Steady-state membrane, pseudo

In PAMPA measurements each well is usually a one-point-in-time (single-timepoint) sample. By contrast, in the conventional multitimepoint Caco-2 assay, the acceptor solution is frequently replaced with fresh buffer solution so that the solution in contact with the membrane contains no more than a few percent of the total sample concentration at any time. This condition can be called a physically maintained sink. Under pseudo-steady state (when a practically linear solute concentration gradient is established in the membrane phase see Chapter 2), lipophilic molecules will distribute into the cell monolayer in accordance with the effective membrane-buffer partition coefficient, even when the acceptor solution contains nearly zero sample concentration (due to the physical sink). If the physical sink is maintained indefinitely, then eventually, all of the sample will be depleted from both the donor and membrane compartments, as the flux approaches zero (Chapter 2). In conventional Caco-2 data analysis, a very simple equation [Eq. (7.10) or (7.11)] is used to calculate the permeability coefficient. But when combinatorial (i.e., lipophilic) compounds are screened, this equation is often invalid, since a considerable portion of the molecules partitions into the membrane phase during the multitimepoint measurements. 

Assuming perfect mixing in each compartment of the membrane pack and reservoir of the ED unit shown in Figure 9, the solute concentration in any of them is uniform and equal to that of the outlet stream. Therefore, by assuming pseudo-steady state conditions in any compartment, the differential solute and water mass balances in the diluted (D) and concentrated (C) reservoirs can be written as follows ... 

A major breakthrough in the study of gas and v or transport in polymer membranes was achieved by Daynes in 1920 He pointed out that steady-state permeability measurements could only lead to the determination of the product EMcd and not their separate values. He showed that, under boundary conditions which were easy to achieve experimentally, D is related to the time retired to achieve steady state permeation throu an initially degassed membrane. The so-called diffusion time lag , 6, is obtained by back-extrapolation to the time axis of the pseudo-steady-state portion of the pressure buildup in a low pressure downstream receiving vdume for a transient permeation experiment. As shown in Eq. (6), the time lag is quantitatively related to the diffusion coefficient and the membrane thickness, , for the simple case where both ko and D are constants. 

Dutta et al. [32] modified the pseudo-steady-state advancing reaction front model of Stroeve and Varanasi [30] by considering the polydispersity of the emulsion globules and the external phase mass transfer resistance. They also included the outer membrane film resistance in their model [5]. Their results were in good agreement with experimental data for phenol extraction. 

Assuming a homogeneous fluid phase and a pseudo steady-state membrane (a linear but changing concentration gradient), we can write a material balance of species i for the fluid phase,... 

There is an 11.3% difference between the areas of these two curves (based on the theoretical area). This results from a flaw in the assumption of the pseudo steady-state membrane. For this to be true, the gas flux at the fluid interface must always equal the flux on the vacuum side of the membrane. The integration of the flux at the interface gives the initial amount contained in the fluid. A similar integration at the mem-... 

Now the analyses make sense. The steady-state analysis agrees with the transient analysis. However, let us consider all of this one more time. In what manner did the analysis show us we should move if we wish to get the ultimate removal of B from the feed stream with the areas, feed flow, and permeances all fixed The answer is obvious. The pseudo-steady-state analysis showed us that if we could somehow reduce the concentration of B on the permeate side to near zero values, then we could remove nearly 50% of it versus only 33% with these conditions. How could we do this How about raising the sweep flow rate on permeate side This will have the effect of keeping the concentration of B very low and increasing the driving force for B across the membrane. How much higher would the sweep flow have to be to accomplish this The answer is in what follows on the order of a factor of 10 increase will do it ... 

We assume that no reaction is taking place inside of the membrane and also assume a pseudo-steady-state for the membrane. Furthermore, we assume constant sugar diffusivity through the membrane. Based on these assumptions, the sugar material balance inside the membrane becomes... 

Consider a control volume (CV) extending from the membrane surface to a distance z into the feed liquid, where z < Si, the thickness over which the concentration changes (Figure 6.3.26(a)). Assume a pseudo steady state. Then a solute balance over the CV leads to the following ... 

The above analysis/description of solvent flux and macrosolute rejection/retention/ttansmission far an ultra-flllration membreme was carried out in the context of a pseudo steady state analysis in a batch cell (Figure 6.3.26 (a)). Back diffusion of the macrosolute from the feed solution-membrane interface to the bulk solution takes place by simple difflision against the small bulk flow parallel to the force direction. The resulting mass-transfer coefficients for macrosolutes will be quite small the solvent flux levels achievable will be quite low. For practically useful ultrafiltration rates, the mass-transfer coefficient is increased via different flow configurations with respect to the force. 

The membrane permeability is determined using a pseudo-steady state analysis based on Pick s law, equilibrium partitioning to the membrane surface, and the observed concentration difference across the membrane. The instantaneous flux,7, through the matrix or membrane (in a diffusion cell apparatus) is then given by... 

The ID pseudo-homogeneous model is the most used model to describe packed bed membrane reactors, especially for laboratory-scale applications. In its simplest form, namely the plug flow steady state model, the model describes only axial profiles of radially averaged temperatures and concentrations. 

---