Beta concentration polarization

Beta, sometimes called the "concentration polarization factor," is the ratio of the concentration of a species at the membrane surface to that in the bulk solution. Hence, Beta is a way of quantifying concentration polarization. 

Beta affects both the flux through an RO membrane and the salt rejection. The increase in Beta due to concentration polarization at the membrane surface results in increased osmotic pressure and decrease is water flux, as shown in Equation 9.1 (modified Equation 4.1). Salt passage also increases, as shown in Equation 9.2 (modified Equation 4.2). 

Figures 9.8 and 9.9 shows how Beta affects flux and salt passage (rejection), respectively, for two different brackish water concentrations (assumes membrane will deliver 20 gfd at 400 psi with a rejection of 99% at Beta equal to one (no concentration polarization)).8 From the Figures, it is shown that at Beta values greater than about 1.1, the water flux and salt passage (rejection) are significantly affected by Beta. Also shown is that the effect of Beta on performance is more pronounced at higher TDS feed water than with lower TDS feed water.

In reality, Beta for RO systems is greater than 1.0, and hence, concentration polarization always exists. While concentration polarization cannot be eliminated, it can be minimized by judicial RO system design ... 

Adherence to recommended concentrate flow rates and membrane module recovery can also minimize Beta and the effects of concentration polarization. 

Concentration polarization as reflected by the limiting diffusion current is observed for protein-free solutions at U s slightly negative to the corrosion potential, and at potentials lower than about —0.5 V for both protein-free and protein-containing solutions. The activation polarization region with a Tafel slope of beta = 0.22 V is higher by almost a factor of 2 from the beta = 0.12... 

Beta is not a property of the membrane it is an artifact of the system design that is selected. Specifically, Beta is a function of how quickly the influent stream is dewatered through the RO system. If water is removed too quickly from the influent stream. Beta will increase, as a relatively high volume of dissolved soHds is left behind on the membrane because of the high volume of water that permeates out through the membrane. Concentration polarization further exacerbates the problem because of the diffusional-only flow away from the membrane surface. See Chapter 9.6 for more information about Beta and its relationship with water flux and salt passage. 

Based on the dielectric and dynamic mechanical data, it appears that water and small polar molecules contribute to three dispersions in this poly(amide-imide). One is the low temperature relaxation between -100 and 0°C. This may be a hydrogen bonded relaxation since the activation enthalpy was 30 kJ/mol. This occurs at concentrations of water ranging between 0 to 4 weight percent. Two, the dielectric relaxation between 0 and 70 C can probably be attributed to conductive contaminants whose mobility is dependent upon a minimum amount of water. Three, at high water concentrations, greater than 2 weight percent, the water/NMP contributes to the beta relaxations observed between 50 and 150 C. 

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