The Mathematical Institute, University of Oxford, Eprints Archive

The effect of surfactants on expanding free surfaces

Breward, C. J. W. and Darton, R. C. and Howell, P. D. and Ockendon, J. R. (2001) The effect of surfactants on expanding free surfaces. Chemical Engineering Science, 56 . pp. 2867-2878.


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This paper develops a systematic theory for the flow observed in the so-called ``overflowing cylinder'' experiment. The basic phenomenon to be explained is the order of magnitude increase in the surface velocity of a slowly overflowing beaker of water that is caused by the addition of a small amount of soluble surfactant. We perform analyses of (i) an inviscid bulk flow in which diffusion is negligible, (ii) a hydrodynamic boundary layer in which viscous effects become important, (iii) a diffusive boundary layer where diffusion is significant, and by matching these together arrive at a coupled problem for the liquid velocity and surfactant concentration. Our model predicts a relation between surface velocity and surface concentration which is in good agreement with experiment. However a degeneracy in the boundary conditions leaves one free parameter which must be taken from experimental data. We suggest an investigation that may resolve this indeterminacy.

Item Type:Article
Subjects:D - G > Fluid mechanics
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:107
Deposited By: Peter Howell
Deposited On:04 Aug 2004
Last Modified:29 May 2015 18:16

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