Copyright Brian J. Kirby. With questions, contact Prof. Kirby here.
This material may not be distributed without the author's consent. When linking to these pages, please use the URL http://www.kirbyresearch.com/textbook.
This web posting is a draft, abridged version of the Cambridge University Press text. Follow the links to buy at Cambridge or Amazon or Powell's or Barnes and Noble. Contact Prof. Kirby
here.
[Return to Table of Contents]
Jump To:
[Kinematics]
[Couette/Poiseuille Flow]
[Fluid Circuits]
[Mixing]
[Electrodynamics]
[Electroosmosis]
[Potential Flow]
[Stokes Flow]
[Debye Layer]
[Zeta Potential]
[Species Transport]
[Separations]
[Particle Electrophoresis]
[DNA]
[Nanofluidics]
[InducedCharge Effects]
[DEP]
[Solution Chemistry]
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 NernstPlanck 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 NernstEinstein 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.
[Return to Table of Contents]
Jump To:
[Kinematics]
[Couette/Poiseuille Flow]
[Fluid Circuits]
[Mixing]
[Electrodynamics]
[Electroosmosis]
[Potential Flow]
[Stokes Flow]
[Debye Layer]
[Zeta Potential]
[Species Transport]
[Separations]
[Particle Electrophoresis]
[DNA]
[Nanofluidics]
[InducedCharge Effects]
[DEP]
[Solution Chemistry]
Copyright Brian J. Kirby. Please contact Prof. Kirby here with questions or corrections.
This material may not be distributed without the author's consent. When linking to these pages, please use the URL http://www.kirbyresearch.com/textbook.
This web posting is a draft, abridged version of the Cambridge University Press text. Follow the links to buy at Cambridge or Amazon or Powell's or Barnes and Noble. Contact Prof. Kirby
here.
