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Electrokinetic Flow 319
Now for our clarifications of this list in light of our example:

Strong and weak constraints should not be mixed on adjacent
boundaries. But Neurnann boundary conditions do not count as strong
(automatically weak), so they can be mixed on adjacent boundaries.
Our “electrodes” were surrounded by Neumann BC segments with no
apparent difficulty. This is consistent with the policy that Neumann
boundary conditions do not count as a constraint for the purposes
of a weak boundary constraint.
You must always have a constraint on boundaries when you enable the
weak boundary constraint. We used three zero boundary conditions for
boundaries bnds 5,6, 21 and still got the correct answer. So even a
homogeneous constraint still counts as a constraint.

9.3 Electrokinetic Flow

9.3.1 Background
Electrokinetic flow is produced by the interaction of an electric field and charged
(ion) species in a liquid. Two distinct interactions are present: the electric force
on the liquid in the double layer region adjacent to wall surfaces where there is a
net charge and the movement of individual ions in the bulk of the flow (outside
the double layer region) where there is generally no net charge. The double
layer may be taken as infinitesimal for channel sizes of interest (say greater than
about 1 pm) and its effect on the flow is then equivalent (MacInnes, 2002) to
application of the boundary conditions for velocity, u;, electric field, 4, and
mass fraction of a relevant chemical species, Y :

where ni is the unit normal vector to the wall surface.
The system of equations that must be solved comprises the momentum
equation, the continuity of mass equation, the charge continuity equation and a
species equation. A simplest case may be expressed in non-dimensional form by
Momentum transport and continuity (Navier-Stokes):