Steady state in two-dimensional diffusion-controlled reactions

1997 ◽  
Vol 89 (1-2) ◽  
pp. 369-377
Author(s):  
C. A. Condat ◽  
G. J. Sibona ◽  
C. E. Budde
Keyword(s):  
Steady State ◽  
Two Dimensional ◽  
Dimensional Diffusion ◽  
Diffusion Controlled

A Total-Concentration Fixed-Grid Method for Two-Dimensional Diffusion-Controlled Wet Chemical Etching

2005 ◽  
Author(s):  
P. Rath ◽  
J. C. Chai ◽  
H. Y. Zheng ◽  
Y. C. Lam ◽  
V. M. Murukeshan
Keyword(s):  
Chemical Etching ◽  
Total Concentration ◽  
Diffusion Problem ◽  
Two Dimensional ◽  
Concentration Method ◽  
Dimensional Diffusion ◽  
Diffusion Controlled ◽  
Grid Approach ◽  
Wet Chemical ◽  
Wet Chemical Etching

This article presents a total concentration method for two-dimensional wet chemical etching. The proposed procedure is a fixed-grid approach. It is analogous to the enthalpy method used for modeling melting/solidification problems. The governing equation is formulated using the total concentration of the etchant. It includes the reacted and the unreacted concentrations of the etchant. The proposed governing equation includes the interface condition. The reacted concentration is used to capture the etchant-substrate interface implicitly. Since the grids are fixed, a diffusion problem remains a diffusion problem unlike the moving grid approach where the diffusion problem becomes the convection-diffusion problem due to the mesh velocity. For demonstration purposes, the finite volume method is used to solve for the transient concentration distribution of etchant. In this article, two-dimensional diffusion-controlled wet chemical etching processes are modeled. The results obtained from the proposed total concentration method are compared with available “analytic” solutions and solutions from moving-grid approach.

scholarly journals Two dimensional diffusion-controlled triplet–triplet annihilation kinetics

2019 ◽  
Vol 10 (32) ◽  
pp. 7633-7640 ◽  
Author(s):  
Grégoire C. Gschwend ◽  
Morgan Kazmierczak ◽  
Astrid J. Olaya ◽  
Pierre-François Brevet ◽  
Hubert H. Girault
Keyword(s):  
Harmonic Generation ◽  
Second Harmonic ◽  
Molecular Crowding ◽  
Two Dimensional ◽  
Time Resolved ◽  
Dimensional Diffusion ◽  
Diffusion Controlled ◽  
Kinetics Of ◽  
Annihilation Reaction ◽  
Triplet Triplet Annihilation

We show with time-resolved second harmonic generation and molecular mechanics simulations that the kinetics of a two-dimensional triplet–triplet annihilation reaction at the liquid–liquid interface is affected by molecular crowding.

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