Micro/Nano Flows: Vorticity Generation

Micro/Nano Flows: Vorticity Generation

Trevor H. Moulden

The university of Tennessee Space Institute, USA

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| Citation



Vortical structures have been observed to develop in electrically driven fluid motion at the micro/nano scale, but no coherent theory has been put foreword in the literature to explain such a development. The present paper gives several results in a theory based upon the classical field equations. In particular, it is shown that the origin of vorticity production resides in the applied electric field interacting with any ion concentration gradients present in the fluid as defined by the vorticity equation. This is in addition to any viscous layer vorticity diffusion that may also exist in the flow.


Micro/nano Scale Flows, Maxwell Tensor, Vorticity Production


[1] Silber–Li, Z–H, Zheng, X., Kong, G–P. & Moulden, T.H., Vortices in Micro/Nano Channel flows. Advances in Fluid Mechanics, Vol. IX, eds. M. Rahman & C.A. Brebia, WIT Press: England, pp. 533–545, 2012.

[2] Moulden, T.H., On Causal Structures in Fluid Mechanics. Proc. 31th ISTS Conference, Matsuyama, Japan, 2017.

[3] Levich, V.G., Physicochemical Hydrodynamics. Prentic Hall, Englewood Cliffs, NJ, 1962.

[4] Chang, H–C, Yossifon, G. & Demekhin, E.A., Nanoscale electrokinetics and microvortices: how microhydrodynamics affects nanofluidic Ion flux. Annual Review of Fluid Mechanics, 44, pp. 401–426, 2012. https://doi.org/10.1146/annurev-fluid-120710-101046

[5] Mao, M, Ghosal, S. & Hu, G–H., Hydrodynamic flow in the vicinity of a nanopore induced by an applied coltage. Nanotechnology, 24, 245202, 2013. https://doi.org/10.1088/0957-4484/24/24/245202

[6] Park, S.Y, Russo, C.J, Branton, D. & Stone, H.A., Eddies in a bottleneck: an arbitrary Debye length theory for capillary electroosmosis. Journal of Colloid and Interface Science, 297, pp. 833–839, 2006. https://doi.org/10.1016/j.jcis.2005.11.045

[7] Gurtin, M.E., An Introduction to Continuum Mechanics. Academic Press, New York, 1981.

[8] Silber–Li, Z–H, Zheng, X, Kong, G–P. & Moulden, T.H., The impact of Ion Concentration and pH values on the Vortices in Micro/Nano Channel Flows. μFlu12. Proceedings of the 3rd European Conference on Microfluidics, Heidelberg, 2012.

[9] Korvetz, A., Electromagnetic Theory. Oxford University Press, Oxford, 2000.

[10] Galdi, G.P., Heywood, J.G. & Rannacher, R. (eds), Fundamental Directions in Mathematical Fluid Mechanics. Springer, Basel, 2000.

[11] Moulden, T.H., Uniqueness Theorems in Turbulence Models. Proc. 29th ISTS Conference, Nagoya, Japan, 2013.

[12] Leng, M., Mathematics and Reality. Oxford University Press, Oxford, 2010.

[13] Cartwright, N., How the Laws of Physics Lie. Oxford University Press, Oxford, 1983.

[14] Probstein, R.F., Physicochemical Hydrodynamics, 2nd edn., Wiley Interscience, Hoboken, NJ, 2003.

[15] Constantine, P., A few results and open problems regarding incompressible fluids. AMS Notices, 47, pp. 658–663, 1995.