L Membrane thickness

K dimensionless equilibrium constant Keq equilibrium constant L - membrane thickness M - molarity, gmol/1... 

L = membrane thickness L = disk diameter CO = rotation rate (radians/sec)... 

Local flow rate inside the membrane separator G General driving force property H Henry s constant K Equilibrium distribution coefficient k Mass transfer coefficient L Membrane thickness M Molecular weight M Factor defined by Equation 18.26 N Flux P Total pressure Pm Permeability p Partial pressure Pm Permeance... 

TTie membrane interface coupled to an ICP is shown schematically in Fig. S.l. Two separators have been studied with membrane thicknesses of 12 and IS pm respectively. TTie interface with the thicker membranes used a Meinhard TR-20-C2 nebulizer rather than the more common TR-20-B2, because it is cheaper and better suited for this application (less cavitation). TTie outlets of the separators were at room temperature (20°C). 

Five membranes (thickness, 40 /am) were stacked and the concentration of ligand and cation in each membrane was measured before and immediately after the transport experiment as well as 5 days after restacking the membranes. Since a concentration gradient of valinomycin developed (Fig. 11, f = 3hr), which decayed almost completely after a relaxation period (Fig. 11, l = 5 days), the a-phenylethylammonium cation had obviously been transported by a carrier mechanism. During the transport process a cation profile built up (Fig. 12, t = 3 hr) that had the same trend as the ligand profile. This cation gradient disappeared after some time (Fig. 12, t = 5 days). 

Remove the gel from the electrophoresis apparatus, and remove any stacking gel that may be present. Measure the size of the gel, and transfer it to a container for incubation with transfer buffer for 15 mm. This incubation is to equilibrate the gel in the new buffer and to reduce the level of SDS, since this reduces the binding of protein to the membrane Gels >l-mm thick will require a 30-min incubation in transfer buffer for this equilibration to take place... 

Fig. 17 General scheme of an IWAO design, where the input and output ARROW waveguides and the active membrane and the optical fibers are indicated. Notice that the analyte diffusion direction is transverse to the light transmission direction. L membrane length and optical path length, d membrane thickness...

Fig. 20 a Conventional configuration, where the optical path length is related to the membrane thickness by L = 2d. b IWAO, where the optical path length (L) is independent of the membrane thickness (d)... 

The product I), K) is normally referred to as the permeability coefficient, P L. For many systems, A, Kf, and thus P-L are concentration dependent. Thus, Equation (2.28) implies the use of values for Dt, K, and P L that are averaged over the membrane thickness. 

For a given driving force, minimization of the membrane resistance requires the smallest possible effective membrane thickness, l. The ability to minimize l without introducing defects relies upon micromorphology control, and this topic impacts virtually all membrane applications. 

An important example of the system with an ideally permeable external interface is the diffusion of an electroactive species across the boundary layer in solution near the solid electrode surface, described within the framework of the Nernst diffusion layer model. Mathematically, an equivalent problem appears for the diffusion of a solute electroactive species to the electrode surface across a passive membrane layer. The non-stationary distribution of this species inside the layer corresponds to a finite - diffusion problem. Its solution for the film with an ideally permeable external boundary and with the concentration modulation at the electrode film contact in the course of the passage of an alternating current results in one of two expressions for finite-Warburg impedance for the contribution of the layer Ziayer = H(0) tanh(icard)1/2/(iwrd)1/2 containing the characteristic - diffusion time, Td = L2/D (L, layer thickness, D, - diffusion coefficient), and the low-frequency resistance of the layer, R(0) = dE/dl, this derivative corresponding to -> direct current conditions. 

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