Membrane permeability regime

In these circumstances of membrane permeability limitations, shown as curves 1 and 2 in figure 7.11 at external substrate concentrations below 0.01 M, the response of the sensor will be completely independent of the enzyme prop>erties. A sensor operated in this regime would be independent of factors affecting enzyme behavior, such as denaturation, temperature, and pH. This is the preferred regime for operating an enzyme biosensor. 

Some other techniques involving membrane permeability have been developed that have not yet been extensively used. Concerning gas permeability, a method called permeametry has been developed [41], based on Adzumi equation. It consists of measuring the variation in membrane permeability when favoring either molecular (Knudsen) or laminar (Poiseuille) flow regime. A mean pore radius is obtained with this method. 

Experimental investigation were carried out on the spreading of small drops of aqueous SDS solutions (capillary regime of spreading) over dry nitrocellulose membranes (permeable in both normal and tangential directions) in the case of partial wetting. Nitrocellulose membranes were chosen because of their partial hydrophiUcity. The time evolution was monitored for the radii of both the drop base and the wetted area inside the porous substrate. 

This chapter will only deal with the possible gas transport mechanisms and their relevance for separation of gas mixtures. Beside the transport mechanisms, process parameters also have a marked influence on the separation efficiency. Effects like backdiffusion and concentration polarization are determined by the operating downstream and upstream pressure, the flow regime, etc. This can decrease the separation efficiency considerably. Since these effects are to some extent treated in literature (Hsieh, Bhave and Fleming 1988, Keizer et al. 1988), they will not be considered here, save for one example at the end of Section 6.2.1. It seemed more important to describe the possibilities of inorganic membranes for gas separation than to deal with optimization of the process. Therefore, this chapter will only describe the possibilities of the several transport mechanisms in inorganic membranes for selective gas separation with high permeability at variable temperature and pressure. 

Concentration polarization may be a possible explanation for this erratic permeability coefficient behavior however, the influence of concentration polarization in gaseous exchange regimes such as the one herein reported is quite doubtful and subject to dispute(7 ). Alternative possibilities include (a) permeator functional loss due to on-going membrane compaction,... 

Wu et al. (1993] have developed a mathematical model based on Knudsen diffusion and intermolecular momentum transfer. Their model applies the permeability values of single components (i.e., pure gases) to determine two parameters related to the morphology of the microporous membranes and the reflection behavior of the gas molecules. The parameters are then used in the model to predict the separation performance. The model predicts that the permeability of carbon monoxide deviates substantially from that based on Knudsen diffusion alone. Their model calculations are able to explain the low gas separation efficiency. Under the transport regimes considered in their study, the feed side pressure and pressure ratio (permeate to feed pressures) are found to exert stronger influences on the separation factor than other factors. A low feed side pressure and a tow pressure ratio provide a maximum separation efficiency. 

Experimental results of water vapor adsorption. Helium relative permeability, Pr, and water vapor permeability, Pe, for the two alumina pellets are presented in figures 6a and 6b, for water relative pressures up to unity. As the amount of water adsorbed starts to rapidly increase with P/Po, due to capillary condensation, a significant increase of its permeability may also be observed due to the resulting capillary enhancement of flow. At a certain value of P/Po where Vs is close to unity, all pores of the membrane are in the capillary condensation regime and thus follow the capillary enhanced type of flux. At this point water vapor permeability reaches its maximum value while, helium relative permeability decreases rapidly and falls to zero well below the point of saturation. This may be attributed, according to percolation theory, to the fact that in a simple cubic lattice, if -75% of the pores are blocked by capillary condensate, the system has reached its percolation threshold and helium... 

One method which is known under the name of permeametry [131] or Poiseuille-Knudsen method [124] is based on the law of gas permeability in a porous media in the two flow regimes molecular flow (Knudsen) and laminar or viscous flow (Poiseuille). According to Darcy s law, the gas flux through a membrane with a thickness / can be written as / = KAP/l, where K is the permeability coefficient and AP (AP = Pi - P2) the pressure difference across the membrane. If the membrane pore diameter is comparable to the mean free path of the permeating gas, K can be expressed as a stun of a viscous and a non-vis-cous term... 

Pulsate flows were applied to mineral microfiltrations membranes during apple juice filtration [36] illustrating the advantage of this method to enhance permeability compared to steady flow regime. With carefully chosen pulsations permeate flux increased up to 45% at 1 Hz pulsation frequency. Moreover well defined pulsations decreased the hydraulic power dissipated in the retentate per unit volume by up to 30%. In an other work on cross-flow filtration of plasma from blood [37] permeate flux increase was also observed when pressure and flow pulsations at 1 Hz are superimposed on the retentate. 

The membranes used to measure the osmotic pressure are impermeable to polyions but permeable to counter-ions. In spite of this, the osmotic pressure of polyelectrolytes in pure water and for rather small concentrations (but in the semi-dilute regime), is huge. Let us assume that the polyelectrolyte has been put in cell I (see Fig. 5.1). It partially ionizes but both cells must remain practically neutral. The counter-ions which, theoretically, can cross the membrane, are retained in cell I and a contact-potential difference appears at the boundary between the cells. Actually, it looks as if the counter-ions contributed like polyions to the osmotic pressure. Let C be the polyion concentration. We may write approximately... 

Two important conclusions can be made from analysis of Equations (5.16) and (5.17). First, selectivity of separation in Knudsen regime is characterized by the ratio ij = (Mj/Mi) . It means that membranes where Knudsen diffusion predominates are poorly selective. For example, separation factor of separation of O2/N2 pair is 1.07. The highest gas separation selectivity can be observed in separation of lightest and heaviest gases, e.g. hydrogen and butane in this case = 5.4. Another unusual feature of Knudsen diffusion is that increases in temperature result in slight decreases of the flux and permeability coefficient, as J and P depend on temperature as Numerous confirmation of this dependence can be found in the literature. 

---