Mass and Charge Transport in Micro and Nanofluidic Channels

Abstract

We consider laminar flow of incompressible electrolytes in long, straight channels driven by pressure and electroosmosis. We use a Hilbert space eigenfunction expansion to address the general problem of an arbitrary cross section and obtain general results in linear-response theory for the mass and charge transport coefficients that satisfy Onsager relations. In the limit of nonoverlapping Debye layers the transport coefficients are simply expressed in terms of parameters of the electrolyte as well as the hydraulic radius with and being the cross-sectional area and perimeter, respectively. In particular, we consider the limits of thin nonoverlapping as well as strongly overlapping Debye layers, respectively, and calculate the corrections to the hydraulic resistance due to electrohydrodynamic interactions.

KEY WORDS:

• microfluidics
• nanofluidics
• transport coefficients
• hydraulic resistance
• electro-osmotic flow

We thank Henrik Flyvbjerg for stimulating discussions that led to the present definition of the geometrical correction factor γ.

Invited paper presented at the Second International Conference on Transport Phenomena in Micro and Nanodevices, II Ciocco Hotel and Conference Center, Barga, Italy, 11–15 June 2006.