Membrane theory

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... 

The other class of phenomenological approaches subsumes the random surface theories (Sec. B). These reduce the system to a set of internal surfaces, supposedly filled with amphiphiles, which can be described by an effective interface Hamiltonian. The internal surfaces represent either bilayers or monolayers—bilayers in binary amphiphile—water mixtures, and monolayers in ternary mixtures, where the monolayers are assumed to separate oil domains from water domains. Random surface theories have been formulated on lattices and in the continuum. In the latter case, they are an interesting application of the membrane theories which are studied in many areas of physics, from general statistical field theory to elementary particle physics [26]. Random surface theories for amphiphilic systems have been used to calculate shapes and distributions of vesicles, and phase transitions [27-31]. 

The first step in studying phenomenological theories (Ginzburg-Landau theories and membrane theories) has usually been to minimize the free energy functional of the model. Fluctuations are then included at a later stage, e.g., using Monte Carlo simulations. The latter will be discussed in Sec. V and Chapter 14. 

Before the first indication of the existence of cannabinoid receptors, the prevailing theory on the mechanism of cannabinoid activity was that cannabinoids exert their effects by nonspecific interactions with cell membrane lipids (Makriyannis, 1990). Such interactions can increase the membrane fluidity, perturb the lipid bilayer and concomitantly alter the function of membrane-associated proteins (Loh, 1980). A plethora of experimental evidence suggests that cannabinoids interact with membrane lipids and modify the properties of membranes. However, the relevance of these phenomena to biological activities is still only, at best, correlative. An important conundrum associated with the membrane theories of cannabinoid activity is uncertainty over whether cannabinoids can achieve in vivo membrane concentrations comparable to the relatively high concentrations used in in vitro biophysical studies (Makriyannis, 1995). It may be possible that local high concentrations are attainable under certain physiological circumstances, and, if so, some of the cannabinoid activities may indeed be mediated through membrane perturbation. 

Burggraaf A.J. (1999) Single gas permeation of thin zeolite (MFI) membranes theory and analysis of... 

At the same time (1902), a membrane theory was proposed for the electrical properties of cells and tissues by Overton [80] and Bernstein [8], whose principles remain valid to the present day. 

This volume is the result of a symposium honoring Drs. Sidney Loeb and S. Sourirajan on the 20th anniversary of their discovery of the first functionally useful reverse osmosis membrane. Both of these esteemed gentlemen participated as plenary speakers and described not only how their membrane originated but also reviewed membrane theory and put the membrane field into present and future perspective. 

Various theories have been proposed to describe the transport in all of these types of polymer membranes. Theories for macroporous and microporous membranes have been based on hydrodynamic and frictional considerations while those for nonporous gels have been based on Eyring s theory and use a free volume approach to describe the movement of solute through the mesh of the polymer. 

Dorling, J. (1969) The dimensionality of time. American Journal of Physics. 38 539 2. Duff, M. (1998) The theory formerly known as strings. Scientific American. February, 278(2) 64-69. (Discusses membrane theory.)... 

Tien, H. T. Bimolecular Lipid Membranes, Theory and Practice , Dekker, M., New York, 1974... 

Reverse Osmosis and Synthetic Membranes. Theory-Technology-Engineering Edited by Sourirajan, S., National Research Council, Canada (1977)... 

The equilibrium equations of a hyperboloid of revolution used for cooling towers derived by using membrane theory under an arbitrary static normal load are reduced to a single partial differential equation with constant coefficients. The problem of finding displacements is reduced to a similar type of equation so that the solution for this problem becomes straightforward. 11 refs, cited. 

Finkelstein, A. (1987). In Water Movement through Lipid Bilayers, Pores and Plasma Membranes, Theory and Reality. Wiley, New York. 

Sten-Knudsen O. Biological Membranes Theory of Transport, Potentials and Electric Impulses. 2002. Cambridge University Press, Cambridge, UK. 

A. Finkelstein, Water Movement Through Lipid Bilayers, Pores, and Plasma Membranes Theory and Reality, Wiley-Interscience, New York, 1987. 

Noble RD and Way ID Eds. Liquid Membranes. Theory and Applications. ACS symposium series 347, ACS, Washington DC 1987. Strzelbicki J and Schlosser S. Influence of surface-active substances on pertraction of cobalt(II) cations through bulk and emulsion liquid membranes. Hydrometallurgy, 1989 23(1) 67-75. 

Noble, R.D. and Way, J.D., Liquid membrane Theory and Applications, ACS Symposium Series No. 347, American Chemical Society, Washington, DC, 1987. 

Tzlil, S., Ben-Shaul, A. Flexible charged macromolecules on mixed fluid lipid membranes Theory and Monte-Carlo simulations. Biophys. J. 2004, 89, 2972-87. 

R. Mellis, W.N. Gill and G. Belford, Fluid d)mamics in a tubular membrane theory and experiment. Chem. Eng. Commun., 122 (1993) 103. 

Rozelle, L.T. Cadotte, J.E. Cobian, K.E. Kopp, C.V., Jr. Nonpolysaccharide membranes for reverse osmosis NS-lOO membranes. In Reverse Osmosis and Synthetic Membranes, Theory—Technology— Engineering , Sourirajan, S., Ed. National Research Council of Canada Ottawa, 1977 249-261. 

Bartsch, R.A. Charewicz, W.A. Kang, S.I. Walkowiak, W. Proton-coupled transport of alkali metal cations across liquid membranes by ionizable crown ethers. In Liquid Membranes Theory and Applications Noble, R.D., Way, J.D., Eds. ACS Symp. Ser. No. 347 American Chemical Society Washington, D.C., 1987 86-97. 

Because of this the Donnan membrane theory states that the activity quotient inside the gel and outside the gel are equal at equilibrium. In mathematical terms then, the following equation is true ... 

Equation 4-36 is for membrane shells with a negligible thickness. As the pressure and the shell thickness increase, the stress distribution across the thickness is non-uniform. Therefore, some correction to the membrane theory is required. The modified code equation as given by the ASME Unfired Pressure Code, Section VIII, Division 1 is ... 

Majumdar S, Sirkar KK. HoUow-fiber contained liquid membrane. Theory. In Ho WSW, Sirkar KK, eds. Membrane Handbook. Van Nostrand Reinhold, New York, NY, 1992 777-796. 

Noble, R. D., Way, J. D. (1987). Liquid Membranes Theory and Applications, ACS Symp. Ser. American Chemical Society, Washington, D.C. 

The Donnan membrane theory was developed in 1911 to explain the unequal diflusion of ions across a semipermeable membrane and is accepted as a reasonable explanation of the exchange mechanism for the organic type resins. The solution-bead surface interface is deemed to be similar to the membrane in the Donnan theoiy. 

Refer to the description of the Donnen membrane theory presented in Chapter 23, p. 273. Use the resin in the K form. Let C Figure 25-8. Organic acid standards by ion be the concentration of salt in the sample outside of the resin, and exclusion. 

---