Mechanical filtration coefficient

If we consider a membrane having the same solute concentration on both sides, we have All 0 However, a hydrostatic pressure difference AP exists between the two sides, and we have a flow Jv that is a linear function of AP. The term Lp is called the mechanical filtration coefficient, which represents the velocity of the fluid per unit pressure difference between the two sides of the membrane. The cross-phenomenological coefficient Ldp is called the ultrafiltration coefficient, which is related to the coupled diffusion induced by a mechanical pressure of the solute with respect to the solvent. Osmotic pressure difference produces a diffusion flow characterized by the permeability coefficient, which indicates the movement of the solute with respect to the solvent due to the inequality of concentrations on both sides of the membrane. 

LP is the hydraulic conductivity coefficient and can have units of m s-1 Pa-1. It describes the mechanical filtration capacity of a membrane or other barrier namely, when An is zero, LP relates the total volume flux density, Jv, to the hydrostatic pressure difference, AP. When AP is zero, Equation 3.37 indicates that a difference in osmotic pressure leads to a diffusional flow characterized by the coefficient Lo Membranes also generally exhibit a property called ultrafiltration, whereby they offer different resistances to the passage of the solute and water.14 For instance, in the absence of an osmotic pressure difference (An = 0), Equation 3.37 indicates a diffusional flux density equal to LopkP. Based on Equation 3.35, vs is then... 

Experiments showed that mechanical dispersion coefficients are directly proportionate with filtration (flow) average seepage velocity, i.e.,... 

Penetration of a substance is measured by the permeability coefficient, P, which could be converted to a measurable diffusional coefficient, D, if Pick s law applied strictly. In the more complex situation of a membrane barrier, Kedem and Katchalsky (1958, 1961) have shown that under rigidly controlled conditions there exist at least three parameters which must be considered when characterizing the behavior of a membrane toward a particular solute (1) the interaction between membrane and solvent (2) the interaction between solute and membrane and (3) the interaction between solute and solvent. The reflection coefficient, (T, measures relative rates of solute and solvent permeabilities in the system (Staverman, 1952) and is therefore a measure of semipermeability. Lp is the mechanical coefficient of filtration or pressure filtration coefficient, and co is the solute mobility or solute diffusional coefficient. In the case of living membranes, conditions such as volume flow, osmotic gradients, and cell volume can be manipulated in order to measure the phenomenological coefficients cr, o>, and Lp. Detailed discussions of the theories, methods, and problems involved in such... 

For the UF of proteins, the concentration polarization model has been found to predict the filtration performance reasonably well [56]. However, this model is inherently weak in describing the two-dimensional mass transport mechanism during crossflow filtration and does not take into account the solute-solute interactions on mass transport that occur extensively in colloids, especially during MF [21,44,158,159]. The diffusion coefficient, which is inversely proportional to the particle radius, is low and underestimates the movement of particles away from the membrane [56]. This results to the well-known flux paradox problem where the predicted permeate flux is as much as two orders of magnitude lower than the observed flux during MF of colloidal suspensions [56,58,158]. This problem has then been underlined by the experimental finding of a critical flux for colloids, which demonstrates the specificity of colloidal suspension filtration wherein just a small variation in physicochemical or hydrodynamic conditions induces important changes in the way the process has to be operated [21]. 

Although diastereoisomers, both quinine and quinidine, have similar physical properties (Fig. 18). In clinical studies, the renal clearance of quinidine was fourfold greater than that of quinine (57). No stereoselective differences in plasma protein binding were observed. The renal filtration and passive reabsorption of these two diastereoisomers should be similar since the compounds have similar octanol-water partition coefficients and pKa values (57). Therefore, stereoselective active renal secretion may be the mechanism responsible for the observed differences in the renal clearances of quinine and quinidine. 

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