Imperial College London
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DrOrySchnitzer

Faculty of Natural Sciences, Department of Mathematics

Reader in Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 3833o.schnitzer Website

 
 
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Location

 

739Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Schnitzer:2015:10.1017/jfm.2015.242,
author = {Schnitzer, O and Yariv, EY},
doi = {10.1017/jfm.2015.242},
journal = {Journal of Fluid Mechanics},
pages = {1--33},
title = {The Taylor–Melcher leaky dielectric model as a macroscale electrokinetic description},
url = {http://dx.doi.org/10.1017/jfm.2015.242},
volume = {773},
year = {2015}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - While the Taylor–Melcher electrohydrodynamic model entails ionic charge carriers, it addresses neither ionic transport within the liquids nor the formation of diffuse space-charge layers about their common interface. Moreover, as this model is hinged upon the presence of non-zero interfacial-charge density, it appears to be in contradiction with the aggregate electro-neutrality implied by ionic screening. Following a brief synopsis published by Baygents & Saville (Third International Colloquium on Drops and Bubbles, AIP Conference Proceedings, vol. 7, 1989, American Institute of Physics, pp. 7–17) we systematically derive here the macroscale description appropriate for leaky dielectric liquids, starting from the primitive electrokinetic equations and addressing the double limit of thin space-charge layers and strong fields. This derivation is accomplished through the use of matched asymptotic expansions between the narrow space-charge layers adjacent to the interface and the electro-neutral bulk domains, which are homogenized by the strong ionic advection. Electrokinetic transport within the electrical ‘triple layer’ comprising the genuine interface and the adjacent space-charge layers is embodied in effective boundary conditions; these conditions, together with the simplified transport within the bulk domains, constitute the requisite macroscale description. This description essentially coincides with the familiar equations of Melcher & Taylor (Annu. Rev. Fluid Mech., vol. 1, 1969, pp. 111–146). A key quantity in our macroscale description is the ‘apparent’ surface-charge density, provided by the transversely integrated triple-layer microscale charge. At leading order, this density vanishes due to the expected Debye-layer screening; its asymptotic correction provides the ‘interfacial’ surface-charge density appearing in the Taylor–Melcher model. Our unified electrohydrodynamic treatment provides a
AU  - Schnitzer,O
AU  - Yariv,EY
DO  - 10.1017/jfm.2015.242
EP  - 33
PY  - 2015///
SN  - 0022-1120
SP  - 1
TI  - The Taylor–Melcher leaky dielectric model as a macroscale electrokinetic description
T2  - Journal of Fluid Mechanics
UR  - http://dx.doi.org/10.1017/jfm.2015.242
UR  - http://hdl.handle.net/10044/1/22007
VL  - 773
ER  -
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