Kedem-Katchalsky model

Note that this equation is identical to the Kedem-Katchalsky model and does not imply a linear concentration gradient as it is frequently reported. It may be expressed as well as [7,8]... 

There are a number of other models of transport of solvent and solute through a reverse osmosis membrane the Kedem-Katchalsky model, the Spiegler-Kedem model, the frictional model, the finely porous model, the preferential sorption-capUlary flow model, etc. Most of these models have heen reviewed and compared in great detail hy Soltanieh and GiU (1981). We will restrict ourselves in this hook to the solution-diffusion and solution-diffusion-imperfection flux expressions for a number of reasons. First, the form of the solution-diffusion equation is most commonly used and is also functionally equivalent to the preferential sorption-capiUary flow model. Secondly, the solution-diffusion-imperfection model is functionally representative of a number of more exact three-transport-coefficient models, even though the transport coefficients in this model are concentration-dependent... 

Note Here Cj, tt and P correspond to infinitely thin solutions in equilibrium with the local section of the membrane therefore C, is the molar concentration of solute i in a solution of osmotic pressure w.) There are three parameters here Qjj (the intrinsic hydraulic permeability), P (the local solute permeahility coefficient) and <7,- (the local solute reflection coefficient). When these two equations are integrated across a membrane of thickness assuming Qsi, P and <7 to be essentially constant across the membrane thickness, one obtains, for the whole membrane, two equations for the Spiegler-Kedem model (based on the Kedem-Katchalsky 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... 

Kedem- Katchalsky -reverse osmosis models [REVERSE OSMOSIS] (Vol 21)... 

Various treatments of Eqs. (12.5) to (12.8) are proposed in the literature for those cases where charge effects cue negligible (microfiltration, ultrafiltration or nanofiltration of neutral solutes), and low concentrated solutions are considered, i.e. with negligible non-idealities and activities assimilated to concentrations. Most of the time, membrane morphology is just considered through simple parameters such as effective pore size, tortuosity accounting for the effect of fouling on measurable transport properties. A well-known model thus obtained is due to Kedem and Katchalsky [5] ... 

A variety of RO membrane models exist that describe the transport properties of the skin layer. The solution-diffusion model( ) is widely accepted in desalination where the feed solution is relatively dilute on a mole-fraction basis. However, models based on irreversible thermodynamics usually describe membrane behavior more accurately where concentrated solutions are involved.( ) Since high concentrations will be encountered in ethanol enrichment, our present treatment adopts the irreversible thermodynamics model introduced by Kedem and Katchalsky.(7.)... 

In addition to the approach using phenomenological equations for modelling ion transport in soils, the theory of irreversible thermodynamics may be adapted to soils [26], as for the case of ion-exchange membranes. Spiegler [251 and Kedem and Katchalsky [27,28] are the prime examples of this approach to transport models. The detailed review by Verbrugge and Pintauro contains a number of other references to mathematical approaches for modelling the fundamental electrokinetic phenomena. 

The Irreversible Thermodynamics Model (Kedem and Katchalsky (1958)) is founded on coupled transport between solute and solvent and between the different driving forces. The entropy of the system increases and free energy is dissipated, where the free energy dissipation function may be written as a sum of solute and solvent fluxes multiplied by drivir forces. Lv is the hydrodynamic permeability of the membrane, AII v the osmotic pressure difference between membrane wall and permeate, Ls the solute permeability and cms the average solute concentration across the membrane. 

As a model, Kedem and Katchalsky (1963) assumed alternating parallel arrays of elements of the two polymers, the elements being perpendicular to the membrane surface. To satisfy the requirements for ion transport, one polymer must be negatively and the other positively charged. 

In this Section, it is implicitly assumed that the mass transport resistance at the fluid-membrane interface on either side of the membrane is negligible. Also the following is information that is made available publicly by the membrane manufacturers, when not otherwise noted. As in technical processes, mass transport across semipermeable medical membranes is conveniently related to the concentration and pressme driving forces according to irreversible thermodynamics. Hence, for a two-component mixture the solute and solvent capacity to permeate a semipermeable membrane under an applied pressure and concentration gradient across the membrane can be expressed in terms of the following three parameters Lp, hydraulic permeability Pm, diffusive permeability and a, Staverman reflection coefficient (Kedem and Katchalski, 1958). All of them are more accurately measured experimentally because a limited knowledge of membrane stmcture means that theoretical models provide rather inaccurate predictions. 

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