Electrostatic interactions, solid-fluid

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,... 

As mentioned above, most MIPs are synthesized in organic solvents to preserve the hydrogen and electrostatic interactions between template and monomer. However, for the application to solid-phase extraction (SPE) where the target is most of the time in water samples or in biological fluids, a lot of studies have been carried out to examine the influence of binding media parameters (solvent polarity and composition, buffer pH, concentration, ionic strength, etc.) with the aim of attenuating non-specific adsorption of the analyte due to hydrophobic interactions which predominate in such media. For a recent review, see Tse Sum Bui and Haupt [95]. 

For many purposes, the Lennard-Jones 12-6 potential is considered to be a satisfactory starting point for establishing the pairwise adsorbate-adsorbent and adsorbate-adsorbate interactions. If the adsorbed molecule has a permanent dipole or quadrupole moment, it is necessary to allow for electrostatic interactions and possibly also additional polarization effects. To obtain the required overall fluid-fluid and fluid-solid potential functions, it is customary to assume that the pairwise interactions are additive. With some systems, however, the solid can be regarded as a continuum, and integration is then possible in place of more laborious summation (Steele, 1974). 

The coefficients a(p, c) and tj(p, c) describe chemical and physical effects on the kinetics of deposition. The transport of particles from the bulk of the flowing fluid to the surface of a collector or media grain by physical processes such as Brownian diffusion, fluid flow (direct interception), and gravity are incorporated into theoretical formulations for fj(p, c), together with corrections to account for hydrodynamic retardation or the lubrication effect as the two solids come into close proximity. Chemical effects are usually considered in evaluating a(p, c). These include interparticle forces arising from electrostatic interactions and steric effects originating from interactions between adsorbed layers of polymers and polyelectrolytes on the solid surfaces. 

We studied, by GCMC simulation [1], the adsorption of ethane and carbon dioxide on pure-silica MCM-41 and on MCM-41 with surface phenyl and aminopropyl groups. The fluid-fluid and fluid-solid potentials took into account dispersion and, where appropriate, electrostatic interactions. The surface groups - phenyl and aminopropyl - are modelled as flexible chain molecules. The solid-fluid potentials are transferable that is, they are applicable to all the oxide materials we have studied, and are not optimised for particular materials this is an indicator of the consistency of the approach. The silicon atoms are ignored in the simulation of adsorption. Further details of the kMC and GCMC simulation methods are given in reference [2]. 

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. 

Relevant forces are external volume forces like gravity, particle-particle interactions such as contact forces or electrostatic interactions, and the force exerted by the fluid on a particle. Some of these forces (that do not act on the center of mass) have a torque associated to it. The torque associated with the fluid—particle interaction follows from the antisymmetric part of the particle stress contributions. A detailed discussion of dominant forces in the case of gas-solid, liquid-bubble, and gas-droplet interactions will be provided in the topical sections (Sections 4—6). 

There is a significant scatter between the values of the Poiseuille number in micro-channel flows of fluids with different physical properties. The results presented in Table 3.1 for de-ionized water flow, in smooth micro-channels, are very close to the values predicted by the conventional theory. Significant discrepancy between the theory and experiment was observed in the cases when fluid with unknown physical properties was used (tap water, etc.). If the liquid contains even a very small amount of ions, the electrostatic charges on the solid surface will attract the counter-ions in the liquid to establish an electric field. Fluid-surface interaction can be put forward as an explanation of the Poiseuille number increase by the fluid ionic coupling with the surface (Brutin and Tadrist 2003 Ren et al. 2001 Papautsky et al. 1999). 

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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