Christian J. C. Biscombe

Microfluidic circuit analysis I: Ion current relationships for thin slits and pipes

Existing microfluidic circuit theories consider conservation of volume and conservation of total charge at each channel intersection (node) that exists within a circuit. However, in a strict sense conservation of number (or charge) for each ion species that is present should also be applied. To be able to perform such a conservation the currents due to the movement of each ion species (electrokinetic ion currents) that occur within each channel need to be known. Hence, we here present analytical and numerical methods for calculating these ion currents (and fluid flowrates) in Newtonian binary electrolyte solutions flowing within two-dimensional thin slits and pipes. Analytical results are derived in the limits of low potential, high potential, and thin double layers. We show that irrespective of double layer overlap, the Boltzmann distribution is valid provided that a local geometric mean is used for the reference ion concentration. While the real significance of the work lies in its application to multi-channel microfluidic circuit theory (see the accompanying paper of Biscombe et al. [1]), the present results show that even in single channels, ion current behaviour can be surprisingly complex.

Microfluidic circuit analysis II: Implications of ion conservation for microchannels connected in series

A mathematical framework for analysing electrokinetic flow in microchannel networks is outlined. The model is based on conservation of volume and total charge at network junctions, but in contrast to earlier theories also incorporates conservation of ion charge there. The model is applied to mixed pressure-driven/electro-osmotic flows of binary electrolytes through homogeneous microchannels as well as a 4:1:4 contraction-expansion series network. Under conditions of specified volumetric flow rate and ion currents, non-linear steady-state phenomena may arise: when the direction of the net co-ion flux is opposite to the direction of the net volumetric flow, two different fully developed, steady-state flow solutions may be obtained. Model predictions are compared with two-dimensional computational fluid dynamics (CFD) simulations. For systems where two steady states are realisable, the ultimate steady behaviour is shown to depend in part upon the initial state of the system.

The Discovery of Electrokinetic Phenomena: Setting the Record Straight

Electro-osmosis and electrophoresis were discovered by F. F. Reuss in Moscow in 1807. Or so the story goes. This Essay critically examines the contributions of three scientists to the discovery of electrokinetic phenomena. The evidence suggests that Reuss did indeed discover electro-osmosis, which takes its name (indirectly) from the work of Porrett. Contrary to current consensus, Gautherot made the earliest known observation of electrophoresis.