Chapter 11
Species and charge transport

Understanding charge and species transport is critical to understanding how electric fields couple to fluid flow in dynamic systems. So far, the only species transport we have discussed is passive scalar diffusion in Chapter 4, and the only treatment of ion transport was the equilibrium distribution of ions specified by Boltzmann statistics in Chapter 9. Brief mention of the charge transport equation (albeit with diffusion ignored) was made in Section 5.2.1. Now, we describe a general framework for species and charge transport equations, which assists us in understanding electrophoretic separations (Chapter 12), dynamic modeling of electrical double layers (Chapter 16), and dielectrophoresis (Chapter 17), among other topics.

In the following sections, we first describe the basic sources of species fluxes. These constitutive relations include the diffusivity (first discussed in the context of microfluidic mixing in Chapter 4), electrophoretic mobility, and viscous mobility. The species fluxes, when applied to a control volume, lead to the basic conservation equations for species, the Nernst-Planck equations. We then consider the sources of charge fluxes, which lead to constitutive relations for the charge fluxes and definitions of parameters such as the conductivity (first discussed in Chapter 3), as well as the molar conductivity. Since charge in an electrolyte solution is carried by ionic species (in contrast to electrons, as is the case for metal conductors), the charge transport and species transport equations are closely related—in fact, the charge transport equation is just a sum of species transport equations weighted by the ion valence and multiplied by the Faraday constant.

We show in this chapter that the transport parameters D, μ_EP, μ_i, σ, and Λ are all closely related, and we write equations such as the Nernst-Einstein relation to link these parameters. These issues affect microfluidic devices because ion transport couples to and affects fluid flow in microfluidic systems. Further, many microfluidic systems are designed to manipulate and control the distribution of dissolved analytes for concentration, chemical separation, or other purposes.

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