Across a membrane

Facilitated transport membranes can be used to separate gases membrane transport is then driven by a difference in the gas partial pressure across the membrane. Metal ions can also be selectively transported across a membrane driven by a flow of hydrogen or hydroxyl ions in the other direction. This process is sometimes called coupled transport. 

Fig. 44. Schematic examples of facUitated transport of gases and metal ions. The gas-transport example shows the transport of oxygen across a membrane using hemoglobin (HEM) as the carrier agent. The ion-transport example shows the transport of copper ions across the membrane using a Uquid...

The individual membrane filtration processes are defined chiefly by pore size although there is some overlap. The smallest membrane pore size is used in reverse osmosis (0.0005—0.002 microns), followed by nanofiltration (0.001—0.01 microns), ultrafHtration (0.002—0.1 microns), and microfiltration (0.1—1.0 microns). Electro dialysis uses electric current to transport ionic species across a membrane. Micro- and ultrafHtration rely on pore size for material separation, reverse osmosis on pore size and diffusion, and electro dialysis on diffusion. Separation efficiency does not reach 100% for any of these membrane processes. For example, when used to desalinate—soften water for industrial processes, the concentrated salt stream (reject) from reverse osmosis can be 20% of the total flow. These concentrated, yet stiH dilute streams, may require additional treatment or special disposal methods. 

Various types of detector tubes have been devised. The NIOSH standard number S-311 employs a tube filled with 420—840 p.m (20/40 mesh) activated charcoal. A known volume of air is passed through the tube by either a handheld or vacuum pump. Carbon disulfide is used as the desorbing solvent and the solution is then analyzed by gc using a flame-ionization detector (88). Other adsorbents such as siUca gel and desorbents such as acetone have been employed. Passive (diffuse samplers) have also been developed. Passive samplers are useful for determining the time-weighted average (TWA) concentration of benzene vapor (89). Passive dosimeters allow permeation or diffusion-controlled mass transport across a membrane or adsorbent bed, ie, activated charcoal. The activated charcoal is removed, extracted with solvent, and analyzed by gc. Passive dosimeters with instant readout capabiUty have also been devised (85). 

Salt flux across a membrane is due to effects coupled to water transport, usually negligible, and diffusion across the membrane. Eq. (22-60) describes the basic diffusion equation for solute passage. It is independent of pressure, so as AP — AH 0, rejection 0. This important factor is due to the kinetic nature of the separation. Salt passage through the membrane is concentration dependent. Water passage is dependent on P — H. Therefore, when the membrane is operating near the osmotic pressure of the feed, the salt passage is not diluted by much permeate water. 

Driving Force Gas moves across a membrane in response to a difference in chemical potential. Partial pressure is sufficiently proportional to be used as the variable for design calculations for most gases of interest, but fugacity must be used for CO9 and usually for Hg... 

The clean water flux across a membrane without any material being deposited follows Darcy s Law ... 

The net pressure differential across a membrane, taking into consideration the osmotic pressure is given by (AP - AH), and hence, the expression for the permeate flux is ... 

Just how fast can proteins move in a biological membrane Many membrane proteins can move laterally across a membrane at a rate of a few microns per minute. On the other hand, some integral membrane proteins are much more restricted in their lateral movement, with diffusion rates of about 10 nm/sec or even slower. These latter proteins are often found to be anchored to the cytoskeleton (Chapter 17), a complex latticelike structure that maintains the cell s shape and assists in the controlled movement of various substances through the ceil. 

Proteins that can flip phospholipids from one side of a bilayer to the other have also been identified in several tissues (Figure 9.11). Called flippases, these proteins reduce the half-time for phospholipid movement across a membrane from 10 days or more to a few minutes or less. Some of these systems may operate passively, with no required input of energy, but passive transport alone cannot establish or maintain asymmetric transverse lipid distributions. However, rapid phospholipid movement from one monolayer to the other occurs in an ATP-dependent manner in erythrocytes. Energy-dependent lipid flippase activity may be responsible for the creation and maintenance of transverse lipid asymmetries. 

For a charged species, the situation is slightly more complicated. In this case, the movement of a molecule across a membrane depends on its electrochemical potential. This is given by... 

FIGURE 10.1 Passive diffusion of an uncharged species across a membrane depends only on the concentrations (Q and Cg) on the two sides of the membrane. 

FIGURE 10.2 The passive diffusion of a charged species across a membrane depends upon the concentration and also on the charge of the particle, Z, and the electrical potential difference across the membrane, Ai/<. 

Potentiometry (discussed in Chapter 5), which is of great practical importance, is a static (zero current) technique in which the information about the sample composition is obtained from measurement of the potential established across a membrane. Different types of membrane materials, possessing different ion-recognition processes, have been developed to impart high selectivity. The resulting potentiometric probes have thus been widely used for several decades for direct monitoring of ionic species such as protons or calcium, fluoride, and potassium ions in complex samples. 

We can draw another inference from these models in regard to the flow of water through the membrane. When the concentration of the solute in the membrane increases abruptly with a small change in the lipophilicity, it is likely that the membrane would approach saturation, that is, the cavities among the membrane cells would be extensively occupied. Trauble has proposed that water and small solutes are carried across a membrane by occupying discontinuities or... 

Permeability is a kinetic property expressed by the permeability coefficient (centimeters per second), a number indicating the rate at which molecules pass from aqueous solution across a membrane to another solution on the other side. Permeability is a molecular property used to screen for more complex absorption processes (i.e. in vitro permeabihty is measured to estimate in vivo absorption). 

Until this point, the sample preparation techniques under discussion have relied upon differences in polarity to separate the analyte and the sample matrix in contrast, ultraflltration and on-line dialysis rely upon differences in molecular size between the analyte and matrix components to effect a separation. In ultrafiltration, a centrifugal force is applied across a membrane filter which has a molecular weight cut-off intended to isolate the analyte from larger matrix components. Furusawa incorporated an ultrafiltration step into his separation of sulfadimethoxine from chicken tissue extracts. Some cleanup of the sample extract may be necessary prior to ultrafiltration, or the ultrafiltration membranes can become clogged and ineffective. Also, one must ensure that the choice of membrane filter for ultrafiltration is appropriate in terms of both the molecular weight cut-off and compatibility with the extraction solvent used. 

The percutaneous absorption picture can be qualitatively clarified by considering Fig. 3, where the schematic skin cross section is placed side by side with a simple model for percutaneous absorption patterned after an electrical circuit. In the case of absorption across a membrane, the current or flux is in terms of matter or molecules rather than electrons, and the driving force is a concentration gradient (technically, a chemical potential gradient) rather than a voltage drop [38]. Each layer of a membrane acts as a diffusional resistor. The resistance of a layer is proportional to its thickness (h), inversely proportional to the diffusive mobility of a substance within it as reflected in a... 

Finally, a general expression describing the steady state flux across a membrane, dM/dt can be written as ... 

This equation teaches us that the total stead-state flux (total rate of permeation across a membrane in the steady state of permeation), dM/dt, is proportional to the involved area (A) and the concentration differential expressed across the membrane, AC. In an experiment, flux is the experimentally measured parameter while A and AC are fixed in value when setting up an experiment. The value of the permeability coefficient, Ptotai, is what is calculated upon completion of an experiment using Eq. (8). The permeability coefficient, besides having the specific attributes ascribed to it, is... 

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... 

Figure 3 shows a steady diffusion across a membrane. As in the previous case, the membrane separates two well-mixed dilute solutions, and the diffusion coefficient Dm is assumed constant. However, unlike the film, the membrane has different physicochemical characteristics than the solvent. As a result, the diffusing solute molecules may preferentially partition into the membrane or the solvent. As before, applying Fick s second law to diffusion across a membrane, we... 

Figure 3 Diffusion across a membrane. The solute molecules diffuse from the well-mixed higher concentration cY to the well-mixed lower concentration c2. Equilibrium is assumed at the interfaces of membrane and solutions. The concentrations on both sides of the membrane are kept constant. At steady state, the concentrations cm remain constant at all points in the membrane. The concentration profile inside the membrane is linear, and the flux is constant.

C. Steady Diffusion Across a Membrane with Aqueous Diffusion Layers... 

In the example above, the solutions are assumed to be well stirred and mixed the aqueous resistance is negligible, and the membrane is the only transport barrier. However, in any real case, the solutions on both sides of the membrane become less and less stirred as they approach the surface of the membrane. The aqueous diffusion resistance, therefore, very often needs to be considered. For example, for very highly permeable drugs, the resistance to absorption from the gastrointestinal tract is mainly aqueous diffusion. In the section, we give a general solution to steady diffusion across a membrane with aqueous diffusion resistance [5],... 

We have discussed steady diffusion across a membrane with or without aqueous diffusion resistance. If the membrane is extremely thick or if solute diffusion in the membrane is extremely slow, the membrane may behave as if it is almost... 

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