Fine pore model

The fine-pore model was developed assuming the presence of open micropores on the active surface layer of the membrane through which the mass transport occurs (10). The existence of these different pore geometries also means that different models have been developed to describe transport adequately. The simplest representation is one in which the membrane is considered as a number of parallel cylindrical pores perpendicular to the membrane surface. The length of each of the cylindrical pores is equal or almost equal to the membrane thickness. The volume flux through these pores can be described by the Hagen-Poiseuille equation. Assuming all the pores have the same radius, then we have... 

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... 

However, a distinction should be made in that Eq. (12) is purely phenomenological and does not require any transport mechanism model while the Nermst-Planck equation used in the previous finely-porous membrane model requires a specific pore model. Another difference is that the salt concentration in Eq. (12) is that in the membrane while the quantity appearing in the Nernst-Planck equation refers to the salt concentration in the membrane pores. 

For example, the capillary forces mentioned in Chapter 1 become extensively involved in the movement of water through a sponge. Sponges consist of many interconnected capillaries. An oil reservoir can be considered a simplified model of a sponge. If the reservoir is finely pored and sponge-like, then oil recovery is very poor (less than 30%), while if the pores are of large diameter, then recovery will be very high (over 60%). 

The finely-porous model is based on a balance of applied and frictional forces in a 1-dimentional pore.7 The model considers friction between the solute and solvent, and between the solute and the membrane material. The model also includes the membrane thickness and the fractional pore area of the membrane surface. 

These observations can be rationalised with the following (qualitative) models. To obtain ultra-fine pores in a structure by more or less regular packing of primary particles [1,4], these primary particles should be small. In the case of... 

Finely Porous Model. In this model, solute and solvent permeate the membrane via pores which connect the high pressure and low pressure faces of the membrane. The finely porous model, which combines a viscous flow model eind a friction model (7, ), has been developed in detail and applied to RO data by Jonsson (9-12). The most recent work of Jonsson (12) treated several organic solutes including phenol and octanol, both of which exhibit solute preferential sorption. In his paper, Jonsson compared several models including that developed by Spiegler eind Kedem (13) (which is essentially an irreversible thermodynamics treatment), the finely porous model, the solution-diffusion Imperfection model (14), and a model developed by Pusch (15). Jonsson illustrated that the finely porous model is similar in form to the Spiegler-Kedem relationship. Both models fit the data equally well, although not with total accuracy. The Pusch model has a similar form and proves to be less accurate, while the solution-diffusion imperfection model is even less accurate. 

The advantage of the preferential sorption-capillary flow approach to reverse osmosis lies in its emphasis on the mechanism of separation at a molecular level. This knowledge is useful when it becomes necessary to predict membrane performance for unknown systems. Also, the approach is not restricted to the so-called "perfect", defect-free membranes, but encompasses the whole range of membrane pore size. Until recently, the application of a quantitative model to the case of solute preferential sorption has been missing. Attempts to change this situation have been made by Matsuura and Sourirajan (21) by using a modified finely porous model. In addition to the usual features of this model (9-12), a Lennard-Jones type of potential function is Incorporated to describe the membrane-solute interaction. This model is discussed elsewhere in this book. 

Although the previous models well describe the binding of surfactant with the polymer network, they do not explain the issue of the electric field and deformation in the first and third steps. We propose and introduce the adsorption equation based on the Langmuir s theory for the second step. The model of simplicity explains the connection between the first and third steps. The following assumptions have been made to apply the theory to the gel a) the gel is the porous plate made of polymers like activated carbon b) the effective surface of the polymer network is the total area of the fine pores c) the bound molecules do not affect the free molecules once the pore is occupied by a certain numbers of molecules. Accordingly, the polymer network is approximated by a three-dimensional monolayer. 

Samples prepared as described above can be good models for working catalysts of either the oxide or metal types and many infrared studies of surface phenomena are undertaken in conjunction with catalytic investigations. Loose powders can alternatively be studied by diffuse reflection, with the advantage for kinetic studies that surface reactions, rather than diffusion processes, are more likely to be rate determining than is the case with the fine-pored pressed discs. 

Surface-enhanced resonance Raman scattering (SERRS), 21 327-328 advantage of, 21 329 Surface Evolver software, 12 11 Surface excess, 24 135, 136 Surface extended X-ray absorption fine structure (SEXAFS), 19 179 24 72 Surface filtration, 11 322-323 Surface finish(es). See also Electroplating in electrochemical machining, 9 591 fatigue performance and, 13 486-487 Surface finishing agents, 12 33 Surface force apparatus, 1 517 Surface force-pore flow (SFPF) model,... 

Laboratory data collected over honeycomb catalyst samples of various lengths and under a variety of experimental conditions were described satisfactorily by the model on a purely predictive basis. Indeed, the effective diffusivities of NO and NH3 were estimated from the pore size distribution measurements and the intrinsic rate parameters were obtained from independent kinetic data collected over the same catalyst ground to very fine particles [27], so that the model did not include any adaptive parameters. 

The estimation of the surface area of finely divided solid particles from solution adsorption studies is subject to many of the same considerations as in the case of gas adsorption, but with the added complication that larger molecules are involved whose surface orientation and pore penetrability may be uncertain. A first condition is that a definite adsorption model is obeyed, which in practice means that area determination data are valid within the simple Langmuir Equation 5.23 relation. The constant rate is found, for example, from a plot of the data, according to Equation 5.23, and the specific surface area then follows from Equations 5.21 and 5.22. The surface area of the adsorbent is generally found easily in the literature. 

---