Imperial College London
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ProfessorDarrenCrowdy

Faculty of Natural Sciences, Department of Mathematics

Professor in Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8587d.crowdy Website

 
 
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Location

 

735Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Crowdy:2021:10.1007/s10665-021-10180-w,
author = {Crowdy, D},
doi = {10.1007/s10665-021-10180-w},
journal = {Journal of Engineering Mathematics},
title = {Exact solutions for the formation of stagnant caps of insoluble surfactant on a planar free surface},
url = {http://dx.doi.org/10.1007/s10665-021-10180-w},
volume = {133},
year = {2021}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - A class of exact solutions is presented describing the time evolutionof insoluble surfactant to a stagnant-cap equilibrium on the surface of deepwater in the Stokes flow regime at zero capillary number and infinite surfaceP´eclet number. This is done by demonstrating, in a two-dimensional modelsetting, the relevance of the forced complex Burgers equation to this problemwhen a linear equation of state relates the surface tension to the surfactantdensity. A complex-variable version of the method of characteristics can thenbe deployed to find an implicit representation of the general solution. A specialclass of initial conditions is considered for which the associated solutions canbe given explicitly. The new exact solutions, which include both spreading andcompactifying scenarios, provide analytical insight into the unsteady formation of stagnant caps of insoluble surfactant. It is also shown that first-orderreaction kinetics modelling sublimation or evaporation of the insoluble surfactant to the upper gas phase can be incorporated into the framework; this leadsto a forced complex Burgers equation with linear damping. Generalized exactsolutions to the latter equation at infinite surface P´eclet number are also foundand used to study how reaction effects destroy the surfactant cap equilibrium.
AU  - Crowdy,D
DO  - 10.1007/s10665-021-10180-w
PY  - 2021///
SN  - 0022-0833
TI  - Exact solutions for the formation of stagnant caps of insoluble surfactant on a planar free surface
T2  - Journal of Engineering Mathematics
UR  - http://dx.doi.org/10.1007/s10665-021-10180-w
UR  - https://link.springer.com/article/10.1007%2Fs10665-021-10180-w
UR  - http://hdl.handle.net/10044/1/91552
VL  - 133
ER  -
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