Membranes semipermeable ideal

Membranes are semipermeable barriers that permit the separation of two compartments of different composition or even condition, with the transport of components from one compartment to another being controlled by the membrane barrier. Ideally, this barrier is designed to let pass selectively only certain target compounds, while retaining all others—hence the denotation semipermeable . Membrane separations are particularly suitable for food applications because (1) they do not require any extraction aids such as solvents, which avoids secondary contamination and, hence, the necessity for subsequent purification (2) transfer of components from one matrix to another is possible without direct contact and the risk of cross-contamination (3) membrane processes can, in general, be operated under smooth conditions and therefore maintaining in principle the properties and quality of delicate foodstuff. 

For example, the measurements of solution osmotic pressure made with membranes by Traube and Pfeffer were used by van t Hoff in 1887 to develop his limit law, which explains the behavior of ideal dilute solutions. This work led direcdy to the van t Hoff equation. At about the same time, the concept of a perfectly selective semipermeable membrane was used by MaxweU and others in developing the kinetic theory of gases. 

The nion term is simply an expression for the osmotic pressure generated across a semipermeable membrane effectively, the gel serves as a membrane which restricts the polyelectrolytes to one phase, while small ions can readily redistribute between phases. Assuming that the ions form an ideal solution, the expression for nion becomes simply... 

In vivo microdialysis is based on the principle of dialysis, the process whereby concentration gradients drive the movement of small molecules and water through a semipermeable membrane. In vivo microdialysis involves the insertion of a small semipermeable membrane into a specific region of a living animal, such as the brain. The assembly that contains this semipermeable membrane is called a probe, which is composed of an inlet and an outlet compartment surrounded by a semipermeable membrane (see O Figure 9-1). Using a microinfusion pump set at a low flow rate (0.2-3 /rL/min), an aqueous solution known as the perfusate is pumped into the inlet compartment of the microdialysis probe. Ideally, the... 

Becaus-e of the similarity in the relations for osmotic pressure in dilute solutions and the equation for an ideal gas, van t Hoff proposed his bombardment theory in which osmotic pressure is considered in terms of collisions of solute molecules oil the semipeniieable membrane. This theoiy has a number of objections and has now been discarded. Other theories have also been put forward involving solvent bombardment on the semipermeable membrane, and vapor pressure effects. For example, osmotic pressure has been considered as the negative pressure which must be applied to the solvent to reduce its vapor pressure to that of the solution. It is, however, more profitable to interpret osmotic pressures using thermodynamic relations, such as the entropy of dilution,... 

Solvent from a lower concentration solution will move spontaneously to a higher concentration solution across an ideal semipermeable membrane, permeable only to the solvent but impermeable to the solute. Although the solvent flows in both directions, the rate of flow from the dilute concentration (or pure solvent) is much faster than from the concentrated solution. This phenomenon is called osmosis. The flow of the solvent can be reduced by directly applying pressure to the higher concentration side of the membrane as shown in Figure 3.17. At a certain pressure, equilibrium is reached, causing the movement of water to cease. This pressure is called the osmotic pressure and is the sole property of the solution. 

The membrane selectivity toward an osmotic agent and water, described by the osmotic reflection coefficient a. An ideal semipermeable membrane has the a value of 1, which means that it allows the passage of only water molecules. In contrast, a leaky semipermeable membrane with a value approaching zero does not exhibit such selectivity and permits the transport of not only water, but also an osmotic agent. 

Osmosis is defined as the spontaneous transport of a solvent from a dilute solution to a concentrated solution across an ideal semipermeable membrane that impedes passage of the solute but allows the solvent to flow. Solvent flow can be reduced by exerting pressure on the solution side of the membrane. If the pressure is increased above the osmotic pressure on the solution side, the flow reverses. Pure solvent will then pass from the solution into the solvent. As applied to metal finishing wastewater, the solute is the metal and the solvent is pure water. 

The net work of 0.52 MW for the separation section assumes that we perform all separations mechanically, i.e., with compressors and semipermeable membranes. In reality we use evaporation, partial condensation, and distillation to separate the components. We can use Eq. (5.8) to estimate how much heat, from 75 psia steam, we must supply to an ideal separation device to provide the necessary separation work. Again, this is only a rough estimate of the required heat. 

R is the dimensionless parameter that varies from 100% for an ideal semipermeable membrane to 0% when the species and the solvent pass freely through the membrane... 

As described in the Introduction, the process of diffusion of a solvent through a semipermeable membrane from a less-concentrated solution into a more-concentrated solution is osmosis. This results in the development of a hydrostatic pressure head on the more-concentrated solution side of the membrane. Alternatively, pressure may be applied to the moreconcentrated solution side of the semipermeable membrane to prevent the diffusion of solvent. This applied pressure on the concentrated solution is identical to the hydrostatic pressure head that may develop owing to osmosis. It is known as the osmotic pressure and is directly proportional to the solute concentration in an ideal solution. A semipermeable membrane is one that allows the movement of only solvent molecules, and if the membrane is not semipermeable, osmosis may not be observed because the solute will diffuse quickly through the membrane to equalize the concentration on two sides of the membrane. 

A membrane is a semipermeable barrier between two phases. If one component of a mixture moves through the membrane faster than another mixture component, a separation can be accomplished. The basic properties of membrane operations make them ideal for industrial production they are simple in concept and operation they are modular and easy to scale-up and they are low in energy consumption with a remarkable potential for an environmental impact, and energetic aspects. 

Osmosis and osmotic pressure. Osmosis is the movement of solvent from a dilute solution to a more concentrated solution through a semipermeable membrane. The pressure that must be applied to the more concentrated solution to stop this flow is the osmotic pressure. The osmotic pressure, like the pressure exerted by a gas, may be treated quantitatively by using an equation similar in form to the ideal gas equation tt = MRT. By convention the molarity of particles that is used for osmotic pressure calculations is termed osmolarity (osmol). 

It is interesting to note the equivalence between equations (5.208) and (5.209) and the ideal gas law PV nRT However, no direct significance can be attached to this similarity. It is sometimes thought that osmotic pressure can be visualized as a bombardment of solute molecules against the semipermeable membrane just as gas pressure is due to bombardment of gas molecules, but this view is incorrect. The phenomenon must be explained in terms of the flow of solvent molecules or interpreted in terms of thermodynamic arguments, as has been done above. 

If an ideal semipermeable membrane separates an aqueous organic or inorganic solution from pure water, the tendency to equalize concentrations would result in the flow of the pure water through the membrane to the solution. The pressure needed to stop the flow is called the osmotic pressure. If the pressure on the solution is increased beyond the osmotic pressure, then the flow would be reversed and the fresh water would pass from the solution through the membrane, whence the name reverse osmosis. In actual reverse osmosis systems the applied pressure must be sufficient to overcome the osmotic pressure of the solution and to provide the driving force for adequate flow rates. 

Soil has long been considered as a chemical system due to its semipermeability to chemicals, bioactivity, interactions with chemicals, and so on. As a result, soil has been idealized as a leaky semipermeable membrane in chemical osmosis to explain various abnormal transport phenomena of water and chemicals in soil (Hanshaw, 1972 Marine and Fritz, 1981 Fritz and Marine, 1983 Yeung, 1990 Keijzer, Kleingeld, and Loch, 1999) as a Donnan membrane (Donnan, 1924) to examine the influences of soil type, water content, electrolyte concentration, and the cation and anion distribution in pore fluid on electroosmotic flow of fluid in soil (Gray and Mitchell, 1967) as a bioreactor to evaluate the impact of oxygen transfer on efficiency of bioremediation (Woo and Park, 1997) and so on. 

Microdialysis and ultrafiltration are separation techniques that involve moving a ( emical across a semipermeable membrane. In microdialysis (Fig. lA), a fluid is pumped through the membrane capillary of a probe. Ibe analyte crosses the membrane by diffusion. The driving force is a concentration gradient. Under ideal conditions, the perfusion fluid is isos-... 

This process, however, is the same as if there would be a semipermeable membrane for compound (1) to still another chamber as shown in Fig. 6.6. We can understand this by the fact that the addition of compound (2) would not change the partial pressure p of the compound (1) in the ideal case. In other words, by performing such a process, there would not be any flow of the compound (1) through the membrane. If we think of the analogous process in the field of osmosis, by such a process, we would not need a membrane at all to find out the increase in pressure by adding a solute with the properties of compound (2). 

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