NAMS 2002 Workshop - ICOM 2008

drop are linearly related (although the diffusion coefficients in the membrane and
solution are not the same). The boundary layers are more complex, because
both electromigration and diffusion are operative. An analytical mathematical
model describing the relationships among concentration (profile), current density,
and potential gradient in the boundary layers for an ideal one-dimensional
system at steady state has been developed and solved, and this model illustrates
all of the important characteristics and limitations of real ED systems. The model
has been solved for both a single salt (one cation and one anion) and two salt
(one cation and two anions, or vice versa) situations; more complex mixtures
require numerical solutions which are under development at the time of writing.
To our knowledge, such a model has not previously been presented.
The analytical model elucidates the influence of several factors on ED design
and operation more directly than more complex numerical models. For example:
(i) The concentration for the single-salt solution varies linearly with distance in the
boundary layer, and the absolute value of the slope increases with increasing
current and decreasing diffusion coefficient of the selected ion. (ii) The
concentration decreases from either membrane to the bulk in the boundary
layers of the concentrate, and decreases from the bulk to the membrane in the
boundary layers of the diluate. (ii) The potential drop is expressed by a
logarithmic function with distance in the boundary layer, but the relevant
variables have similar functionality as in the concentration expressions. (iv) ED is
most efficient when the total dissolved solids (TDS) concentration of the influent
is much less than that of seawater and when the effluent TDS can be sufficiently
high to allow current passage; these conditions exactly fit brackish water RO
concentrate as a feedstock to create drinking water.
Along with development of the model, laboratory scale experiments are being
performed using a five cell-pair electrodialyzer from PCCell, GmbH (Heusweiler,
Germany). A computerized drive controls the flow rate, while a direct current
regulated power supply controls the applied potential (or current). Conductivity
and pH of the treatment streams are monitored continuously. A digital balance is
used in flow rate calibrations and osmosis quantification. A graphical user
interface and data acquisition system round out the system. A wide range of
experiments have been and will be performed, and a selection of results that test
and demonstrate the utility of the model will be presented.