Modeling of separation of aqueous solutions of FeCl3 and AlCl3 by zeolite–clay composite membranes using a space-charge model

2004 ◽  
Vol 274 (1) ◽  
pp. 204-215 ◽  
Author(s):  
Anupam Shukla ◽  
Anil Kumar
Keyword(s):  
Aqueous Solutions ◽  
Space Charge ◽  
Composite Membranes ◽  
Charge Model ◽  
Space Charge Model

An application of the space charge model to the electrolyte conductivity inside a charged microporous membrane

1999 ◽  
Vol 161 (1-2) ◽  
pp. 275-285 ◽  
Author(s):  
Anthony Szymczyk ◽  
P. Fievet ◽  
B. Aoubiza ◽  
C. Simon ◽  
J. Pagetti
Keyword(s):  
Space Charge ◽  
Microporous Membrane ◽  
Electrolyte Conductivity ◽  
Charge Model ◽  
Space Charge Model

scholarly journals The quantum zero space charge model for semiconductors

1999 ◽  
Vol 10 (4) ◽  
pp. 395-415 ◽  
Author(s):  
A. UNTERREITER
Keyword(s):  
Space Charge ◽  
Debye Length ◽  
Doping Profile ◽  
Quantum Model ◽  
Compatibility Conditions ◽  
Thermal Equilibrium State ◽  
Quantum Fluid ◽  
Charge Model ◽  
Differential Algebraic System ◽  
Space Charge Model

The thermal equilibrium state of a bipolar, isothermal quantum fluid confined to a bounded domain Ω⊂ℝd, d = 1, 2 or d = 3 is the minimizer of the total energy [Escr ]ελ; [Escr ]ελ involves the squares of the scaled Planck's constant ε and the scaled minimal Debye length λ. In applications one frequently has λ2[Lt ]1. In these cases the zero-space-charge approximation is rigorously justified. As λ → 0, the particle densities converge to the minimizer of a limiting quantum zero-space-charge functional exactly in those cases where the doping profile satisfies some compatibility conditions. Under natural additional assumptions on the internal energies one gets an differential-algebraic system for the limiting (λ = 0) particle densities, namely the quantum zero-space-charge model. The analysis of the subsequent limit ε → 0 exhibits the importance of quantum gaps. The semiclassical zero-space-charge model is, for small ε, a reasonable approximation of the quantum model if and only if the quantum gap vanishes. The simultaneous limit ε = λ → 0 is analyzed.

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