Membrane mass-transfer coefficient

The membrane mass-transfer coefficient kim is usually based on Knudsen flows and can be derived by ... 

As demonstrated by means of residue curve analysis, selective mass transfer through a membrane has a significant effect on the location of the singular points of a batch reactive separation process. The singular points are shifted, and thereby the topology of the residue curve maps can change dramatically. Depending on the structure of the matrix of effective membrane mass transfer coefficients, the attainable product compositions are shifted to a desired or to an undesired direction. 

Ki denotes overall mass-transfer coefficient (m/s) ki denotes liquid mass-transfer coefficient (m/s) kg denotes gas mass-transfer coefficient (m/s) feiji denotes membrane mass-transfer coefficient (m/s) H denotes Henry s constant... 

The mass-transfer efficiencies of various MHF contactors have been studied by many researchers. Dahuron and Cussler [AlChE 34(1), pp. 130-136 (1988)] developed a membrane mass-transfer coefficient model (k ) Yang and Cussler [AIChE /., 32(11), pp. 1910-1916 (1986)] developed a shell-side mass-transfer coefficient model (ks) for flow directed radially into the fibers and Prasad and Sirkar [AIChE /., 34(2), pp. 177-188 (1988)] developed a tube-side mass-transfer coefficient model (k,). Additional studies have been published by Prasad and Sirkar [ Membrane-Based Solvent Extraction, in Membrane Handbook, Ho and Sirkar, eds. (Chapman Hall, 1992)] by Reed, Semmens, and Cussler [ Membrane Contactors, Membrane Separations Technology Principle. and Applications, Noble and Stern, eds. (Elsevier, 1995)] by Qin and Cabral [MChE 43(8), pp. 1975-1988 (1997)] by Baudot, Floury, and Smorenburg [AIChE ]., 47(8), pp. 1780-1793 (2001)] by GonzSlez-Munoz et al. [/. Memhane Sci., 213(1-2), pp. 181-193 (2003) and J. Membrane Sci., 255(1-2), pp. 133-140 (2005)] by Saikia, Dutta, and Dass [/. Membrane Sci., 225(1-2), pp. 1-13 (2003)] by Bocquet et al. [AIChE... 

Fluid to membrane mass transfer coefficient in Equation 8.29 (m/s) Constants in Equations 8.18 through 8.21... 

A Effective membrane area C, Concentration of metal ion in bulk feed at time t Co Initial concentration of metal ion in bulk feed Membrane thickness Thickness of aqueous boundary layer Membrane diffusion coefficient Aqueous diffusion coefficient Aqueous feed film mass transfer coefficient Organic membrane phase mass transfer coefficient Overall mass transfer coefficient Distribution ratio Two-phase extraction constant Aqueous feed mass transfer coefficient Membrane mass transfer coefficient Aqueous strip mass transfer coefficient Length of the fiber Molecular weight of the complex Number of fibers Permeability coefficient (cm/s)... 

We can use Faxen s expression (3.1.112e) for GDr Ti,Tp) as long as (ri/fp) < 0.5. Further, Kt may be obtained from relation (3.3.88a). The membrane mass-transfer coefficient and the permeability coefficient in the case of hindered ditfiision and geometrical partitioning are defined as follows ... 

Example 3.4.5 Calculate the membrane mass-transfer coefficients and the permeability coefficients of two solutes, sodium sulfate and sucrose, through a microporous light denitrated cellulose membrane whose properties, along with those of the two solutes, are provided below (Lane and Higgle, 1959). The temperature is 20 °C, and dilute aqueous solutions are under consideration with essentially no convection through the membrane. For sodium sulfate M = 142 diffusion coefficient in water = 7.7 x 10 cm /s density />, = 2.698 g/cm. For sucrose Mj = 342 diffusion coefficient in water =... 

Here the membrane mass-transfer coefficient ki can be described by (3.4.95c,d). It is known that each of the local boundary layer transfer coefficients, ktfc and kidc, is a function of the distance from the liquid channel inlet z in the manner of (l/z)° . This z-dependence is influenced by the nature of the flow channel geometry. Consult Kessler and Klein (2001) to develop a better understanding of the important role of the boundary-layer transfer coefficients. 

For the membrane, we similarly calculate the membrane mass transfer coefficient kH2m, as... 

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