Page 326 - Process Modelling and Simulation With Finite Element Methods

Chapter 9

ELECTROKINETIC FLOW

W. B. J. ZIMMERMAN and J. M. MACINNES
Department of Chemical and Process Engineering, University of Sheffield,
Newcastle Street, Sheffield S1 3JD United Kingdom

E-mail: j. m. macinnes @ she$ ac. uk

This chapter explores the multiphysics modeling appropriate for electrokinetic flow in
microchannel networks. In setting up our case study, we learned how FEMLAB’s weak
boundary constraints are needed for coupled boundary conditions that incorporate non-
tangential boundary conditions. To illustrate the utility of weak boundary conditions in
accurate flux computations, we revisit the electrical capacitance tomography forward
problem defined in 17.3.2. After this simple example, we move on to implementing
more complicated weak boundary constraints in the electrokinetic flow model. The latter
explores FEMLAB’s guidelines for when to use a weak boundary constraint and when
they fail.

9.1 Introduction

The purpose of this chapter is to demonstrate the facility of setting up a model
for electrokinetic flow in FEMLAB. A cutting edge application for
electrokinetic flow is microfluidics, wherein small quantities of chemicals
(nanoliters) are transported “just-in-time’’ for complicated switching and
sequencing in a network of microchannels to achieve high reproducibility of
chemical reactions and compositional changes by tight control. Moving fluids
by physicochemical phenomena is especially important since it involves fast
response times and no moving mechanical parts that can become damaged.
There is a strong overlap between microfluidics and micromechanical machines
(MEMs). For instance, moving macromolecules adjacent to walls and side
channels as soft actuators is considered microfluidics, but these are also
molecular machines, but at a scale too small to be considered conventional
moving parts.
In order to set up even our simplest electrokinetic model, however,
multiphysics is essential - coupling electric potential, chemical transport, and
momentum transport (Navier-Stokes). Furthermore, a first approach introduces
some coupling through boundary conditions to approximate the electrochemical
boundary layer motion. Although this coupling is linear, we found that to get an
acceptable model in FEMLAB, the set up requires weak boundary constraints.

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