The Osmotic Pressure

We now add a solute to the compartment on the left. The solute is confined to this compartment, since we have chosen a membrane that will allow the flow of solvent, but not the flow of solute. Such a device is called a semipermeable membrane. 

We can prevent the flow of solvent by placing a piston on top of the chamber on the left and applying a pressure p to maintain equilibrium so that the liquid levels on the two sides of the membrane stay equal. The difference in pressure p - p° is known as the osmotic pressure II so that 

By applying the pressure p to the mixture, we keep the chemical potential of the solvent in the solution on the left equal to the chemical potential of the pure solvent on the right where the pressure is p°. We can write this equality as 

If we change the (p. T,, V ) conditions of the mixture such that the chemical potential changes by d/q, then /q 0 would need to change by an equivalent amount to maintain equilibrium. That is 

Substitution of equations (7.113) and (7.116) into equation (7.112) gives an equation that relates p to. yj. The result is 

In an osmotic pressure experiment, the additional pressure II exerted on the polymer solution results in the solvent chemical potential being rendered equal to that of the pure solvent at ambient pressure p  

If it is possible to assume that V2 is small, which is somewhat in conflict with the assumptions adopted above, then 

The first virial term in this power series is the classical van t Hoff infinite dilution expression for the osmotic pressure. It is associated with the movement of the centres of mass of the solute molecule over the available volume. The second term, which turns out not to be entirely correct for a real 

Experiments show that whereas B2 is predicted by the FIory-Huggins theory to be independent of molecular weight, measured values of B2 decrease slowly with increasing molecular weight of the polymer. Much more sophisticated theories (e.g. perturbation theories), which lie outside our current scope, are required to account for this behaviour. 

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To review briefly, the osmotic pressure in a three-dimensional situation is that pressure required to raise the vapor pressure of solvent in a solution to that of pure solvent. Thus, remembering Eq. Ill-16,... 

In the preceding derivation, the repulsion between overlapping double layers has been described by an increase in the osmotic pressure between the two planes. A closely related but more general concept of the disjoining pressure was introduced by Deijaguin [30]. This is defined as the difference between the thermodynamic equilibrium state pressure applied to surfaces separated by a film and the pressure in the bulk phase with which the film is equilibrated (see section VI-5). 

The criterion for phase equilibrium is given by Eq. (8.14) to be the equality of chemical potential in the phases in question for each of the components in the mixture. In Sec. 8.8 we shall use this idea to discuss the osmotic pressure of a... 

The solute molecular weight enters the van t Hoff equation as the factor of proportionality between the number of solute particles that the osmotic pressure counts and the mass of solute which is known from the preparation of the solution. The molecular weight that is obtained from measurements on poly disperse systems is a number average quantity. 

In this section we briefly consider the osmotic pressure of polymers which carry an electric charge in solution. These include synthetic polymers with ionizable functional groups such as -NH2 and -COOH, as well as biopolymers such as proteins and nucleic acids. In this discussion we shall restrict our consideration... 

Neglecting the higher-order terms, we can write the osmotic pressure for this three-component system in terms of the van t Hoff equation ... 

These results show more clearly than Fq. (8.126)-of which they are special cases-the effect of charge and indifferent electrolyte concentration on the osmotic pressure of the solution. In terms of the determination of molecular weight of a polyelectrolyte by osmometry. ... 

The osmotic pressure of polystyrene fractions in toluene and methyl ethyl ketone was measuredt at 25°C and the following results were obtained ... 

When the superfluid component flows through a capillary connecting two reservoirs, the concentration of the superfluid component in the source reservoir decreases, and that in the receiving reservoir increases. When both reservoirs are thermally isolated, the temperature of the source reservoir increases and that of the receiving reservoir decreases. This behavior is consistent with the postulated relationship between superfluid component concentration and temperature. The converse effect, which maybe thought of as the osmotic pressure of the superfluid component, also exists. If a reservoir of helium II held at constant temperature is coimected by a fine capillary to another reservoir held at a higher temperature, the helium II flows from the cooler reservoir to the warmer one. A popular demonstration of this effect is the fountain experiment (55). 

Ultrafiltration. Membranes are used that are capable of selectively passing large molecules (>500 daltons). Pressures of 0.1—1.4 MPa (<200 psi) are exerted over the solution to overcome the osmotic pressure, while providing an adequate dow through the membrane for use. Ultrafiltration (qv) has been particulady successhil for the separation of whey from cheese. It separates protein from lactose and mineral salts, protein being the concentrate. Ultrafiltration is also used to obtain a protein-rich concentrate of skimmed milk from which cheese is made. The whey protein obtained by ultrafiltration is 50—80% protein which can be spray dried. 

Ophthalmic Dosage Forms. Ophthalmic preparations can be solutions, eg, eye drops, eyewashes, ointments, or aqueous suspensions (30). They must be sterile and any suspended dmg particles must be of a very fine particle size. Solutions must be particle free and isotonic with tears. Thus, the osmotic pressure must equal that of normal saline (0.9% sodium chloride) solution. Hypotonic solutions are adjusted to be isotonic by addition of calculated amounts of tonicity adjusters, eg, sodium chloride, boric acid, or sodium nitrate. 

The pressure difference between the high and low pressure sides of the membrane is denoted as AP the osmotic pressure difference across the membrane is defined as Att the net driving force for water transport across the membrane is AP — (tAtt, where O is the Staverman reflection coefficient and a = 1 means 100% solute rejection. The standardized terminology recommended for use to describe pressure-driven membrane processes, including that for reverse osmosis, has been reviewed (24). 

Reverse osmosis is created when sufficient pressure is appHed to the concentrated solution to overcome the osmotic pressure. This pressure is... 

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. 

Concentration of Seawater by ED. In terms of membrane area, concentration of seawater is the second largest use. Warm seawater is concentrated by ED to 18 to 20% dissolved soHds using membranes with monovalent-ion-selective skins. The EDR process is not used. The osmotic pressure difference between about 19% NaCl solution and partially depleted seawater is about 20,000 kPa (200 atm) at 25°C, which is well beyond the range of reverse osmosis. Salt is produced from the brine by evaporation and crystallisa tion at seven plants in Japan and one each in South Korea, Taiwan, and Kuwait. A second plant is soon to be built in South Korea. None of the plants are justified on economic grounds compared to imported solar or mined salt. 

Limitations It is desirable to have an estimate for the smallest particle size that can be effectively influenced by DEP. To do this, we consider the force on a particle due to DEP and also due to the osmotic pressure. This latter diffusional force will randomize the particles and tend to destroy the control by DEP Figure 22-32 shows a plot of these two forces, calciilated for practical and representative conditions, as a func tion of particle radius. As we can see, the smallest particles that can be effec tively handled by DEP appear to be in range of 0.01 to 0.1 piTidOO to 1000 A). 

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. 

For many years, it was thought that the macro solute forms a new phase near the membrane—that of a gel or gel-like layer. The model provided good correlations of experimental data and has been widely used. It does not fit known experimental facts. An explanation that fits the known data well is based on osmotic pressure. The van t Hoff equation [Eq. (22-75)] is hopelessly inadequate to predict the osmotic pressure of a macromolecular solution. Using the empirical expression... 

A hybridoma can live indefinitely in a growth medium that includes salts, glucose, glutamine, certain amino acids, and bovine serum that provides essential components that have not been identified. Serum is expensive, and its cost largely determines the economic feasibihty of a particular ciilture system. Only recently have substitutes or partial replacements for serum been found. Antibiotics are often included to prevent infection of the culture. The pH, temperature and dissolved oxygen, and carbon dioxide concentration must be closely controlled. The salt determines the osmotic pressure to preserve the integrity of the fragile cell. 

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 ... 

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