Diffusion-controlled growth of multi-component gas bubbles

1987 ◽  
Vol 22 (3) ◽  
pp. 919-924 ◽  
Author(s):  
M. Cable ◽  
J. R. Frade
Keyword(s):  
Gas Bubbles ◽  
Controlled Growth ◽  
Diffusion Controlled

The influence of surface tension on the diffusion-controlled growth or dissolution of spherical gas bubbles

1988 ◽  
Vol 420 (1859) ◽  
pp. 247-265 ◽  
Keyword(s):  
Surface Tension ◽  
Analytical Solutions ◽  
Spherical Symmetry ◽  
Gas Bubbles ◽  
Solute Concentration ◽  
Numerical Results ◽  
Controlled Growth ◽  
Saturation Parameter ◽  
Interfacial Concentration ◽  
Diffusion Controlled

Surface tension can markedly affect the growth or dissolution of small gas bubbles but, even when spherical symmetry is maintained and the interfacial concentration assumed constant, generally valid analytical solutions for the change of size with time cannot be obtained; approximations of limited validity are therefore often used. However, accurate and efficient methods for computing the diffusion-controlled growth or dissolution of spheres in such conditions have recently been developed; the results obtained when interfacial solute concentration is assumed constant have been published and validated by comparing them, where possible, with the equivalent analytical solutions. This paper extends that work to include the effects of a constant surface tension, for both Henry’s and Sievert’s laws. The numerical results are valid for as wide a range of parameters as is likely to be needed and are compared with the few analytical solutions available for particular cases. It is shown that, when surface tension is introduced, a complete description of the problem requires an additional saturation parameter as well as the dimensionless surface tension. It is also shown that Henry’s and Sievert’s laws can have very different effects on dissolving bubbles: when Sievert’s law applies a higher surface tension can increase time for a bubble to dissolve but this paradox can be resolved by examining the competing effects involved.

Suppression of vigorous liquid Sn/Te reactions by Sn–Cu solder alloys

2008 ◽  
Vol 23 (12) ◽  
pp. 3303-3308 ◽  
Author(s):  
Chien-Neng Liao ◽  
Ching-Hua Lee
Keyword(s):  
Reaction Time ◽  
Layered Structure ◽  
Controlled Growth ◽  
Square Root ◽  
Solder Alloys ◽  
Cu Content ◽  
Cu Alloys ◽  
Diffusion Controlled ◽  
Morphology Changes

Reactions of molten Sn–xCu (x = 0.05 to 1.0) alloys with Te substrate at 250 °C were investigated. A dosage of 0.1 wt% Cu in Sn is found to be effective in suppressing the vigorous Sn/Te reaction by forming a thin CuTe at the solder/Te interface. The CuTe morphology changes from irregular clusters into a layered structure with increasing Cu content in Sn. With the same reaction time, the CuTe thickness increases proportionally to the square root of Cu content in Sn–Cu alloys, suggesting a diffusion-controlled growth for CuTe.

Modeling the Diffusion-Controlled Growth of Needle and Plate-Shaped Precipitates

2002 ◽  
Vol 731 ◽  
Author(s):  
Z. Guo ◽  
W. Sha
Keyword(s):  
Free Energy ◽  
Transformation Strain ◽  
Interfacial Free Energy ◽  
Growth Theory ◽  
Controlled Growth ◽  
Precipitate Morphology ◽  
Interface Kinetics ◽  
Diffusion Controlled ◽  
Precipitate Growth ◽  
Strain Stress

AbstractVarious theories have been developed to describe the diffusion-controlled growth of precipitates with shapes approximating needles or plates. The most comprehensive one is due to Ivantsov, Horvay and Cahn, and Trivedi (HIT theory), where all the factors that may influence the precipitate growth, i.e. diffusion, interface kinetics and capillarity, are accounted for within one equation. However, HIT theory was developed based on assumptions that transformation strain/stress and interfacial free energy are isotropic, which are not true in most of the real systems. An improved growth theory of precipitates of needle and plate shapes was developed in the present study. A new concept, the compression ratio, was introduced to account for influences from the anisotropy of transformation strain/stress and interfacial free energy on the precipitate morphology. Experimental evidence supports such compression effect. Precipitate growth kinetics were quantified using this concept. The improved HIT theory (IHIT theory) was then applied to study the growth of Widmanstatten austenite in ferrite in Fe-C-Mn steels. The calculated results agree well with the experimental observations.

Refinement of Size Distributions for Primary Crystallizations

1997 ◽  
Vol 481 ◽  
Author(s):  
E. Pineda ◽  
T. Pradell ◽  
D. Crespo ◽  
N. Clavaguera ◽  
J. ZHU ◽  
...  
Keyword(s):  
Grain Size ◽  
Metastable Phase ◽  
Primary Crystallization ◽  
Controlled Growth ◽  
Diffusion Controlled ◽  
Average Grain Size ◽  
Soft Impingement ◽  
Single Grain ◽  
Kinetics Of ◽  
And Diffusion

ABSTRACTThe microstructure developed in primary crystallizations is studied under realistic conditions. The primary crystallization of an amorphous alloy is modeled by considering the thermodynamics of a metastable phase transition and the kinetics of nucleation and crystal growth under isothermal annealing. A realistic growth rate, including an interface controlled growth at the beginning of the growth of each single grain and diffusion controlled growth process with soft impingement afterwards is considered. The reduction in the nucleation rate due to the compositional change in the remaining amorphous matrix is also taken into account. The microstructures developed during the transformation are obtained by using the Populational KJMA method, from the above thermodynamic and kinetic factors. Experimental data of transformed fraction, grain density, average grain size, grain size distribution and other related parameters obtained from annealed metallic glasses are modeled.

scholarly journals Ringwoodite rim around olivine core in shock-induced melt-vein of GRV 022321 chondrite: Transformation kinetics of olivine to ringwoodite

2021 ◽  
Author(s):  
Zhidong Xie ◽  
Thomas G. Sharp ◽  
Shuhao Zuo ◽  
Xiaochun Li
Keyword(s):  
Electron Microscopy ◽  
Raman Spectroscopy ◽  
Natural Occurrence ◽  
Controlled Growth ◽  
Rock Fragments ◽  
Nano Crystalline ◽  
Diffusion Controlled ◽  
State Diffusion ◽  
Crystallite Sizes ◽  
Electron Imaging

Abstract Here we report the natural occurrence of the ringwoodite rims around olivine cores in shock-induced melt veins of the Antarctic chondrite GRV 022321. Electron microprobe analysis (EMPA), Raman spectroscopy, Scanning electron microscopy (SEM) and Transmission electron microscopy (TEM) were used to examine the sample to better elucidate the mechanisms of transformation of the olivine to ringwoodite and Fe-Mg partitioning in olivine under the shock. The GRV 022321 is an L6 chondrite with a network of black veins enclosing abundant olivine host-rock fragments. Some of the enclosed fragments ranging from 5 µm to 100 µm in size have bright rims up to 20 µm wide, and a dark core under reflected light and backscatter electron imaging. Raman spectroscopy reveals that rims are made of ringwoodite, and cores are predominantly olivine. EMPA data show the ringwoodites in rims are richer in Fe (Fa46) than the olivine cores (Fa10-Fa23). The olivine cores have variable contrast in BSE images with the heterogeneities in fayalite content (Fa10 to Fa23) and a branching network of low-Fa olivine. FIB-TEM observations reveal that the ringwoodite rims are polycrystalline with crystallite sizes from 200 nm to 800 nm, while the olivine cores are also polycrystalline, but with smaller crystallites from 100 nm to 200 nm. Based on observation, we conclude that the original Fa23 olivine transformed to Fa10 olivine and Fa46 ringwoodite by a solid-state diffusion-controlled growth mechanism during shock, and the branching network of low-Fa olivine acted as long-range(up to 10µm)high-diffusion pathways for grain-boundary Fe-Mg interdiffusion through highly deformed nano-crystalline olivine to accommodate the diffusion-controlled growth of ringwoodite.

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