Excess osmotic pressure

This latter expression allows us to compute all the excess properties of dilute electrolytic solutions for instance, the excess osmotic pressure is determined by Eq. (138). The most remarkable result is of course that all these thermodynamic properties are non-anaiytic functions of the concentration ... 

The electrolyte ions in the electrical double layer thus exert an excess osmotic pressure ATI(r) on the particle, which is given by... 

When two charged colloidal particles approach each other, their electrical double layers overlap so that the concentration of counterions in the region between the particles increases, resulting in electrostatic forces between them (Fig. 8.2). There are two methods for calculating the potential energy of the double-layer interaction between two charged colloidal particles [1,2] In the first method, one directly calculates the interaction force P from the excess osmotic pressure tensor All and... 

FIGURE 8.1 Electrical double layer around a charged particle exert the excess osmotic pressure AH and the Maxwell stress T on the particle. 

The interaction force P can be calculated by integrating the excess osmotic pressure An and the Maxwell stress tensor T over an arbitrary closed surface 21 enclosing either one of the two interacting particles (Fig. 8.3), which is written as [8]... 

As shown in Chapter 8, the interaction force P can be calculated by integrating the excess osmotic pressure AH and the Maxwell stress T over an arbitrary closed surface E enclosing either one of the two interacting plates (Eq. (8.6)). As an arbitrary surface E enclosing plate 1, we choose two planes x= —oo and x = 0, since )J/(x) = d)J//dx = 0 at x=—oo (Eqs. (10.3) and (10.4)) so that the excess osmotic pressure AH and the Maxwell stress T are both zero at x = —oo. Thus, the force P(h) of the double-layer interaction per unit area between plates 1 and 2 can be expressed as... 

The electrostatic interaction force acting between plates 1 and 2 per unit area can be calculated from an excess osmotic pressure at the midpoint between the plates, namely. 

A nonadsorbing polymer added to dispersions will often cause aggregation of particles. Asakura and Oosawa were the first to describe the cause of this instability as two particles approach the finite size of the polymer chains ensures their exclusion from the region between the two particles. The osmotic pressure is dependent on the concentration of macromolecule and hence it is diminished in this overlap region. The excess osmotic pressure in the main bulk fiuid causes the two particles to be pushed together. This is called the depletion potential and has been extensively studied.This is shown in Fig. 6. 

As pointed out by Langmuit the electrostatic disjoining pressure, n i, can be identified with the excess osmotic pressure in the middle of the film ... 

When the Donnan potential and the excess osmotic pressure within the gel are sufficiently reduced by additional salt, the swelling and dissolution can be prevented but salt may also exert a salting-in effect which can compensate for the abolition of the electric and osmotic Donnan effects. When the salting-in threshold is very low, therefore, proteins caused to dissolve by shifting the pH away from the isoelectric point are not precipitated by addition of salt. This is true at pH 7 of tropomyosin, a relatively soluble protein for which the salting-in limit is particularly low and the salting-out limit is particularly high (Table VII). 

Hesselink etal. 91 ) have preferred the designation osmotic for the major free energy change in the interpenetrational domain. This terminology accurately portrays the consequences of the steric interaction. The interaction of the steric layers generates a difference in the chemical potential between molecules of the dispersion medium in the interactional zone and those in the bulk dispersion medium. This chemical potential difference could, of course, be related to an excess osmotic pressure. 

The excess osmotic pressure can be expressed by the virial expansion viz... 

This equation allows theoretically predicted values of to be transformed into an excess osmotic pressure, or a disjoining pressure in the terminology of Deijaguin (1955, 1964). 

This phenomenon must not be confounded with that observed when any blood corpuscles are placed in water. As a result of plasmolysis, the protoplasmic sac breaks under the influence of the excessive osmotic pressure and allows the contents to flow into the external liquid, which thus colors bright red. There is indeed haemolysis but this is entirely physical and is produced only in hypotonic media. On the contrary, the Bordet phenomenon appears in a solution of serum, perfectly isotonic. In addition the haemolsdic serum of A is specific it acts only on the corpuscles of the animal species B, which have served by peritoneal injections in making the preparation. In the example given above, the serum of the rabbit thus sensitized will haemolyze only the corpuscles of sheep, and not those of cattle, of guinea-pigs, of dogs, etc. 

Pressure drop p has the meaning of force acting on a unit area of the boundary plane and aspiring to pull the planes apart. In a sense, p is excessive osmotic pressure at the symmetry axis of the planes in comparison with the pressure in the bulk of the solution. 

Figure 3.35 can be translated into a simple geometric argument if it is assumed that the adsorbed layers are uniform and that overlap of the two layers occurs on approach. The latter introduces, therefore, firstly the volume of the overlap region and secondly, a term related to interactions in the layw which is related to the excess osmotic pressure, tte. Thus when the particles are far apart it can be considered that the solution is ideal and of chemical potential fiQ, and whoi overlap occurs it becomes non-ideal and of chemical potential /j., so that... 

In a simplified model, which generalizes the Daoud-Cotton approach [21], the condition of a local balance between the elastic tension in the extended branches and the excess osmotic pressure due to (repulsive) monomer-monomer interactions ... 

Addition of salt in the solution leads to the screening of electrostatic repulsions between the coronal chains and a decrease in the excess osmotic pressure, as soon as the corona is found in the salt-dominated regime [28]. This regime is entered when the bulk concentration of added salt exceeds significantly the concentration of counterions trapped inside the corona, Oion > Here, one... 

The products from a reverse osmosis separation step consist of a purified solvent stream and a solution somewhat more concentrated than the feed stream. Therefore, it is not a complete separation process and must be accompanied by additional processing steps if complete separation or high recovery of solvent is desired. The degree of recovery or extent of concentration of the reject stream is lirrrited by the osmotic pressure of the concentrated solution. The membrane must irraintain its integriQ and permit reasonable flux of solvent with a pressure difference across the membrane exceeding the osmotic pressure, in general, excessive osmotic pressures are encountered when the solute mole fraction in the concentrated solution exceeds 0.03-0.06. 

The ionic concentration at a point midway between the two charged surfaces (at A in Fig. 4.14) will be greater than that far away from the surfaces (at B). This gives rise to an excess osmotic pressure II that acts to push the surfaces apart. The excess osmotic pressure at A is given by (1)... 

As already mentioned, the electrostatic component of disjoining pressure can be defined as the excess osmotic pressure in the film midplane with respect to the bulk solution, see Equation 4.189. Hence, if all coions are expelled from the film, the expression for the disjoining pressure acquires the form [589] ... 

Because the surfactant concentration in the oil phase (the disperse phase) is higher than the equilibrium concentration, surfactant molecules cross the oil-water interface toward the aqueous phase. Thus, surfactant accumulates within the film, because the bulk diffusion throughout the film is not fast enough to transport promptly the excess surfactant into the Plateau border. As the background surfactant concentration in the aqueous phase is not less than CMC, the excess surfactant present in the film is packed in the form of micelles (denoted by black dots in Figure 4.60a). This decreases the chemical potential of the surfactant inside the film. Nevertheless, the film is subjected to osmotic swelling because of the increased concentration of micelles within. The excess osmotic pressure... 

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