Osmosis modeling

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... 

Reverse osmosis membrane process, 27 637 Reverse osmosis membrane cleaning citric acid application, 6 647 Reverse-osmosis membranes, 75 811, 825 development of, 75 797 Reverse osmosis models, 27 638-639 Reverse osmosis permeators, 76 19 Reverse osmosis seawater desalination process, 26 85 Reverse osmosis systems blending in, 26 80-81 brackish and nanofiltration, 26 80-83 Reverse osmosis technology... 

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

Phillip, W.A., Yong, J.S. Elimelech, M. (2010) Reverse draw solute permeation in forward osmosis modeling and experiments. Environmental Science Technology, 44 (13), 5170-5176. 

Transport Models. Many mechanistic and mathematical models have been proposed to describe reverse osmosis membranes. Some of these descriptions rely on relatively simple concepts others are far more complex and require sophisticated solution techniques. Models that adequately describe the performance of RO membranes are important to the design of RO processes. Models that predict separation characteristics also minimize the number of experiments that must be performed to describe a particular system. Excellent reviews of membrane transport models and mechanisms are available (9,14,25-29). 

Given the first type of simulation, it is advantageous to be able to design a system of RO modules that can achieve the process objective at a minimal cost. A model has been iategrated iato a process simulation program to predict the stream matrix for a reverse osmosis process (132). In the area of waste minimization, the proper placement of RO modules is essential for achieving minimum waste at a minimum cost. Excellent details on how to create an optimal network of RO modules is available (96). 

H. Mehdizadeh, "Modeling of Transport Phenomena in Reverse Osmosis Membranes," dissertation, McMaster University, Hamilton, Ont., Canada, 1990. 

J. Siler, "Reverse Osmosis Membranes-Concentration Polarization and Surface Fouling Predictive Models and Experimental Verifications," dissertation. University of Kentucky, Lexington, Ky., 1987. 

Ultrafiltration separations range from ca 1 to 100 nm. Above ca 50 nm, the process is often known as microfiltration. Transport through ultrafiltration and microfiltration membranes is described by pore-flow models. Below ca 2 nm, interactions between the membrane material and the solute and solvent become significant. That process, called reverse osmosis or hyperfiltration, is best described by solution—diffusion mechanisms. 

Over the past three decades, there has been a growing industrial interest in using reverse osmosis for several objectives such as water purification and demineralization as well as environmental plications (e.g.. Comb, 1994 Rorech and Bond, 1993, El-Halwagi, 1992). The first step in designing the system is to understand the operating principles and modeling of RO modules. 

Soltanieh, M., and Gill, W. N. (1984). An experimental study of the complete mixing model for radial flow hollow fiber reverse osmosis systems. Desalination, 49, 57-88. 

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... 

Irreversible thermodynamics has also been used sometimes to explain reverse osmosis [14,15]. If it can be assumed that the thermodynamic forces responsible for reverse osmosis are sufficiently small, then a linear relationship will exist between the forces and the fluxes in the system, with the coefficients of proportionality then referred to as the phenomenological coefficients. These coefficients are generally notoriously difficult to obtain, although some progress has been made recently using approaches such as cell models [15]. 

The simulations to investigate electro-osmosis were carried out using the molecular dynamics method of Murad and Powles [22] described earher. For nonionic polar fluids the solvent molecule was modeled as a rigid homo-nuclear diatomic with charges q and —q on the two active LJ sites. The solute molecules were modeled as spherical LJ particles [26], as were the molecules that constituted the single molecular layer membrane. The effect of uniform external fields with directions either perpendicular to the membrane or along the diagonal direction (i.e. Ex = Ey = E ) was monitored. The simulation system is shown in Fig. 2. The density profiles, mean squared displacement, and movement of the solvent molecules across the membrane were examined, with and without an external held, to establish whether electro-osmosis can take place in polar systems. The results clearly estab-hshed that electro-osmosis can indeed take place in such solutions. 

C. S. Slatter, C. A. Brooks. Development of a simulation model predicting performance of reverse osmosis batch systems. Sep Sci Tech 27 1361, 1992. 

H. Mehdizadeh, J. M. Dickson. Theoretical modifications of the finely porous model for reverse osmosis. J Appl Polym Sci 42 1143, 1991. 

A. E. Yaroshchuk, S. S. Durkhin. Phenomenological theory of reverse osmosis in macroscopically homogeneous membranes and its specification for the capillary charged model. J Memb Sci 79 133, 1993. 

This can be further integrated from the wall to the boundary layer thickness y = 8, where the component is at the bulk concentration Cj,. Substituting / = - o and k = D/o, the mass-transfer coefficient yields the stagnant film model [Brian, Desalination by Reverse Osmosis, Merten (ed.), M.I.T. Press, Cambridge, Mass., 1966, pp. 161-292] ... 

In the pharmaceutical sciences, the nonequilibrium thermodynamics approach has been particularly important in the design of osmotic drug delivery devices, as discussed in Chapter 11. It has also been used to describe the convective transport of a binding antibody in an in vitro model of a solid tumor [8], As our appreciation of the roles of convection and osmosis in drug delivery increases, the nonequilibrium thermodynamics approach may find wider appeal. 

The nature of the plant material subjected to osmotic dehydration is the key point for both modeling and optimizing the osmosis in itself and as a pretreatment to further processing. The same osmotic medium, applied to different raw materials, under identical process conditions causes substantially different rates of dehydration and solute uptake. Data on these findings were reviewed previously (Lazarides et al., 1999 Torreggiani, 1995) and have been confirmed by recent research. 

Landau-Fermi liquid, 23 840 Landau quasiparticle model, 23 840 Land cost, 9 527 Landering, 8 438-439 Land-farming, 3 768 defined, 3 759t Landfill gas, 25 880 Landfill leachate treatment, reverse osmosis in, 21 646-647 Landfill liners, 25 877-878... 

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

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