Hydrodynamic permeability

Following Cohen Stuart (10) we choose a semi-empirical continuous function to relate the hydrodynamic permeability, k, to the volume fraction... 

Deviation of parameter a from 0.5 in this equation may be caused by volumetric effects in good sol-vents or partial hydrodynamic permeability of the coil, promoted by skeletal rigidity of macromo-lecules. Selection of a model for quantitative estimation of rigidity by these properties is usually complicated by the absence of reliable criterion, especially in the cases, when the value of parame-ter a falls within the range of 0.5 - 0.8. That is why to describe behavior of macromolecules in tolu-ene, the authors [56] have used the model of perturbed Gaussian non-permeable coil and the model of worm-like backbone. 

The parameters of the rotatory and translational diffusion of the macromolecule as a whole and those of intramolecular large-scale motions depend on the size and shape of the macromolecule, on its hydrodynamic permeability and on the possible solvation of the solvent. (It is known that the latter factor should be taken into account in the study of compact protein globules in water.)... 

Because ion exchange membranes have a tight structure, hydrodynamic permeability is rather low. An electrical potential is thus generated across the... 

Hydrodynamic permeability, I, is defined by permeated water across the ion exchange membrane per unit time and unit membrane area (volume transfer per unit time and unit membrane area across the membrane, V) in the presence of an hydraulic pressure difference, AP,... 

When both sides of the membrane are short-circuited, the hydrodynamic permeability, ZV, is as follows, from Eq. (2.87),... 

Then, hydrodynamic permeability in the absence of an electrical potential gradient is... 

Alternatively the hydrodynamic permeability (Lv) can be used to describe water throughput. This parameter is very useful when different processes or transmembrane pressures are to be compared, as it is normalised by the transmembrane pressure AP. 

The Irreversible Thermodynamics Model (Kedem and Katchalsky (1958)) is founded on coupled transport between solute and solvent and between the different driving forces. The entropy of the system increases and free energy is dissipated, where the free energy dissipation function may be written as a sum of solute and solvent fluxes multiplied by drivir forces. Lv is the hydrodynamic permeability of the membrane, AII v the osmotic pressure difference between membrane wall and permeate, Ls the solute permeability and cms the average solute concentration across the membrane. 

Experimental set-up used for the measurement of hydrodynamic permeability, thermo-osmotic permeability and thermo-osmotic pressure difference is shown in Eig. 3.3. The membrane was fixed with araldite between two ground-glass joints. Thermocouples were inserted through the adjoining tubes so that the junctions touched the membrane. 

Figure 3.3. Cell for the measurement of hydrodynamic permeability, thermo-osmotic permeabihty and thermo-osmotic pressure, L, capillary tube, H, constant pressure head, K, thermo-couple, M, Membrane, T = temperature of one air-thermostat, T2 = temperature of second air thermostat...

Figure 3.5. Estimation of hydrodynamic permeability of water and methanol.

Studies on hydrodynamic permeability, thermo-osmotic permeability for DjO have also been carried out and heat of transport has been estimated. Similar measurements have been made for solutions of KCl in H2O and DjO using a copper ferrocyamide membrane. These results support the theory of non-equilibrium thermodynamics within a limited range of departure from equilibrium [28]. 

The water permeability coefficient A (also defined as the hydrodynamic permeability coefficient) is a constant for a given membrane and contains the following parameters (see also chapter V - 6.1). 

The flux (in m m s ) through a porous membrane per unit cross-sectional area A (= Ap Je), which is also called the hydrodynamic permeability of a membrane, is defined as ... 

The chargeability of sedimentaiy rocks was studied in early papers by Vacquier et al. (1957) and Marshall and Madden (1959). These and subsequent investigations are directed mostly on correlations between IP parameters and reservoir properties (clay content, hydrodynamic permeability). 

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