Equation reversible adsorption

The main disadvantage of the perfect sink model is that it can only be applied for irreversible deposition of particles the reversible adsorption of colloidal particles is outside the scope of this approach. Dahneke [95] has studied the resuspension of particles that are attached to surfaces. The escape of particles is a consequence of their random thermal (Brownian) motion. To this avail he used the one-dimensional Fokker-Planck equation... 

The equation reflects dual site reversible adsorption. Methanol and formaldehyde compete for sites, while oxygen is dissociatively adsorbed on different sites. At a not-too-low oxygen pressure (>0.01 atm) the coverage of the oxygen sites is complete and the equation reduces to... 

Sedlak and Andren (1991b) modeled hydroxyl radical reaction kinetics in the presence of particulate. They found that the reaction kinetics for PCB oxidation in the presence of particulate resulted from the complex interplay between solution-phase OH reactions and reversible adsorption-desorption reactions. A model predicting the reaction kinetics can be described by the following equation ... 

In this note, an equation is established for the rata cl reversible adsorption on the basis of the quasi steady state assumption over too entire thickness of too interaction -force boundary layer. When an interaction force boundary layer occurs fcT), we find that the epproxi-... 

Kinetic equations for reversible adsorption and reversible coagulation are established when the interaction potential has primary and secondary minima of comparable depths. The process is assumed to occur in two successive steps. First the particles move from the bulk of the fluid to the secondary minimum. A fraction of the particles which have arrived al the secondary minimum move further to the primary minimum. Quasi-steady state is assumed for each of the steps separately. Conditions are identified under which rates of reversible adsorption or coagulation at the primary minimum can be computed by neglecting the rate of accumulation at the secondary minimum. The interaction force boundary layer approach has been improved by introducing the tangential velocity of the particles near the surface of the collector into the kinetic equations. To account for reversibility a short-range repulsion term is included in the interaction potential. 

By splitting the quasi-steady-state assumption of diffusion of particles under the action of the interaction force field into two parts, kinetic equations which account for accumulation at both the primary and secondary minimum are formulated. Conditions are established under which, after a short transient, reversible adsorption or coagulation can be treated by neglecting accumulation at the secondary minimum. The effect of tangential velocity of particles on the rate of reversible adsorption is analyzed and a criterion established when the effect... 

Benhamou and Guastalla (1960) were the first to question the assumption of irreversibility with an analysis of the adsorption of insulin, /3-lactoglobulin, and ribonuclease. They investigated whether the Gibbs adsorption equation was obeyed. This basic equation, applicable to reversible adsorption, is firmly based on thermodynamics and has been amply verified experimentally. It can be written in the simple form... 

A derivation based on the mass-action law produces equation 10.4 as follows Consider the reversible adsorption of an adsorbate. A, onto sites given the label... 

Kinetics equation of the reversible adsorption. The flux j of surfactants from the bulk to the surface is given by the kinetic equation... 

The important assumptions for the pesticide model are instantaneous, linear, reversible adsorption described by an adsorption partition coefficient, K, and first-order decay described by an overall decay rate, k. Parameters for the pesticide model include universal soil loss equation parameters (if erosion loss is to be modeled), pesticide application information (rate, date, and method of application), K, k, and a dispersion coefficient. 

Ammons et al. studied the adsorption of methyl mercuric chloride from aqueous solutions on Filtrasorb-200 activated carbon at room temperature and found that the adsorption isotherms were nonlinear and did not fit either the Freundlich or the Langmuir isotherm equation. The adsorption was, however, reversible. Carrot et al. carried out adsorptive removal of mercury(ll) ions on five different commercial activated carbons associated with varying amounts of acidic and basic surface complexes. These workers observed that significant amounts of HgC and HgCl were adsorbed, but there was little adsorption of neutral HgCl2 or Hg + ions, hi the case of the basic carbons, the adsorption of the anions decreased with increase in the pH of the solution, but the uptake of cations was very small at pH = 0.2. They are of... 

Experimental effluent profiles may be fitted directly to the analytic form of Equation 7.15, provided that the solute experiences only dispersion, equilibrium linear reversible adsorption and/or excluded-volume effects. Figure 7.2 shows an analytical fit to the experimental effluent profile of a tracer flood indicating that only dispersion occurs in this case. In some experimental situations, however, the analytic form in Equation 7.15 is inadequate to describe the observed effluent profiles, and other phenomena need to be considered, as discussed in the following section. 

When the adsorption isotherm in Equations 7.18 and 7.19 is non-linear, these equations have no analytical solution. However, analytical solutions have been found (Van Geneuchten and Wierenga, 1976 De Smedt and Wierenga, 1979 Van Geneuchten, 1981) for the case of a linear reversible adsorption isotherm. Such solutions are now characterised by four quantities— D, Fr,/pv and a (and additionally, if it is a slug-type experiment, the pulse or slug size)—which are contained in the analytical solution. The dimensionless mass transfer coefficient, co, and Peclet number are defined in this case... 

Equation (142) is a general expression describing reversible adsorption of particles under linear conditions (for negligible surface-blocking effects). Under equilibrium conditions when j = 0, Eq. (142) becomes... 

Note The reactions of chemical and electrochemical combination [Eqs. (3) and (6)/(7)] leadto H2(aq) dissolved in the electrolyte, so the rate equations for the reverse adsorption reactions involve the activity of H2 dissolved in water, ajj2. However, as the reaction of dissolution of H2(g is in equilibrium, <7j 2 fm FT,... 

Because of their prevalence in physical adsorption studies on high-energy, powdered solids, type II isotherms are of considerable practical importance. Bmnauer, Emmett, and Teller (BET) [39] showed how to extent Langmuir s approach to multilayer adsorption, and their equation has come to be known as the BET equation. The derivation that follows is the traditional one, based on a detailed balancing of forward and reverse rates. 

Rapid e / h recombination, the reverse of equation 3, necessitates that D andM be pre-adsorbed prior to light excitation of the Ti02 photocatalyst. In the case of a hydrated and hydroxylated Ti02 anatase surface, hole trapping by interfacial electron transfer occurs via equation 6 to give surface-bound OH radicals (43,44). The necessity for pre-adsorbed D andM for efficient charge carrier trapping calls attention to the importance of adsorption—desorption equihbria in... 

It is seen, from equation (5), that a graph relating the reciprocal of the corrected retention volume to the concentration of the moderator can provide values for the adsorption/desorption coefficient and the surface area of the stationary phase. Scott and Simpson [1] used this technique to measure the surface area of a reversed phase and the curves relating the reciprocal of the corrected retention volume to moderator concentration are those shown in Figure 2. 

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