Surface force-pore flow model

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... 

Transport equations, for the surface force-pore flow model, 21 640—641 Transport gasifier, 6 798 Transport models, reverse osmosis, 21 638-639... 

Calculation of Solute Separation and Product Rate. Once the pore size distribution parameters R, ou R >,2, 02, and h2 are known for a membrane and the interfacial interaction force parameters B and D are known for a given system of membrane material-solute, solute separation f can be calculated by eq 6 for any combination of these parameters. Furthermore, because the PR-to-PWP ratio (PR/PWP) can also be calculated by the surface force-pore flow model (9), PR is obtained by multiplying experimental PWP data by this ratio. 

The interfacial force constants available in the literature for many organic solutes that constitute potential pollutants in water enable one to calculate the separation of such solutes at various operating conditions by a membrane of a given average pore size and pore size distribution on the basis of the surface force-pore flow model. The product rate of the permeate solution can also be calculated. Such data further allow us to calculate the processing capacity of a membrane to achieve a preset ratio of concentration in the concentrate to concentration of the initial feed solution. 

In the earlier work (1 ) transport equations were developed on the basis of surface force-pore flow model in which a surface potential function and a frictional function are incorporated. The results can be briefly summarized as follows ... 

The differences between the surface force-pore flow model and the solution-diffusion model are (1) the microscopic structure of the membrane is incorporated explicitly into the transport equations as the pore radius in the surface force-pore flow model (2) the interaction force working between the permeant and the membrane is also incorporated into the transport equations as an interaction force parameter in the surface force-pore flow model (3) as mentioned in Chapter 5, the solution-diffusion model describes the transport of permeants through the membrane, as an uncoupled diffusive flow. Mass transfer by the diffusive flow is expressed by a set of transport parameters that are intrinsic to the polymeric material. Any flow other than the above intrinsic diffusive flow is... 

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,... 

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. 

Common conceptual models for liquid distribution and transport in variably saturated porous media often rely on oversimplified representation of media pore space geometry as a bundle of cylindrical capillaries, and on incomplete thermodynamic account of pore scale processes. For example, liquid adsorption due to surface forces and flow in thin films are often ignored. In this study we provide a review of recent progress in modeling liquid retention and interfacial configurations in variably saturated porous media and application of pore scale hydrodynamic considerations for prediction of hydraulic conductivity of unsaturated porous media. 

Filtration Model. A model based on deep-bed filtration principles was proposed by Soo and Radke (12), who suggested that the emulsion droplets are not only retarded, but they are also captured in the pore constrictions. These droplets are captured in the porous medium by two types of capture mechanisms straining and interception. These were discussed earlier and are shown schematically in Figure 22. Straining capture occurs when an emulsion droplet gets trapped in a pore constriction of size smaller than its own diameter. Emulsion droplets can also attach themselves onto the rock surface and pore walls due to van der Waals, electrical, gravitational, and hydrodynamic forces. This mode of capture is denoted as interception. Capture of emulsion droplets reduces the effective pore diameter, diverts flow to the larger pores, and thereby effectively reduces permeability. 

For solids with continuous pores, a surface tension driven flow (capillary flow) may occur as a result of capillary forces caused by the interfacial tension between the water and the solid particles. In the simplest model, a modified form of the Poiseuille flow can be used in conjunction with the capillary forces equation to estimate the rate of drying. Geankoplis (1993) has shown that such a model predicts the drying rate in the falling rate period to be proportional to the free moisture content in the solid. At low solid moisture contents, however, the diffusion model may be more appropriate. 

Solving this flow model for the velocity the pressure is calculated from the ideal gas law. The temperature therein is obtained from the heat balance and the mixture density is estimated from the sum of the species densities. It is noted that the viscous velocity is normally computed from the pressure gradient by use of a phenomenologically derived constitutive correlation, known as Darcy s law, which is based on laminar shear flow theory [139]. Laminar shear flow theory assumes no slip condition at the solid wall, inducing viscous shear in the fluid. Knudsen diffusion and slip flow at the solid matrix separate the gas flow behavior from Darcy-type flow. Whenever the mean free path of the gas molecules approaches the dimensions of pore diameter, the individual gas molecules are in motion at the interface and contribute an additional flux. This phenomena is called slip flow. In slip flow, the layer of gas next to the surface is in motion with respect to the solid surface. Strictly, the Darcy s law is valid only when the flow regime is laminar and dominated by viscous forces. The theoretical foundation of the dusty gas model considers that the model is applied to a transition regime between Knudsen and continuum bulk diffusion. To estimate the combined flux, the model is based on the assumption that the combined flux can be expressed as a linear sum of the Knudsen flux and the convective flux due to laminar flow. 

Finally increase in n shown by several systems during postdrying (3) (see Table I) stems from subterranean absorption processes e.g. interconnection of partially filled pores and localized surface fibre wicking. The values of n which in several cases are close to the theoretical value, 0.5, for a Lucas-Washbum type capillary model, suggest that the condition of flow through completely filled and interconnected capillaries to supply the spreading front, is ultimately attained. This final stage reflects lag in the equilibration of bulk and surface capillary forces. 

Another concept of water and salt transport in reverse osmosis is the preferential sorption-capillary flow mechanism. In this model, the surface of a membrane is microporous and heterogeneous at all levels of solute separation. It is hypothesized that, due to the chemical nature of the membrane skin layer in contact with the aqueous solution, a preferential sorption for the water causes a sorbed water layer to be formed at the skin. This layer of purified water is then forced through the capillary pores by pressure. 

Erosion corrosion is mainly observed in hydraulic installations (pumps, turbines, or tubes). This form of corrosion appears at a point where the flow velocity of the bulk solution exceeds a critical limit, or where this limit is exceeded by local turbulence. Erosion corrosion results from an interaction between mechanical and chemical influences. Fig. 1-26. One model describing the mechanism of erosion corrosion assumes that local shear forces acting on the metal surface as a result of the high flow velocity forms pores or unprotected areas. Accelerated mass transfer then occurs in these areas and aggravates corrosion damage. 

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