Nonporous membranes solution-diffusion 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... 

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 ... 

Understand the solution-diffusion model for separation of liquid and gas mixtures using dense, nonporous membranes. 

Solution-diffusion model is the generally accepted mechanism of mass transport through nonporous membranes (Figure 9.3). According to this mechanism, PV consists of three consecutive steps ... 

The last part of.Ais chapter will be devoted to a comparison of meiribr c processes v where transport occurs through nonporous membranes. A solution-diffusion model will be used where each component dissolves into the membrane and diffuses through the membrane independently [41]. A similar approach was recently followed by Wijmans[43]. As a result, simple equations will be obtained for the component fluxes involved in the various processes which allows to compare the processes in terms of transport parameters. 

In Section 3.4.2.1, the phenomenon of reverse osmosis (RO) through a nonporous membrane was introduced. If the hydraulic pressure of a solution containing a microsolute, e.g. common salt, on one side of a nonporous membrane exceeds that of another solution on the other side of the same membrane by an amount more than the difference of the osmotic pressures of the same two solutions, then, according to the solution-diffusion model, the solvent will flow from the solution at higher pressure to the one at a lower pressure (equation (3.4.54)) at the following rate ... 

Gas permeation through a nonporous dense polymer membrane is described using a solution-diffusion model in which the permeability coefficient (Pa) [cm standard temperature and pressure (STP) cm/cm s cm Hg] of gas molecule A is the product of a diffusion coefficient (Da) (cm /s) and a solubility coefficient (Sa) (cm -gas/cm -polymer cm Hg) ... 

Most theoretical studies of osmosis and reverse osmosis have been carried out using macroscopic continuum hydrodynamics [5,8-13]. The models used include those that treat the wall as either nonporous or porous. In the nonporous models the membrane surface is assumed homogeneous and nonporous. Transport occurs by the molecules dissolving in the membrane phase and then diffusing through the membrane. Mass transfer across the membrane in these models is usually described using the solution-diffusion... 

The simplest practicable approach considers the membrane as a continuous, nonporous phase in which water of hydration is dissolved.In such a scenario, which is based on concentrated solution theory, the sole thermodynamic variable for specifying the local state of the membrane is the water activity the relevant mechanism of water back-transport is diffusion in an activity gradient. However, pure diffusion models provide an incomplete description of the membrane response to changing external operation conditions, as explained in Section 6.6.2. They cannot predict the net water flux across a saturated membrane that results from applying a difference in total gas pressures between cathodic and anodic gas compartments. 

Transport models fall into three basic classifications models based on solution/diffusion of solvents (nonporous transport models), models based on irreversible thermodynamics, and models based on porous membranes. Highlights of some of these models are discussed below. 

The solution-diffusion transport model was originally described by Lonsdale et al. This model assumes that the membrane is nonporous (without imperfections). The theory is that transport through the membrane occurs as the molecule of interest dissolves in the membrane and then diffuses through the membrane. This holds true for both the solvent and solute in solution. 

Equation 2 is an analytical statement of the solution-diffusion mqdel of penetrant transport in polymers, which is the most widely accepted explanation of the mechanism of gas permeation in nonporous polymers (75). According to this model, penetrants first dissolve into the upstream (i.e, high pressure) face of Ae film, diffuse through the film, and desorb at the downstream (Le. low pressure) face of the film. Diffusion, the second step, is the rate limiting process in penetrant permeation. As a result, much of the fundamental research related to the development of polymers with improved gas separation properties focuses on manipulation of penetrant diffusion coefficients via systematic modification of polymer chemical structure or superstructure and either chemical or thermal post-treatment of polymer membranes. Many of the fundamental studies recorded in this book describe the results of research projects to explore the linkage between polymer structure, processing history, and small molecule transport properties. 

Peppas and Reinhart have also proposed a model to describe the transport of solutes through highly swollen nonporous polymer membranes [155], In highly swollen networks, one may assume that the diffusional jump length of a solute molecule in the membrane is approximately the same as that in pure solvent. Their model relates the diffusion coefficient in the membrane to solute size as well as to structural parameters such as the degree of swelling and the molecular weight between crosslinks. The final form of the equation by Peppas and Reinhart is... 

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