scholarly journals Lattice Model of Diffusion-Limited Bimolecular Chemical Reactions in Confined Environments

2009 ◽  
Vol 102 (21) ◽  
Author(s):  
Jeremy D. Schmit ◽  
Ercan Kamber ◽  
Jané Kondev
Keyword(s):  
Chemical Reactions ◽  
Lattice Model ◽  
Diffusion Limited

Diffusion-Limited Chemical Reactions in a Turbulent Shear Layer

AIAA Journal ◽  
1976 ◽  
Vol 14 (1) ◽  
pp. 70-76 ◽  
Author(s):  
Irwin E. Alber ◽  
Richard G. Batt
Keyword(s):  
Shear Layer ◽  
Chemical Reactions ◽  
Turbulent Shear ◽  
Turbulent Shear Layer ◽  
Diffusion Limited

THOMPSON'S METHOD APPLIED TO DIFFUSION LIMITED CHEMICAL REACTION A+B→0, WITH DIFFERENT INITIAL CONCENTRATIONS OF THE TWO SPECIES

2001 ◽  
Vol 15 (01) ◽  
pp. 33-41 ◽  
Author(s):  
CLÁUDIO NASSIF ◽  
P. R. SILVA
Keyword(s):  
Renormalization Group ◽  
Chemical Reactions ◽  
Chemical Reaction ◽  
Group Method ◽  
Renormalization Group Method ◽  
Rigorous Result ◽  
Stretched Exponential ◽  
Diffusion Limited

In this work we use Thompson's renormalization group method to treat diffusion limited chemical reactions A + B →0 (inert product), with unequal initial concentrations of the two species, by considering ρ A (0)≪ρ B (0). For d≤2, we obtain stretched exponential decaying of the specie A, which is in agreement with rigorous result of Bramson and Lebowitz. For d>2, we obtain simple exponential decaying of the specie A.

Diffusion-limited aggregation

1989 ◽  
Vol 423 (1864) ◽  
pp. 133-148 ◽  
Keyword(s):  
Lattice Model ◽  
Mean Field ◽  
Fractal Dimensionality ◽  
Lattice Diffusion ◽  
Field Theories ◽  
Two Dimensional ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited ◽  
Hypercubic Lattice ◽  
Mean Field Theories

Improved algorithms have been developed for both off-lattice and hypercubic lattice diffusion-limited aggregation (DLA) in dimensionalities ( d ) 3-8 and for two-dimensional off-lattice DLA. In two-dimensional off-lattice DLA a fractal dimensionality ( D ) of about 1.71 was obtained for clusters containing up to 10 6 particles. This is significantly larger than the value of ( d 2 + 1)/( d + 1) (5/3 for d = 2) predicted by mean field theories. For d > 2 the off-lattice simulations give results that are consistent with the mean field theories. For d = 3 and d = 4 the effects of lattice anisotropy can easily be seen for clusters containing 3 x 10 6 and 10 6 sites respectively and the effective fractal dimensionalities are slightly smaller for the lattice model clusters than for the off-lattice clusters. Results are also presented for two-, three- and four- dimensional lattice model clusters with noise reduction.

scholarly journals UNIFIED TREATMENT OF A+B→0 AND A+A→0 CHEMICAL REACTIONS THROUGH THOMPSON'S APPROACH

1999 ◽  
Vol 13 (22n23) ◽  
pp. 829-836 ◽  
Author(s):  
CLÁUDIO NASSIF ◽  
P. R. SILVA
Keyword(s):  
Chemical Reactions ◽  
Mean Field ◽  
Reaction Rates ◽  
Rigorous Results ◽  
Critical Dimensions ◽  
Long Wavelength ◽  
Diffusion Limited ◽  
First Case ◽  
Long Time ◽  
The Mean

In this work we propose an action to describe diffusion limited chemical reactions belonging to various classes of universality. This action is treated through Thompson's approach and can encompass both cases where we have segregation as in the A + B →0 reaction, as well as the simplest one, namely the A + A →0 reaction. Our results for long-time and long-wavelength behaviors of the species concentrations and reaction rates agree with exact results of Peliti for A + A →0 reaction and rigorous results of Bramson and Lebowitz for A + B →0 reaction, with equal initial concentrations. The different classes of universality are reflected by the obtained upper critical dimensions varying continuously from d c =2 in the first case to d c =4 in the last one. Just as at the upper critical dimensions, we find universal logarithmic corrections to the mean field behavior.

scholarly journals Theory for diffusion-limited oscillating chemical reactions

1997 ◽  
Vol 87 (5-6) ◽  
pp. 1165-1178 ◽  
Author(s):  
Harmen J. Bussemaker ◽  
Ricardo Brito
Keyword(s):  
Chemical Reactions ◽  
Diffusion Limited

Surface reactions observed by photoemission electron microscopy (PEEM)

1992 ◽  
Vol 50 (1) ◽  
pp. 286-287
Author(s):  
H.H. Rotermund
Keyword(s):  
Electron Microscopy ◽  
Electron Microscope ◽  
Work Function ◽  
Chemical Reactions ◽  
Reaction Diffusion ◽  
Dynamic Processes ◽  
Clean Surface ◽  
Crystal Surfaces ◽  
Single Crystal Surfaces ◽  
Photoemission Electron

Chemical reactions at a surface will in most cases show a measurable influence on the work function of the clean surface. This change of the work function δφ can be used to image the local distributions of the investigated reaction,.if one of the reacting partners is adsorbed at the surface in form of islands of sufficient size (Δ>0.2μm). These can than be visualized via a photoemission electron microscope (PEEM). Changes of φ as low as 2 meV give already a change in the total intensity of a PEEM picture. To achieve reasonable contrast for an image several 10 meV of δφ are needed. Dynamic processes as surface diffusion of CO or O on single crystal surfaces as well as reaction / diffusion fronts have been observed in real time and space.

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