Hostname: page-component-7479d7b7d-rvbq7 Total loading time: 0 Render date: 2024-07-12T01:22:08.690Z Has data issue: false hasContentIssue false

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
Affiliation:
Lyman Laboratory, Harvard University, Cambridge, Massachusetts 02138

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 Fa2/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
Copyright
© 1978 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Berg, H. C. & Purcell, E. M. 1977 Physics of chemoreception. Biophys. J. (in press).Google Scholar
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics, pp. 5354. Pergamon.
Smoluchowski, M. V. 1916a Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen. Z. Phys. Chem. 92, 154156.Google Scholar
Smoluchowski, M. V. 1916b Drei Vorträge über Diffusion, Brownsche Molekularbewegung and Koagulation von Kolloidteilchen. Phys. Z. 17, 598599.Google Scholar