Capillary flow 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. 

It is instructive to consider steady fluid flow (sometimes called Poiseuille flow) in a thin capillary tube. This example has many purposes it provides (1) a model flow calculation, (2) an illustration of how velocity profiles arise, (3) an explanation of the nature of flow in capillary chromatography, and (4) a foundation for capillary flow models of packed beds. 

Preferential Sorption - Capillary Flow Model (porous model)... 

This model is based on a generalized capillary flow model that includes viscous flow for water and solute transport, and for pore... 

A number of models have been developed over the years to describe reverse osmosis. These models Include the solution-diffusion model, the finely porous model, and the preferential sorption - capillary flow model. In each case, the model was originally developed based on the separation of aqueous,salt solutions. The application of each of these models to systems which exhibit anomalous behavior will be discussed in this section. 

Preferential Sorption-Capillary Flow Model. An alternative approach to those mentioned above has been presented by... 

The Preferential Sorption/Capillary Flow Model (Sourirajan and Matsuufa (1985)) is based on the assumption that a layer of water sorbs at the membrane surface, creating a deficit of solute at the surface. The membrane is viewed as a microporous medium, and transport is controlled by the surface chemistry of the membrane and water transport through the membrane. Ions with large hydrated radii are retained better, since they also have to overcome more energy to strip off the water. Ions diffuse through the laj et of strucmred water at the membrane surface and through water cluster channels in the membrane (Staude (1992)), where B is the pure water permeability of the membrane. 

The preferential sorption-capillary flow model starts from the consideration of the solid-liquid interface. For example, aqueous sodium chloride solution is in contact with a solid surface. Sodium chloride solution represents the reverse osmosis system where the separation of solute (sodium chloride) flrom solvent (water) occurs. This system also represents one of the most important applications of reverse osmosis, i.e., seawater desalination. A concentration gradient should inevitably appear at the solution-solid interface, as shown in Figure 6.1. The Gibbs adsorption isotherm... 

Figure 6 2. Preferential sorption-capillary flow model. (Reproduced from [51 ] with permission.)...

The results of these analyses demonstrate that the three-phase contact fine location follows the square root of time. Coumarin fluorescent dye was utilized in small quantities to develop sufficient contrast of the three-phase line under UV irradiation for the comparison of experimental data to the models. The investigators of this approach conclude that exhaustive solutions to the capillary flow model can be realized however, approximations via Eq. (15) can be employed for sufficiently accurate predictive models [5, 6]. 

This model is based on a generalized capillary flow model that includes viscous flow for water and solute transport, and for pore diffusion. It further relies on film theory for transport through the boundary layers. The model states that by applying pressure, both the solvent and solute permeate through the micropores of the membrane, with water preferentially adsorbed onto the pore walls. Salt is rejected at the membrane surface for physiochemical reasons. Transport through the membrane is only through pores. 

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