Macroscopic Banding Pattern of Collagen Gel Formed by a Diffusion-Reaction Process

AbstractA model is developed to understand the morphological stability of a SiC film on a Si substrate during carbonization where the Si substrate is exposed to a carbon precursor. The morphological stability is determined by considering the surface evolution along a slightly wavy film surface and film-substrate interface. The morphological evolution along the film surface is dominated by surface diffusion and along the interface by a chemical reaction. The kinetic analysis shows the stability is controlled by the film surface energy, the interface energy, the diffusion-reaction process of the carbon precursor, and the strain energy. At small wavelengths of the surface profiles, the two types of surface energy dominate, which results in stable morphology. The diffusion-reaction process dictates the surface stability at large wavelengths. The strain energy may cause the surfaces to become unstable at moderate wavelengths; the instability can be completely suppressed by the diffusion-reaction process and the film surface energy, while it is enhanced by a large value of interface energy.

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Exact Solutions for a Diffusion-Reaction Process in One Dimension

Physical Review Letters ◽

10.1103/physrevlett.60.1885.4 ◽

1988 ◽

Vol 60 (18) ◽

pp. 1885-1885 ◽

Cited By ~ 8

Author(s):

John L. Spouge

Keyword(s):

Exact Solutions ◽

Reaction Process ◽

Diffusion Reaction ◽

One Dimension

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Model for a Turbulent Two-Dimensional Diffusion-Reaction Process. Comparison with Growth Phenomena Results

EPL (Europhysics Letters) ◽

10.1209/0295-5075/15/6/003 ◽

1991 ◽

Vol 15 (6) ◽

pp. 579-584 ◽

Cited By ~ 1

Author(s):

G Albinet

Keyword(s):

Reaction Process ◽

Diffusion Reaction ◽

Two Dimensional ◽

Process Comparison ◽

Dimensional Diffusion

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MODELING AN ENZYMATIC DIFFUSION-REACTION PROCESS IN ONE DIMENSIONAL SPACE

IFAC Proceedings Volumes ◽

10.3182/20060920-3-fr-2912.00078 ◽

2006 ◽

Vol 39 (18) ◽

pp. 435-440

Author(s):

J. Santos ◽

E. Castellanos ◽

R. Lozano ◽

A. Friboulet ◽

S. Mondié

Keyword(s):

Dimensional Space ◽

Reaction Process ◽

Diffusion Reaction ◽

One Dimensional

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Probability distribution of the life time of a drift-diffusion-reaction process inside a sphere with applications to transient cathodoluminescence imaging

Monte Carlo Methods and Applications ◽

10.1515/mcma-2018-0007 ◽

2018 ◽

Vol 24 (2) ◽

pp. 79-92 ◽

Cited By ~ 2

Author(s):

Karl K. Sabelfeld ◽

Anastasiya Kireeva

Keyword(s):

Broad Class ◽

Life Time ◽

Stochastic Simulation Algorithm ◽

Reaction Process ◽

Diffusion Reaction ◽

Threading Dislocations ◽

Time Behavior ◽

Drift Diffusion ◽

Robin Boundary ◽

Cathodoluminescence Imaging

Abstract Exact representations for the probability density of the life time and survival probability for a sphere and a disc are derived for a general drift-diffusion-reaction process. Based on these new formulas, we suggest an extremely efficient stochastic simulation algorithm for solving transient cathodoluminescence (CL) problems without any mesh in space and time. The method can be applied to a broad class of drift-diffusion-reaction problems where the time behavior of the absorbed material is of interest. The important advantage of the method suggested is the ability to incorporate local inclusions like dislocations, point defects and other singular folds and complicated structures. General Robin boundary conditions on the boundary are treated in a probabilistic way. The method is tested against exact solutions for a series of examples with bounded and unbounded domains. An application to the dislocation imaging problem, which includes thousand threading dislocations, is given.

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