Page 362 - Process Modelling and Simulation With Finite Element Methods

Electrokinetic Flow 349

The design issues of nlicrofluidic switches can be profitably explored by such
2DAD networks - our Y-junction is an idealized geometry which could be
tailored to achieve greatest segregation among the switching slugs.

9.4 Summary

This chapter explored the multiphysics modeling appropriate for electrohnetic
flow in microchannel networks. In setting up our case study, we discovered how
to use FEMLAB’s weak boundary constraints for coupled boundary conditions
that incorporate non-tangential boundary conditions. We showed the utility of
weak boundary conditions in accurate flux computations by revisiting the
electrical capacitance tomography forward problem defined in $7.3.2. An order
of magnitude improvement in convergence rate was found for little extra cost.
After this simple example, we moved on to implementing more complicated
weak boundary constraints in the electrokinetic flow model. The latter
illustrated FEMLAB’s guidelines for when to use a weak boundary constraint
and when they fail. One typically has the connotation that constraints on the
function should be implemented as Dirichlet-type boundary conditions, but that
constraints on the derivative should be implemented as Neumann-type boundary
conditions. In the context of a weak boundary condition, if you can implement it
as a Neumann boundary condition, it does not count as a constraint. Thus, only
Dirichlet-type boundary conditions can be treated with weak boundary
constraints, and the distinction between constraints on the function and on its
derivatives does not apply.

Acknowledgements

We are indebted to Johan Sundqvist and Niklas Rom of COMSOL for
consultation on the handling of weak boundary constraints in this chapter.

References

1. FEMLAB 2.3 User’s Guide and Introduction, p. 1-398ff (2002).
2. W.B. Zimmerman and G.M. Homsy, “Nonlinear viscous fingering in
miscible displacement with anisotropic dispersion.” Physics of Fluids A 3(8)
1859 (1991).
3. J. M. MacInnes, “Computation of Reacting Electrokinetic Flow in
Microchannel Geometries”, Chemical Engineering Science, 57 (21), 4539-
4558 (2002).