Solid-fluid equilibrium electrostatic interactions

Some components in a gas or liquid interact with sites, termed adsorption sites, on a solid surface by virtue of van der Waals forces, electrostatic interactions, or chemical binding forces. The interaction may be selective to specific components in the fluids, depending on the characteristics of both the solid and the components, and thus the specific components are concentrated on the solid surface. It is assumed that adsorbates are reversibly adsorbed at adsorption sites with homogeneous adsorption energy, and that adsorption is under equilibrium at the fluid- adsorbent interface. Let (m" ) be the number of adsorption sites and (m 2) the number of molecules of A adsorbed at equilibrium, both per unit surface area of the adsorbent. Then, the rate of adsorption r (kmol m s ) should be proportional to the concentration of adsorbate A in the fluid phase and the number of unoccupied adsorption sites. Moreover, the rate of desorption should be proportional to the number of occupied sites per unit surface area. Here, we need not consider the effects of mass transfer, as we are discussing equilibrium conditions at the interface. At equilibrium, these two rates should balance. Thus,... 

Until now we did not mention the interaction between liquid drops in a gas. In principle, such drops interact hke solid surfaces. In the absence of electrostatic charging, this interaction is dominated by van der Waals attraction. We just have to take into account a possible deformation of the surfaces. Therefore, we do not discuss it here. We would, however, like to mention one effect, which is typical for the interaction of fluid interfaces very often, the systems are not in equilibrium and the interaction between fluid interfaces is influenced or even dominated by nonequilibrium effects [733, 745]. One is unique for drops of volatile liquids. If the liquid is not in a saturated atmosphere of its vapor, it will evaporate. The flow of the vapor emanating from the liquid surface can lead to an effective repulsive force. Such a repulsion was indeed noticed by Prokhorov, who measured the interaction between two water drops [746]. He observed a repulsion that increased with decreasing relative humidity. 

Adsorption is a physical phenomenon in which some components adsorbates) in a fluid (liquid or gas) move to, and accumulate on, the surface of an appropriate solid adsorbent) that is in contact with the fluid. With the use of suitable adsorbents, desired components or contaminants in fluids can be separated. In bioprocesses, the adsorption of a component in a liquid is widely performed by using a variety of adsorbents, including porous charcoal, silica, polysaccharides, and synthetic resins. Such adsorbents of high adsorption capacities usually have very large surface areas per unit volume. The adsorbates in the fluids are adsorbed at the adsorbent surfaces due to van der Waals, electrostatic, biospecific, or other interactions, and thus become separated from the bulk of the fluid. In practice, adsorption can be performed either batchwise in mixing tanks, or continuously in fixed-bed or fluidized-bed adsorbers. In adsorption calculations, both equilibrium relationships and adsorption rates must be considered. 

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