Membrane pressure gradients

Saracco G., Veldsink J.W., Versteeg G.F. and van Swaaij W.P.M., Catalytic combustion of propane in a membrane reactor with separate feed of reactants. I. Operation in absence of trans-membrane pressure gradients, Chem. Eng. Sci., 56 2005 (1995). 

The diffusing flux through different membranes can be adequately described by Tick s law (Equation [8.4]), indicating that gas transport through porous membranes is driven by a cross membrane pressure gradient. Based on the differences in partial pressures, gas diffusivities, molecular sizes and shapes, gases can be separated when they flow through a membrane. 

Osmotic Pressure Controlled Oral Tablets. Alza Corp. has developed a system that is dependent on osmotic pressure developed within a tablet. The core of the tablet is the water-soluble dmg encapsulated in a hydrophobic, semipermeable membrane. Water enters the tablet through the membrane and dissolves the dmg creating a greater osmotic pressure within the tablet. The dmg solution exits at a zero-order rate through a laser drilled hole in the membrane. Should the dmg itself be unable to provide sufficient osmotic pressure to create the necessary pressure gradient, other water-soluble salts or a layer of polymer can be added to the dmg layer. The polymer swells and pushes the dmg solution through the orifice in what is known as a push-pull system (Fig. 3). The exhausted dmg unit then passes out of the body in fecal matter. 

When pure water is forced through a porous ultrafiltration membrane, Darcy s law states that the flow rate is direcdy proportional to the pressure gradient ... 

The simplest osmotic dosage form, ALZA Corporation s OROS elementary osmotic pump (Fig. 7), combines the dmg and sometimes an osmotic agent in a monolithic core and deflvers the dmg in solution (102). The mass dehvery rate with time dm df) of the dmg solution is described by equation 4, where is the hydrauHc permeabiUty of the membrane, a is the membrane reflection coefficient, Atz is the osmotic pressure gradient, APis the hydrostatic back pressure, A is the area of the membrane, C is the dissolved concentration of the dmg, and b is the membrane thickness. 

The simplifying assumptions that make Tick s law useful for other processes are not vaHd for pei vaporation. The activity gradient across the membrane is far more important than the pressure gradient. Equation (22-110) is generally used to describe the pei vaporation process ... 

In this case study, a zirconia-alumina membrane has been developed using the sol-gel technique with and without support.6-7 The porous ceramic was prepared to fabricate the membrane support. A thin film of aluminum and zirconium were formed on the porous ceramic support. Unsupported membrane was also prepared. The unsupported membrane was not strong enough to hold a high-pressure gradient it was very fragile and not useful... 

The following factors affect net diffusion of a substance (1) Its concentration gradient across the membrane. Solutes move from high to low concentration. (2) The electrical potential across the membrane. Solutes move toward the solution that has the opposite charge. The inside of the cell usually has a negative charge. (3) The permeability coefficient of the substance for the membrane. (4) The hydrostatic pressure gradient across the membrane. Increased pressure will increase the rate and force of the collision between the molecules and the membrane. (5) Temperature. Increased temperature will increase particle motion and thus increase the frequency of collisions between external particles and the membrane. In addition, a multitude of channels exist in membranes that route the entry of ions into cells. 

When Ap=0 (there is no pressure gradient in the system), LJtJl = 0 (diffusion of ions through the membrane can be neglected), and if the conductivities of the two membranes are identical, then in view of the second of Eqs (6.2.18) this condition can be expressed as... 

Membrane separation. Membranes, as discussed in Chapter 10, separate gases by means of a pressure gradient across a membrane, typically 40 bar or greater. Some... 

Possible driving forces for solute flux can be enumerated as a linear combination of gradient contributions [Eq. (20)] to solute potential across the membrane barrier (see Part I of this volume). These transbarrier gradients include chemical potential (concentration gradient-driven diffusion), hydrostatic potential (pressure gradient-driven convection), electrical potential (ion gradient-driven cotransport), osmotic potential (osmotic pressure-driven convection), and chemical potential modified by chemical or biochemical reaction. 

An external gas pressure gradient applied between anode and cathode sides of the fuel cell may be superimposed on the internal gradient in liquid pressure. This provides a means to control the water distribution in PEMs under fuel cell operation. This picture forms the basis for the hydraulic permeation model of membrane operation that has been proposed by Eikerling et al. This basic structural approach can be rationalized on the basis of the cluster network model. It can also be adapted to include the pertinent structural pictures of Gebel et and Schmidt-Rohr et al. ... 

The experimental data (dots) are reproduced very well within the framework of the hydraulic permeation model (solid lines). For the basic case with zero gas pressure gradient between cathode and anode sides, APe = 0, the model (solid line) predicts uniform water distribution and constant membrane resistance at )p < 1 A cm and a steep increase in R/R beyond this point. These trends are in excellent agreement with experimental data (open circles) for Nafion 112 in Figure 6.15. A finife positive gas pressure gradient, APs = P/ - P/ > 0, improves the internal humidification of fhe membrane, leading to more uniform water distribution and significantly reduced dependence of membrane resistance on X. The latter trends are consistent with the predictions of fhe hydraulic permeation model. 

The flux of liquids or gases through the membrane is in most cases driven by a pressure gradient and sometimes by an electric field gradient. Membranes can be used for ... 

For higher temperature operation, a polybenzimid-azole-based polymer electrolyte may be preferred. The PEMFC structures have good mechanical integrity under compression and expansion from differential temperature and pressure gradients that occur during operation. This system has minimal materials problems, except for the cost and operation characteristics of the membrane. The PEMFC operates at 1 A/cm at 0.7 V. The electrode reactions in acidic media have been discussed above. 

The mechanical properties of Nafion materials have not been of the most critical importance, as in the case of commercial thermoplastics or composite materials that are expected to be load-bearing. Rather, the primary focus has been on transport properties. To be sure, the mechanical integrity of membranes as mounted in cells, and under the perturbation of pressure gradients, swelling-dehydration cycles, mechanical creep, extreme temperatures, and the onset of brittleness and tear resistance, is important and must be taken into consideration. 

The driving force for solvent permeation is the total pressure gradient across the membrane, which is related to the chemical potential gradient, according to... 

The addition of a second phase means that there is also an additional degree of freedom. This results in the ability of the membrane system to sustain a pressure gradient in the water because of a possibly unknown stress relation between the membrane and fluid at every point in the membrane. However, diffusion of water becomes meaningless, since the water is assumed to be pure in the models discussed here. Furthermore, unlike the cases of the models discussed above, the water content of the membrane is assumed to remain constant (A = 22) as long as the pores are filled and the membrane has been pretreated appropriately. For cases where the pores do not remain filled, see sections 4.2.4 and 4.2.5. 

On the other hand, when the membrane is saturated, transport still occurs. This transport must be due to a hydraulic-pressure gradient because oversaturated activities are nonphysical. In addition, Buechi and Scherer found that only a hydraulic model can explain the experimentally observed sharp drying front in the membrane. Overall, both types of macroscopic models describe part of the transport that is occurring, but the correct model is some kind of superposition between them. - The two types of models are seen as operating fully at the limits of water concentration and must somehow be averaged between those limits. As mentioned, the hydraulic-diffusive models try to do this, but from a nonphysical and inconsistent standpoint that ignores Schroeder s paradox and its effects on the transport properties. 

Extractant leakage from the pores of the polymeric membrane in SLM is due to osmotic flow of massive quantities of water through the membrane. Membrane stability decreases with increasing osmotic pressure gradient and depends upon composition of the SLM system. A high tendency to solubilize water, low extractant/aqueous interfacial tension, and high wettability of polymeric membrane leads to less stable SLMs. The following measures have been proposed for improvement of stability ... 

Although the driving potential in MF is the hydraulic pressure gradient, MF flux is often also affected by the fluid velocity along the membrane surface. 

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