Homogenous surface diffusion model

Choy and McKay used a homogeneous surface diffusion model (HSDM) taking into account both external and internal transport, and found that the mean value of the solid diffusion coefficient is 3.72 X 10-9 cm2/s while kf = 6.06 X 10- 4 cm/s. 

Smith, E.H. 1991. Modified solution of homogeneous surface diffusion model for adsorption. J Environ. Eng-ASCE 117(3) 320-338. 

Abuzaid, N. S. and G. Nakhla (1997). Predictability of the homogeneous surface diffusion model for activated carbon adsorption kinetics formulation of a new mathematical model, J. Environment. Science Health, Part A Environment. Eng. Toxic Hazardous Substance Control. 32, 7, 1945-1961. 

A multicomponent HSDM for acid cfye/carbon adsorption has been developed based on the ideal adsorbed solution theory (lAST) and the homogeneous surface diffusion model (H SDM) to predict the concentration versus time decay curves. The lAST with the Redlich-P eterson equation is used to determine the pair of liquid phase concentrations, Q and Qj, from the corresponding pair of solid phase concentrations, q j and q jy at fha surface of the carbon particle in the binary component. 

The major difference between the various GRM models is due to the mechanism of intraparticle diffusion that they propose, namely pore diffusion, siuface diffusion or a combination of both, independent or competitive diffusion. The pore diffusion model assumes that the solute diffuses into the pore of the adsorbent mainly or only in the free mobile phase that impregnates the pores of the particles. The surface diffusion model considers that the intraparticle resistance that slows the mass transfer into and out of the pores proceeds mainly through surface diffusion. In the GRM, diffusion within the mobile phase filling the pores is usually assumed to control intraparticle diffusion (pore diffusion model or PDM). This kind of model often fits the experimental data quite well, so it can be used for the calculation of the effective diffusivity. If this model fails to fit the data satisfactorily, other transport formulations such as the Homogeneous Surface Diffusion Model (HSDM) [27] or a model that allows for simultaneous pore and siuface diffusion may be more successful [28,29]. However, how accurately any transport model can reflect the actual physical events that take place within the porous... 

The GRM Formulated with the Homogenous Surface Diffusion Model (HSDM)... 

Hand, D.W., J.C. Crittenden, and W.E. Thacker. 1981. User oriented solutions to the homogeneous surface diffusion model Batch reactor solutions. Proc. 54th Annual Conf, Water Pollution Control Federation, Detroit, ML 4-9 Oct. 1981. Water Pollution Control Federation, Alexandria, VA. 

Reverse osmosis models can be divided into three types irreversible thermodynamics models, such as Kedem-Katchalsky and Spiegler-Kedem models nonporous or homogeneous membrane models, such as the solution—diffusion (SD), solution—diffusion—imperfection, and extended solution—diffusion models and pore models, such as the finely porous, preferential sorption—capillary flow, and surface force—pore flow models. Charged RO membrane theories can be used to describe nanofiltration membranes, which are often negatively charged. Models such as Dorman exclusion and the... 

Solution—Diffusion Model. In the solution—diffusion model, it is assumed that (/) the RO membrane has a homogeneous, nonporous surface layer (2) both the solute and solvent dissolve in this layer and then each diffuses across it (J) solute and solvent diffusion is uncoupled and each is the result of the particular material s chemical potential gradient across the membrane and (4) the gradients are the result of concentration and pressure differences across the membrane (26,30). The driving force for water transport is primarily a result of the net transmembrane pressure difference and can be represented by equation 5 ... 

The basic biofilm model149,150 idealizes a biofilm as a homogeneous matrix of bacteria and the extracellular polymers that bind the bacteria together and to the surface. A Monod equation describes substrate use molecular diffusion within the biofilm is described by Fick s second law and mass transfer from the solution to the biofilm surface is modeled with a solute-diffusion layer. Six kinetic parameters (several of which can be estimated from theoretical considerations and others of which must be derived empirically) and the biofilm thickness must be known to calculate the movement of substrate into the biofilm. 

Membrane deterioration may be merely caused by decrease of acetyl content(C ) in the active surface layer as a result of hydrolysis or oxidation, not by structure change. Analysis was carried out based on solution-diffusion model proposed by Lonsdale etal( ), using their measured values of solute diffusivity and partition coefficient in homogeneous membrnaes of various degree of acetyl content and also using those values of asymmetric membranes heat treated at various temperatures measured by Glueckauf(x) ... 

Good quality RO membranes can reject >95-99% of the NaCl from aqueous feed streams (Baker, Cussler, Eykamp et al., 1991 Scott, 1981). The morphologies of these membranes are typically asymmetric with a thin highly selective polymer layer on top of an open support structure. Two rather different approaches have been used to describe the transport processes in such membranes the solution-diffusion (Merten, 1966) and surface force capillary flow model (Matsuura and Sourirajan, 1981). In the solution-diffusion model, the solute moves within the essentially homogeneously solvent swollen polymer matrix. The solute has a mobility that is dependent upon the free volume of the solvent, solute, and polymer. In the capillary pore diffusion model, it is assumed that separation occurs due to surface and fluid transport phenomena within an actual nanopore. The pore surface is seen as promoting preferential sorption of the solvent and repulsion of the solutes. The model envisions a more or less pure solvent layer on the pore walls that is forced through the membrane capillary pores under pressure. 

These controversial results on the kinetics of Me UPD processes, obtained on the basis of the simplest approach assuming quasi-homogeneous substrate surfaces, led to the development of a different kinetic model including surface inhomogeneities, gradients of Meads> and surface diffusion as discussed in the following. 

In the following, a general model [3.94] including formation of an expanded 2D Meads phase on a homogeneous substrate as well as a first order phase transition leading to a condensed 2D Meads phase is discussed for potentiostatic pulse polarization experiments. In this treatment, surface diffusion of Meads is neglected. 

The solution-diffusion model of transport assumes a non porous, homogeneous membrane surface layer. Each component in a pressurized solution dissolves in the membrane and then diffuses through the membrane. The flow of water and salt through the membrane is uncoupled, i.e., they are independent of each other, and the water transports through the membrane at a more rapid rate than the salt. 

The homogeneous diffusion model is slightly more complex in cyUndrical coordinates relative to the model described above in rectangular coordinates. Additional complexity arises because the radial term of the Laplacian operator (V V = V ) accounts for the fact that the surface area across which radial diffusion occurs increases linearly with dimensionless coordinate r/ as one moves radially outward. Basic information for = f(t]) is obtained by integrating the dimensionless mass balance with radial diffusion and chemical reaction ... 

The limitation of the resistance model lies in its application only for sufficient homogeneous surfaces such as forests, lakes and grasslands. Therefore, in dispersion models dry deposition can be described by using partial areas or weighted partial areas within the grid. The aerodynamic resistance through the upper layer can be calculated using Eq. (4.312) and an approach for the turbulent diffusion coefficient (eddy diffusivity) = Ku,z (valid only for neutral conditions) ... 

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