Coefficient cohesion

Derive the expression (in terms of the appropriate works of adhesion and cohesion) for the spreading coefficient for a substance C at the interface between two liquids A and B. 

Fluidized-bed driers are also widely used due to their large heat- and mass-transfer coefficients. However, materials of even moderate adherence and cohesiveness cannot be dried in a fluid bed. The same applies to materials that are sensitive to oxygen, especially at elevated temperatures. Vacuum drying is often necessary for oxygen sensitive materials and this is not easy to realize in fluid-bed driers, although there are systems to deal with this problem. Fluid-bed driers are not as easy to clean as shelf driers or rotary driers. 

The osmotic pressure of an electrolyte solution jt can be considered as the ideal osmotic pressure jt decreased by the pressure jrel resulting from electric cohesion between ions. The work connected with a change in the concentration of the solution is n dV = jt dV — jrel dV. The electric part of this work is then JteldV = dWcl, and thus jzc] = (dWei/dV)T,n. The osmotic coefficient 0 is given by the ratio jt/jt, from which it follows that... 

Figure 3.4 shows a fair correlation between vo-2ot and the Hildebrand solubility parameter 8 (linear correlation coefficient = 0.930) which makes intuitive sense. The Hildebrand parameter, which is often used to characterize liquids, is defined as the square root of the cohesive energy density (Barton 1991), while vcr2o( can be viewed as reflecting how strongly a molecule interacts with others of the same kind (Murray et al. 1994). 

The Hamaker constant A can, in principle, be determined from the C6 coefficient characterizing the strength of the van der Waals interaction between two molecules in vacuum. In practice, however, the value for A is also influenced by the dielectric properties of the interstitial medium, as well as the roughness of the surface of the spheres. Reliable estimates from theory are therefore difficult to make, and unfortunately it also proves difficult to directly determine A from experiment. So, establishing a value for A remains the main difficulty in the numerical studies of the effect of cohesive forces, where the value for glass particles is assumed to be somewhere in the range of 10 21 joule. 

Fig. 22. The effect of the cohesive force on the excess compressibility. The coefficient of normal restitution is e = 1.0, and granular temperature is T = 1.0. The Hamaker constant is A = 3.0 x 10-12 (circles) and 3.0 x 1CT10 (crosses).

Table 6.2 presents data showing the effect of various CMOS on the activity coefficient or mole fraction solubility of naphthalene, for two different solvent/water ratios. To examine the cosolvent effect, Schwarzenbach et al. (2003) compare the Hildebrand solubility parameter (defined as the square root of the ratio of the enthalpy of vaporization and the molar volume of the liquid), which is a measure of the cohesive forces of the molecule in pure solvent. 

Vibro-fluidization is used for cohesive, sticky solids or friable foods (Bahu, 1997) and for materials which would defluidize in a conventional plug flow drier (Reay and Baker, 1985). Vibration of the bed increases the drying rate due to an increase in the surface-to-bed heat transfer coefficient (Reay and Baker, 1985), particularly below minimum fluidizing velocity. A detailed treatment of the mechanisms of vibration fluidization is given by Reay and Baker (1985). 

As already mentioned, the cavity term corresponds to the endoeigic process of separating the solvent molecules to provide a suitably sized and shaped enclosure for the solute, and measures the work required for such a purpose. This term is related to the tightness or structuredness of solvents as caused by intermolecular solvent/solvent interactions. The association of solvent molecules in the liquid state in order to accommodate the solute molecules can be quantified by means of the surface area and texture of the solute that are related with the m coefficient and by the cohesive pressure of the solvent given by fl. 

Using PCA, Cramer found that more than 95% of the variances in six physical properties (activity coefficient, partition coefficient, boiling point, molar refractivity, molar volume, and molar vaporization enthalpy) of 114 pure liquids can be explained in terms of only two parameters which are characteristic of the solvent molecule (Cramer 111, 1980). These two factors are correlated to the molecular bulk and cohesiveness of the individual solvent molecules, the interaction of which depends mainly upon nonspecific, weak intermolecular forces. 

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