Mass transfer coefficients membranes, structure

The value of the concentration modulus depends on the convective velocity and the mass-transfer coefficient of the concentration boundary layer (D/ i) that means that on the membrane structure and the hydrodynamic conditions. If the retention coefficient is equal to 1, then c /ch = exp(Pe). The larger convective velocity (or smaller diffusion coefficient) causes higher concentration polarization on the membrane interface. 

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. 

Pilot plant smdied have also been performed by Larsen et al. [37], who obtained stable operation and more than 95% SO2 removal from flue gas streams with a gas-side pressure drop of less than 1000 Pa. The importance of the membrane structure on the SO2 removal has been studied by Iversen et al. [6], who calculated the influence of the membrane resistance on the estimated membrane area required for 95% SO2 removal from a coal-fired power plant. Authors performed experiments on different hydrophobic membranes with sodium sulfite as absorbent to measure the SO2 flux and the overall mass-transfer coefficient. The gas mixture contained 1000 ppm of SO2 in N2. For the same thickness, porosity, and pore size, membranes with a structure similar to random spheres (typical of stretched membranes) showed a better performance than those with a closely packed spheres stmcture. 

Table 2.6 Relationships between structure features and mass transfer coefficient estimated for commercial polymeric membranes...

In the AL-DS orientation, arsenite rejection by the folded membrane remained approximately equal to that by the clean membrane. When the support layer is facing the feed solution, membrane fouling can cause two opposite effects on the rejection of inorganic contaminants by FO membrane. On the one hand, foulant entrapment inside the porous support layer will likely reduce porosity of support layer, resulting in a greater structural parameter and thus a reduced mass transfer coefficient. Consequently, alginate fouling inside the membrane support layer can decrease the... 

The lattice model of mass transfer gives self-consistent expressions for sorption isotherms and permeability coefficients for microheterogeneous membranes of variable thickness at an arbitrary degree of filling. The parameters of the lattice model can be related to the molecular structure of a matrix and to the parameters of the interaction between diffusant and matrix [191]. The lattice model can serve as a basis to construct phenomenological models, which are capable of describing the features of a molecular system diffusant-membrane matrix . 

Retention of ionic species modifies ionic concentrations in the feed and permeate liquids in such a way that osmotic pressure or electroosmotic phenomena cannot be neglected in mass transfer mechanisms. The reflection coefficient, o, in Equations 9.4 and 9.5 represents, respectively, the part of osmotic pressure force in the solvent flux and the diffusive part in solute transport through the membrane. One can see that when o is close or equal to zero, the convective flux in the pores is dominant and mostly participates to solute transport in the membrane. On the contrary, when o is close or equal to 1, mainly diffusion phenomena are involved in species transport through the membrane, which means that the transmembrane pressure is exerted across an almost dense structure. Low UF and NF ceramic membranes stand in the former case due to their relatively high porous volume and pore sizes in the nanometer range. Relevant results have been published concerning the use of a computer simulation program able to predict solute retention and flux for ceramic and polymer NF membranes [28]. 

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