DOI: 10.1017/s0022112078000324. The effect of fluid motions on the absorption of molecules by suspended particles

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

10.1017/s0022112078000324

Crossref journal-article

Cambridge University Press (CUP)

Journal of Fluid Mechanics (56)

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.

Bibliography

Purcell, E. M. (1978). The effect of fluid motions on the absorption of molecules by suspended particles. Journal of Fluid Mechanics, 84(3), 551â559.

Authors 1

Edward M. Purcell (first)

References 5 Referenced 24

Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics ,pp.53–54.Pergamon.
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics .Cambridge University Press.
Smoluchowski, M. V. 1916b Drei Vorträge über Diffusion, Brownsche Molekularbewegung and Koagulation von Kolloidteilchen.Phys. Z. 17,598–599.
Berg, H. C. & Purcell, E. M. 1977 Physics of chemoreception.Biophys. J. (in press). (10.1016/S0006-3495(77)85544-6)
Smoluchowski, M. V. 1916a Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen.Z. Phys. Chem. 92,154–156.

Dates

Type	When
Created	19 years, 4 months ago (April 12, 2006, 9:11 a.m.)
Deposited	6 years, 4 months ago (April 7, 2019, 3:38 p.m.)
Indexed	1 year, 10 months ago (Oct. 26, 2023, 9:07 a.m.)
Issued	47 years, 6 months ago (Feb. 13, 1978)
Published	47 years, 6 months ago (Feb. 13, 1978)
Published Online	19 years, 4 months ago (April 12, 2006)
Published Print	47 years, 6 months ago (Feb. 13, 1978)

Funders 0

None

BibTeX

@article{Purcell_1978, title={The effect of fluid motions on the absorption of molecules by suspended particles}, volume={84}, ISSN={1469-7645}, url={http://dx.doi.org/10.1017/s0022112078000324}, DOI={10.1017/s0022112078000324}, number={3}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press (CUP)}, author={Purcell, Edward M.}, year={1978}, month=feb, pages={551–559} }

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