Download Modelling and Simulation of Diffusive Processes: Methods and by S.K. Basu, Naveen Kumar PDF
By S.K. Basu, Naveen Kumar
This publication addresses the major matters within the modeling and simulation of diffusive methods from a large spectrum of alternative functions throughout a wide variety of disciplines. positive factors: discusses diffusion and molecular delivery in dwelling cells and suspended sediment in open channels; examines the modeling of peristaltic shipping of nanofluids, and isotachophoretic separation of ionic samples in microfluidics; stories thermal characterization of non-homogeneous media and scale-dependent porous dispersion caused by pace fluctuations; describes the modeling of nitrogen destiny and delivery on the sediment-water interface and groundwater move in unconfined aquifers; investigates two-dimensional solute delivery from a various pulse style element resource and futile cycles in metabolic flux modeling; reports contaminant focus prediction alongside unsteady groundwater stream and modeling synovial fluid circulate in human joints; explores the modeling of soil natural carbon and crop development simulation.
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Extra info for Modelling and Simulation of Diffusive Processes: Methods and Applications
Example text
In the case of a 1-1 electrolyte, where zc = za , we have: D1 = 2 . 40) 20 N. Kumar and S. K. 2 0 b 2 4 6 8 10 12 14 pH Fig. 3 a Effect of surface contact area on release time with pH. 41) where K is an association constant for the diffusing species, which is independent of the size of the aggregate. The total concentration, Cw for weak electrolyte may be written [85] as: Cw = C1 + 2C2 . 42) Using these equations the diffusion equation in terms of one dependent variable, C1 may be written as: 2 ∂ 2 C 2 ∂C1 ∂C ∂C (1 + 4 KC1 ) 1 = ( D1 + 4 KD2 C1 ) 21 + + 4 KD2 1 .
42) Using these equations the diffusion equation in terms of one dependent variable, C1 may be written as: 2 ∂ 2 C 2 ∂C1 ∂C ∂C (1 + 4 KC1 ) 1 = ( D1 + 4 KD2 C1 ) 21 + + 4 KD2 1 . 43) This is a nonlinear partial differential equation. It suggests strong dependence of the apparent diffusion coefficient of the diffusing substance on the ionic or molecular concentration due to significant interactions among the diffusing species. e. D(C ) = D, in spherical coordinate system may be written as: ∂ 2 C 2 ∂C ∂C = D 2 + .
45) where ∆H d and ∆S d are the corresponding enthalpy and entropy terms. ∆H d is generally positive and N d increases with temperature. 46) where ∆Gm , ∆H m , and ∆S m are the free energy, enthalpy, and entropy changes associated with the movement of the atom from the initial equilibrium condition to the activated complex at the top of the potential energy barrier, which the atom has to surmount during the jump to another equilibrium site. 46 represents the vibration frequency and is of the order of 1013 Hertz.