Dialysate channel

The salt solution is pumped through the dialysate and concentrate channels, with salt removed continuously along the length from the dialysate channel and transferred to the concentrate channel. A dialysate and concentrate channel with the associated membranes are termed a cell pair. A typical electrodialysis stack may have 50 to 300 cell pairs between a single pair of electrodes, and a number of stacks may be used in series to achieve the desired level of salt removal. 

As the salt content is reduced in the dialysate channels, the fluid conductivity decreases. The resulting potential drop for a given current (salt removal) is minimized by making the channel spacing small. Typical channel widths are about 1 mm with channel lengths of from about 0.25 to 1 m. 

Eventually, the diffusion layers fill the channels, and thereafter the ion concentration begins to decrease in the center of the dialysate channel and to increase in the concentrate channel. At infinite channel lengths the concentrations in the dialysate and concentrate channels would tend to limiting values corresponding to the total applied potential drop being taken up by the... 

To model the electrodialysis stack, we assume that since there are many cells in a stack the behaviors in different pairs of adjacent dialysate and concentrate channels are the same. If we neglect the potential drop in the electrode cells adjacent to the electrodes as small compared with that in the rest of the system, the potential drop across a channel pair is constant and equal to the total applied voltage divided by the number of channel pairs. The dialysate and concentrate channels are taken to have the same separation 2h (Fig. 6.2.1). Since there is symmetry about the center plane of each channel, we may model the electrodialysis cell pair of Fig. 6.2.1 by one half of the dialysate channel and one half of the adjacent concentrate channel separated by a membrane, as shown in Fig. 6.2.4. For specificity we choose the cation exchange membrane. Both types of membranes are assumed to have the same resistances and thicknesses and to be perfectly selective. To simplify the problem somewhat further, we take the membrane resistance to be small so that the ohmic drop within the membranes may be neglected. 

Parallel-plate hemodialyzers using flat membranes, with several compartments in parallel, separated by plastic plates, are now only available from Hospal Co (Crystal and Hemospal models). Blood circulates between two membranes and the dialysate between the other side of membrane and the plastic plate. These parallel-plate dialyzers have a smaller blood-pressure drop than hollow-fiber ones and require less anticoagulants as flat channels are less exposed to thrombus formation than fibers, but they are heavier and bulkier and thus less popular. A recent survey of the state-of-the-art in hemodialyzers is given in [13]. 

To illustrate the concentration polarization phenomenon, we consider an infinitely long electrodialysis cell pair having parallel channels in which the flow is fully developed and laminar. The qualitative behavior of the development of the salt concentration and potential distributions along the channels of a dialysate and concentrate cell pair are shown schematically in Fig. 6.2.3 for the case where the inlet salt concentrations are the same in both channels (Probstein 1972). 

With the ion concentration so determined the current-voltage characteristic can be obtained by integrating the equation for the potential distribution. Again, as in the case of the electrolytic cell, some care must be exercised with respect to the boundary conditions. In particular, the total potential drop must equal that in the dialysate half-channel, plus that in the concentrate halfchannel, plus the Donnan potential drop across the membrane. The Donnan potential drop arises from the discontinuities in concentration at the boundaries of the membranes (in this case, the cation exchange membrane for the half-cell as considered). The origin and expression for the Donnan potential are the same as for the electrode concentration overpotential. For the cation exchange membrane the Donnan potential drop is... 

Lee, K.S. and Tsien, R.W. (1983) Mechanism of calcium channel blockade by verapamil, D600, diltiazem and nitrendipine in single dialysed heart cells. Nature, 302 790-794. 

Another approach involved the use of a carbonate membrane bonded to SU8 channels with a glass layer used to seal the device [29]. The system used a stacked approach with a dialysis membrane sandwiched between an SU8 perfusion channel and a poly(dimethylsiloxane) flow channel (Figure 48.4). Bonding the membrane reduced the chance of leakage and resulted in a more robust device. A fluorescent dye and glucose solution were used for optical characterization of the system. A eommercially available glucose sensor was used to determine the concentration of glucose in the dialysate. A recovery of 80% was obtained at flow rate of 1.5 tiL/min. 

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