Convective diffusion adsorption under

Hence, under the quasi-steady approximation, the movement of the species is dictated by a macroscopic convection-diffusion-reaction equation with an instantaneous adsorption/desorption source term. A notable consequence of the three-scale approach is the double-averaging representation for the partition coefficient A which is defined as... 

The problem of mass transfer from a moving Newtonian fluid to a swarm of prolate and/or oblate stationary spheroidal adsorbing particles under creeping flow conditions is solved using a spheroidal-in-cell model. The flow field through the swarm was obtained by using the spheroid-in-cell model proposed by Dassios et al. [5]. An adsorption - 1st order reaction - desorption scheme is used as boundary condition upon the surface of the spheroid in order to describe the interaction between the diluted mass in the bulk phase and the solid surface. The convective diffusion equation is solved analytically for the case of high Peclet numbers where the adsorption rate is also obtained analytically. For the case of low Pe a non-... 

Stages of Adsorption Kinetics of Ionics Under the Condition of Convective Diffusion... 

The analysis of the second case leads to two limiting conditions which are realised also in the case of a strongly retarded surface. Under condition (8.70) the surface concentration variation along the surface is insignificant. In the opposite case at sufficiently large T / C(, the motion of the surface pushes the adsorption layer down to the bottom pole of the bubble so that everywhere condition (8.72) is fulfilled except at 7t. This enables us to use the approximate boundary condition (8.74) for solving the convective diffusion equation. 

The main distinction of the theory of a dynamic adsorption layer formed under weak and strong retardation arises when formulating the convective diffusion equation. At weak retardation the Hadamard-Rybczynski hydrodynamic velocity field is used while at strong retardation the Stokes velocity field. Different formulas for the dependence of the diffusion layer thickness on Peclet numbers are obtained. The problem of convective diffusion in the neighbourhood of a spherical particle with an immobile surface at small Reynolds numbers and condition (8.74) is solved, so that the well-known expression for the density distribution of the diffusion flow along the surface can be used. As a result, Eq. (8.10) takes the form (Dukhin, 1982),... 

Protein Adsorption and Desorption Rates and Kinetics. The TIRF flow cell was designed to investigate protein adsorption under well-defined hydrodynamic conditions. Therefore, the adsorption process in this apparatus can be described by a mathematical convection-diffusion model (17). The rate of protein adsorption is determined by both transport of protein to the surface and intrinsic kinetics of adsorption at the surface. In general, where transport and kinetics are comparable, the model must be solved numerically to yield protein adsorption kinetics. The solution can be simplified in two limiting cases 1) In the kinetic limit, the initial rate of protein adsorption is equal to the intrinsic kinetic adsorption rate. 2) In the transport limit, the initial protein adsorption rate, as predicted by Ldveque s analysis (23), is proportional to the wall shear rate raised to the 1/3 power. In the transport-limited adsorption case, intrinsic protein adsorption kinetics are unobservable. 

Ordinary diffusion involves molecular mixing caused by the random motion of molecules. It is much more pronounced in gases and Hquids than in soHds. The effects of diffusion in fluids are also greatly affected by convection or turbulence. These phenomena are involved in mass-transfer processes, and therefore in separation processes (see Mass transfer Separation systems synthesis). In chemical engineering, the term diffusional unit operations normally refers to the separation processes in which mass is transferred from one phase to another, often across a fluid interface, and in which diffusion is considered to be the rate-controlling mechanism. Thus, the standard unit operations such as distillation (qv), drying (qv), and the sorption processes, as well as the less conventional separation processes, are usually classified under this heading (see Absorption Adsorption Adsorption, gas separation Adsorption, liquid separation). 

In the literature, it is observed from time to time that adsorption processes proceed faster than expected from a diffusion mechanism. This can of course be ascribed to convection in the bulk, however, this is not a good explanation for surfactant systems, where such phenomena are observed under various experimental conditions. 

Many practical processes (foaming, emulsification, dispersing, wetting, washing, solubilization) are influenced by the rate of adsorption from surfactant solutions. This rate depends on whether the adsorption takes place under diffusion, electro-diffusion, barrier, or convective control. The presence of surfactant micelles, which serve as carriers, and a reservoir of surfactants can strongly accelerate the kinetics of adsorption see Secs. 

This equation can be exploited for determining the particle diffusion coefficient by measiuing experimentally the number of irreversibly adsorbed particle as a function of time. This is done under the diffusion transport conditions by eliminating all natural and forced convection ciurents [2,9,10,16]. However, due to the fact that particle flux decreases gradually with the time, diffusion-controlled adsorption becomes very inefficient for long times. Indeed, in these experiments, adsorption times reached tens of hours. 

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