Complementary Method for Deriving Concentration of Diffusing Substance in a Medium for Multi-Dimensional Diffusion

2013 ◽  
Vol 30 (1) ◽  
pp. 29-38
Author(s):  
C.-L. Tsai ◽  
C.-C. Lin ◽  
H.-J. Lee ◽  
C.-H. Wang
Keyword(s):  
Boundary Conditions ◽  
Infinite Medium ◽  
Dimensional Case ◽  
Complementary Method ◽  
Dimensional Diffusion ◽  
Coordinate Direction ◽  
Normalized Solution

ABSTRACTConcentration of a diffusing substance in a medium was derived in various cases of uni-dimensional diffusion, including in a semi-infinite medium and a plate-shaped medium. Multi-dimensional diffusion involves boundary conditions in each coordinate direction. The algorithm dealing with uni-dimensional case becomes very complicated in multi-dimensional cases. This study proposes an algorithm, which is called the complementary method, that combines complementary functions of the normalized solution in uni-dimensional diffusion case by multiplication to solve those in various multi-dimensional diffusion cases with dramatically simplified mathematics. Besides, the complementary method is used to solve various kinds of boundary conditions for multi-dimensional diffusion.

A two-dimensional diffusion model of the Venice lagoon and relative open boundary conditions

1987 ◽  
Vol 37 (1-2) ◽  
pp. 21-45 ◽  
Author(s):  
Camillo Dejak ◽  
Ileana Mazzei Lalatta ◽  
Ettore Messina ◽  
Giovanni Pecenik
Keyword(s):  
Boundary Conditions ◽  
Diffusion Model ◽  
Venice Lagoon ◽  
Open Boundary ◽  
Two Dimensional ◽  
Open Boundary Conditions ◽  
Dimensional Diffusion

Use of Immersed Boundary Method for the Analysis of Electro-Osmotic Flow Generated by a Pair of Cylindrical Electrodes in a Micro-Cavity

2008 ◽  
Author(s):  
Dolfred V. Fernandes ◽  
Sangmo Kang ◽  
Yong K. Suh
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Ionic Concentration ◽  
Ion Concentration ◽  
Dimensional Case ◽  
Immersed Boundary ◽  
Bench Mark ◽  
Step Method ◽  
Fractional Step Method ◽  
Micro Cavity

The bulk motion of an aqueous solution induced by the application of DC electric field is studied numerically. The physical model consists of a micro-cavity with two completely polarizable cylindrical electrodes. The electric double layer (EDL) model coupled with Navier-Stokes equations governing the electroosmotic flow has been described. The Nernst-Planck model uses two extra equations for the prediction of ion concentration. We employed IB (immersed boundary) technique for the implementation of boundary conditions and semi-implicit fractional-step method for solving the governing equations. A new method is described for implementing concentration boundary conditions on the electrodes. The bench mark problems, driven cavity flow and flow over a cylnder were used for the validation of our present code. The numerical results are compared with the analytical results obtained using Gouy-Chapman-Stern model for the one dimensional case. For the two dimensional case the flow field and the ionic concentration distributions obtained shows that the electoosmotic effect is predominant in the thin region around the electrode.

Higher Order Diagonal Padé Schemes for Two-Dimensional Diffusion with Non-local Boundary Conditions

2010 ◽  
Author(s):  
Mohammad Siddique ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Boundary Conditions ◽  
Higher Order ◽  
Two Dimensional ◽  
Local Boundary ◽  
Dimensional Diffusion ◽  
Non Local
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