Modification of the Matalon–Packter Law for Self-Organized Periodic Precipitation Patterns by Incorporating Time-Dependent Diffusion Flux

2021 ◽  
Author(s):  
Masaki Itatani ◽  
Qing Fang ◽  
Hideki Nabika
Keyword(s):  
Diffusion Flux ◽  
Time Dependent ◽  
Periodic Precipitation ◽  
Precipitation Patterns ◽  
Self Organized

Gravity Effect on the Formation of Periodic Precipitation Patterns

2000 ◽  
Vol 65 (9) ◽  
pp. 1438-1442 ◽  
Author(s):  
Vladislav Holba ◽  
Frederik Fusek
Keyword(s):  
Gravitational Field ◽  
Spatial Arrangement ◽  
Experimental Results ◽  
Single Sample ◽  
Gravity Effect ◽  
Periodic Precipitation ◽  
Precipitation Patterns ◽  
Liesegang Bands

The effect of gravity on the formation of Liesegang patterns of Ag2Cr2O7in gelatin and that of PbI2in agar was investigated. Spatial arrangement of Liesegang bands was measured in the parallel and antiparallel orientation to the gravitational field in a single sample with all other parameters kept fixed. The experimental results are discussed in terms of the prenucleation theory of periodic precipitation.

Independence of Primary and Secondary Structures in Periodic Precipitation Patterns

2011 ◽  
Vol 2 (4) ◽  
pp. 345-349 ◽  
Author(s):  
Stoyan K. Smoukov ◽  
István Lagzi ◽  
Bartosz A. Grzybowski
Keyword(s):  
Secondary Structures ◽  
Periodic Precipitation ◽  
Precipitation Patterns

Wet Stamping of Microscale Periodic Precipitation Patterns

2005 ◽  
Vol 109 (7) ◽  
pp. 2774-2778 ◽  
Author(s):  
I. T. Bensemann ◽  
M. Fialkowski ◽  
B. A. Grzybowski
Keyword(s):  
Periodic Precipitation ◽  
Precipitation Patterns

Curiosities in Periodic Precipitation Patterns

Science ◽  
1982 ◽  
Vol 216 (4546) ◽  
pp. 635-637 ◽  
Author(s):  
S. C. MULLER ◽  
S. KAI ◽  
J. ROSS
Keyword(s):  
Periodic Precipitation ◽  
Precipitation Patterns

scholarly journals Landslides, sandpiles, and self-organized criticality

2003 ◽  
Vol 3 (6) ◽  
pp. 505-514 ◽  
Author(s):  
S. Hergarten
Keyword(s):  
Time Dependent ◽  
Mass Movements ◽  
Size Distributions ◽  
Triggering Mechanism ◽  
Self Organized ◽  
Long Time ◽  
Self Organized Criticality ◽  
Relationship Of ◽  
Power Law Distributions

Abstract. Power-law distributions of landslides and rockfalls observed under various conditions suggest a relationship of mass movements to self-organized criticality (SOC). The exponents of the distributions show a considerable variability, but neither a unique correlation to the geological or climatic situation nor to the triggering mechanism has been found. Comparing the observed size distributions with models of SOC may help to understand the origin of the variation in the exponent and finally help to distinguish the governing components in long-term landslide dynamics. However, the three most widespread SOC models either overestimate the number of large events drastically or cannot be consistently related to the physics of mass movements. Introducing the process of time-dependent weakening on a long time scale brings the results closer to the observed statistics, so that time-dependent weakening may play a major part in the long-term dynamics of mass movements.

Numerical predictions of carburisation and crack evolution using a combined diffusion rate and remaining multi-axial creep ductility damage model

2016 ◽  
Vol 26 (6) ◽  
pp. 859-880 ◽  
Author(s):  
Farid R Biglari ◽  
Kamran M Nikbin
Keyword(s):  
Linear Time ◽  
Diffusion Flux ◽  
Damage Model ◽  
Surface Oxidation ◽  
Time Dependent ◽  
Intergranular Cracking ◽  
Creep Ductility ◽  
Mesh Structure ◽  
Numerical Predictions ◽  
Crack Growth Model

A novel numerical damage model has been developed to combine Fick’s second law of diffusivity with microstructure modelling of environmentally assisted creep damage. The environmental acceleration of material degradation has been modelled and compared with experimental observations. The combined multi-site damage and crack growth model for creep and environmentally assisted time-dependent material oxidation/carburisation based on a gas/solid interface diffusion and non-linear time-dependent creep mechanism is proposed. Numerical predictions are presented to develop a methodology for component lifing. The model allows for the development of a hardened layer due to surface oxidation and predicts damage and cracking during subsequent creep under an applied load. The simulated grain mesh structure used can replicate surface healing or diffuse intergranular cracking and material depletion emanating from the gas/solid surface interface by quantifying the strength ratios between grain and grain boundaries. In this article, oxidation/carburisation is estimated both analytically and numerically using Fick’s diffusion laws and carbon/steel diffusion flux properties available in the literature. It is also shown that carbon diffusion distribution can be related to grain hardening due to carburisation as well as grain/grain boundary strength ratios which could vary as much as a factor of 0.5. The model is validated by comparing with actual oxidation/carburisation data for the long-term oxidised 9-12 Cr steels operating at high temperatures. Finally, it is shown that the mode and rate of surface oxidation and hardening, depending on whether the material is homogenous or contains micro-cracks substantially affects the life time of a component under high temperature creep loading.

Periodic Precipitation Patterns during Coalescence of Reacting Sessile Droplets

Langmuir ◽  
2015 ◽  
Vol 31 (42) ◽  
pp. 11484-11490 ◽  
Author(s):  
Marie Jehannin ◽  
Sophie Charton ◽  
Stefan Karpitschka ◽  
Thomas Zemb ◽  
Helmuth Möhwald ◽  
...  
Keyword(s):  
Periodic Precipitation ◽  
Precipitation Patterns
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