Solute mass-transfer coefficient

In a great number of papers dealing with the design of ED stacks, and especially in the recent and comprehensive paper by Lee et al. (2002d), the solute mass transfer coefficient (km) is expressed as a nonlinear function of the superficial flow velocity (vs) ... 

EMPIRICAL CORRELATION FOR PREDICTING THE SOLUTE MASS TRANSFER COEFFICIENT (km) IN ED CELLS WITH EDDY PROMOTERS... 

Current-voltage tests to determine the limiting current intensity (/lim), ion transport numbers (ta, tc+), and surface resistances (ra, rc) in anionic and cationic membranes, as well as solute mass transfer coefficient (Am). 

The solute mass transfer coefficient (km) in ED stacks approximately varies with the square root of the liquid superficial velocity (vs) in agreement with the correlations reported in Table III, even if they can differ from those predicted within a 30% deviation band because of the different cell and spacer configuration used. 

The problem of transferring corrosion rate data from one hydrodynamic system to another has also been considered in some depth by Chen et al. [18], by using the corrosion of 90 10 Cu Ni alloy in aerated 1 m NaCl solution at 25 °C in pipe-flow, annular-flow, and rotating-cylinder systems. The authors recognized that two mass-transfer processes should be distinguished transfer through the diffusion boundary layer in e solution (mass-transfer coefficient, h), and transfer through the corrosion product film ( f). The overall mass-transfer coefficient was defined as... 

Figure 16a and b shows the effect of L on the radial dependence of the steady-state concentration and flux at the substrate/solution interface for a first-order dissolution process characterized by Ki = 10 and L = 0.1, 0.32, and 1.0. As the tip-substrate separation decreases, the effective rate of diffusion between the probe and the surface increases, forcing the crystal/so-lution interface to become more undersaturated. Conversely, as the UME is retracted from the substrate, the interfacial undersaturation approaches the saturated value, since the solution mass transfer coefficient decreases compared to the first-order dissolution rate constant. Movement of the tip electrode away from the substrate also has the effect of promoting radial diffusion, and consequently the area of the substrate probed by the UME increases. 

After integrating with the boundary conditions c = c v for x = 0 and c = Cb for x = 5 for similar solute and solvent densities, constant diffusion coefficient, and constant concentration along the membrane, equation (3.7) can be derived. The wall concentration which determines adsorption is cw, gel formation or precipitation, and ks the solute mass transfer coefficient as defined in equation (3.9),... 

The Fine Porous Model as presented by Xu and Spencer (1997), describes equilibrium and non-equilibrium factors of rejection. Only coupling between solvent and solute is taken into account, and no solute-solute coupling is permitted. Equilibrium parameters dominated separation, and these are described by the reflection coefficient (J in equation (3.28), where kii is the solute mass transfer coefficient in the membrane. 

The solute mass transfer coefficient is required to calculate the solute concentration at the membrane surface. This mass transfer coefficient is in theory independent of the membrane. Equation (7.6) describes the film model relationship between flux and concentration of solute at the membrane surface. 

Duranceau S.J., Taylor J.S. (1993), Solute charge and molecular weight modeling for prediction of solute mass transfer coefficients, Proc. of AWWA Membrane Technology Conf., Baltimore, Aug 93,243-249. 

Applying eq. (11) to the kj a values measured in the CMC/Na2S04 solution mass transfer coefficients kL ate obtained which represent mean values for the total interfacial area. Figure 6 reveals that kL becomes almost constant at high gas velocities at about 0.013 cm s . ... 

Dialysis and diffusion dialysis are membrane processes that consumes generally not much energy. The energy consumption Ep is determined by the pumps to circulate the feed and permeate (dialysate) stream along the membrane (eq. VIII - 87). If concentration polarisation becomes severe higher cross-flow velocities may be required to increase the solute mass transfer coefficient and consequently the energy consumption will increase. 

As we have seen in Section 6.3.3.3, the dead-end mode of operation of reverse osmosis creates major problems steady state is not possible it is difficult to generate a high value of the solute mass-transfer coefficient ku, further, as in Section 6.3.3.5 for gas permeation, it is often easier to pack a lot of membrane surface area when the bulk liquid flow is not parallel to the direction of the force. 

The solute mass-transfer coefficient ku in the membrane feed channel has a high value and can be considered to be essentially constant along the z-coordinate. 

In Section 4.3.1, we were introduced to a hemodialyzer with blood on one side of the membrane and the dialyzing solution on the other side. Solutes (metabolic waste products) from blood diffused through the liquid filled pores of the membrane to the dialysate side. Using a simple lumped analysis based on the overall solute mass-transfer coefficient Ku, we will develop an expression for the solute removal efficiency of a hemodialyzer in which blood as well as the dialyzing solution are in steady cocurrent flow (Section 8.1.7 treated countercurrent dia-lyzers). The analysis is valid for any other system, not just hemodialysis. 

Figure 8.2.6(a) illustrates the schematic of a cocurrent dialyzer with the feed solution (e.g. blood side) C(/o) entering at z = 0 and exiting at z = L, C(/i). The dialyzing solution Cim) is entering at z = 0 also and exiting at z = L, Cwl). The overall molar solute i balance relations for the whole dialyzer based on a device averaged overall solute mass-transfer coefficient Ktc are ... 

The apparent sieving coefficient depends on the permeate flux, the solute mass transfer coefficient, and a fundamental solute-membrane parameter called the intrinsic sieving coefficient ... 

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