Permeation velocity

If the pressure drop across a tubular membrane is 2.8 bars, determine the permeat velocity across the membrane module. The thickness and the porosity of the deposit are 2 mm and 40 %, respectively. The average diameter of the partices is 5 microns. The initial membrane resistance is estimated to be 1.7 X 10 1/m. 

Yabannavar et al. [81] proposed a proportionality relationship valid for spin-filters based on an analogy to Eq. (15). They defined the Reynolds number based on the tangential velocity at the screen surface. Since in spin-filters the permeation velocity, or perfusion flux, is given by Eq. (16), and it can be assumed that the screen porosity e will be maintained constant throughout the scale-up process, it is possible to write a proportionaHty relationship for the ratio from drag to lift force in spin-filters as given by Eq. (17). 

Diffusion coefficient 10-9-10 lom2/s Membrane thickness (100-1000) xl0 6m Permeation velocity 10-4-10 6m/s... 

Ceramic membrane is the nanoporous membrane which has the comparatively higher permeability and lower separation fector. And in the case of mixed gases, separation mechanism is mainly concerned with the permeate velocity. The velocity properties of gas flow in nanoporous membranes depend on the ratio of the number of molecule-molecule collisions to that of the molecule-wall collision. The Knudsen number Kn Xydp is characteristic parameter defining different permeate mechanisms. The value of the mean free path depends on the length of the gas molecule and the characteristic pore diameter. The diffusion of inert and adsorbable gases through porous membrane is concerned with the contributions of gas phase diffusion and sur u e diffusion. 

Jg permeation velocity of solute through membrane, cm/s Jv = volume flux through membrane, cm /cm -s fe = mass transfer coefficient, cm/s... 

The similarity transformation, Eq. (20), tised here Is generally applied to obtain small time solution. However, In the case of gel polarized ultraflltratlon, Trettln and Doshl (1980 b) have used such similarity transformation to obtain an expression for the limiting permeate velocity. We have, therefore, tised similarity transformation to evaluate osmotic pressure limited permeate velocity. In the case of gel polarized ultraflltratlon. 

The dimensionless permeate velocity will be proportional to T when... 

The encapsulation of drug molecules also leads to delivery systems, especially in the case of hydrophilic compounds where a permeation barrier with depot effect is provided. The permeation velocity is controlled by the properties of the membranes, as well as by the lipophilicity and size of the incorporated drug. Even large molecules are released slowly in the body, but unfortunately this also occurs under storage conditions. As liposomes do not have a solid surface, an equilibrium is built up between incorporated or adhered drug and free drug molecules, and this can lead to bursf effects when liposome dispersions are diluted. 

Volume, m, L, or ft also, volume of filtrate collected to time t Volume flux (superficial permeate velocity) in ultrafiltration, m/s or ft/s maximum value... 

Consider first a clean membrane processing solutions with significant osmotic pressure. The solvent is assumed to pass by laminar flow through the small pores of the permselective layer, and the driving force is the applied pressure differential minus the difference of osmotic pressure across the membrane. The volume flux, v, which is the superficial permeate velocity normal to the membrane surface, can be written for a clean membrane as... 

Permeation velocity of solution through membrane Mean mobility, Eq. (5.1.10c)... 

Combining the preceding two equations and using the fact that the osmotic pressure is proportional to the solute concentration, we can show that the permeation velocity of the solution through the membrane = jlp may be written (Gill et al. 1971)... 

Because of the transverse velocity component, the velocity profile is a modification of the usual Poiseuille distribution. This problem has been solved by Berman (1953), including the effect of a constant permeation velocity in altering the velocity profile in the x direction and in causing a streamwise variation in the bulk average velocity. However, when the Reynolds number based on the permeation velocity is small, as it generally is, the streamwise component has the same form as for an impermeable wall and the transverse component is proportional to the constant permeation velocity v -, that is,... 

The boundary condition at the membrane wall derives from conservation of solute flux applied across the membrane. Stated in words At steady state the bulk flow of solute toward the membrane minus the diffusional flux of the solute away from the membrane toward the bulk of the fluid must equal the solute permeation through the membrane. Mathematically, taking into account that the y coordinate is in the direction of the concentration gradient and opposite to the permeation velocity,... 

In writing the above boundary condition, we have allowed for the possibility of a rejection coefficient less than unity, although is supposed constant. With a constant permeation velocity the problem is a linear one. However, were to depend on the concentration at the membrane, as characterized by, say, Eq. (4.4.4), a nonlinearity would be introduced through the boundary condition. Let us assume that is not only constant but equal to 1, in which case the boundary condition becomes... 

Equation (4.4.9b) may be compared with the boundary condition for a mixed heterogeneous reaction k c] = D dcldy),. It is evident that Rj = 1 corresponds to a first-order reaction, whereas if R c , there is a correspondence as well for reactions other than first order. For simplicity, let us consider the perfectly rejecting case of R = 1. Here, the appropriate dimensionless parameter characterizing the boundary condition is the ratio of the permeation velocity to the diffusion velocity... 

While this critical flux phenomena is generally accepted in MF and UF, some authors also mention limiting fluxes in NF (Levenstein et al. (1996)). Cohen and Probstein (1986) determined a characteristic permeation velocity below which no fouling was observed in the RO of colloids. Bacchin et al. (1995) defined a critical flux for the MF, UF, and RO of large colloids. The critical flux Jcot is a function of diffusion and the potential barrier between particles Vb as shown in equation (3.36), where 5 is the boundary layer thickness and D the particle diffusivity. 

Given that neither a pore blocking mechanism nor a reduced cake thickness due to aggregate back-transport can account for the obsen ed differences in flux for cakes formed from rapidly-formed compared to slowly-formed aggregates, we must conclude that the differences in permeation velocity arise from differences in permeability of the cakes formed under the different aggregation regimes. The order of magnitude difference in specific resistances of cakes developed at 20 mM and 100 mM KCl concentrations (approx. 1 10 tti.g versus approx. 0.1 10 respectively) supports the... 

The permeation velocity, V, and the permeate concentration, Cp, can be calculated as follows ... 

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