines the dissipation) by a function F(Ωa2/D), where a is the particle radius and D the diffusion constant for the molecule in question. The function F has been determined experimentally by investigating the corresponding problem in heat transfer. In a fluid of viscosity η, stirring which is vigorous enough to double the mean diffusion current to a particle must entail a power dissipation, per unit volume, not less than 500ηD2/a4. For particles a few microns in size, or smaller, in water, effective stirring is not feasible. The results can be used also to predict the effect of stirring on the coagulation of similar particles. To double, by stirring, the rate at which particles of radius b form dimers requires a stirring power proportional to b−6, and is not feasible in water if b is less than 10−5 cm.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 84 , Issue 3 , 13 February 1978 , pp. 551 - 559
Copyright
© 1978 Cambridge University Press

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References

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