Effects of Bubble Growth and Solidification Rate on Pore Formation in Solid

2012 ◽  
Author(s):  
P. S. Wei ◽  
S. Y. Hsiao
Keyword(s):  
Growth Rate ◽  
Contact Angle ◽  
Solidification Front ◽  
Bubble Growth ◽  
Pore Formation ◽  
Solidification Rate ◽  
Bubble Radius ◽  
Abel Equation ◽  
Spherical Cap ◽  
Factors Affecting

The shapes of a pore in solid resulted from entrapment of a tiny bubble by a solidification front are predicted in this work. Pore formation and its shape in solid are one of the most critical factors affecting properties and microstructure, in materials. For simplicity without loss of generality, the tiny bubble is considered to have a spherical cap. From a geometrical analysis, the contact angle of the bubble cap on the solidification front or the pore shape in solid is found to be governed by the Abel equation of the first kind. The pore becomes closed by imposing a finite bubble growth rate-to-solidification rate ratio which can produce a minimal bubble radius at the contact angle of 90 degrees. Closure of a pore resulted from a greater solidification rate than bubble growth rate, as accepted in the literature, is incorrect.

Zero Dimensional Model for the Growth of Heterogeneous Gas Bubbles

2006 ◽  
Author(s):  
Hatem M. Wasfy ◽  
Tamer M. Wasfy
Keyword(s):  
Contact Angle ◽  
Bubble Growth ◽  
Growth Stage ◽  
Bubble Radius ◽  
Wait Time ◽  
Contact Radius ◽  
Ambient Conditions ◽  
Spherical Cap ◽  
Second Stage ◽  
The Third

A zero dimensional energy based model for heterogeneous gas bubble growth from conical surface pits is presented. The spherical cap bubble growth is divided into 3 stages. In the first stage, the bubble is within the surface pit. In the second stage, the bubble is anchored to the circular opening of the surface cavity and the apparent bubble contact angle decreases while the bubble's contact radius remains the same. The third growth stage starts when the apparent contact angle becomes the same as the contact angle under the ambient conditions. In the third growth stage, the contact radius increases while the contact angle remains constant. The predicted bubble radius versus time since the detachment of the previous bubble was found to be in good agreement with published experimental data for CO2 bubbles growing in water. The long wait time observed in the experiments before a measurable bubble appears after the detachment of the previous bubble was also calculated.

Acoustic Cavitation Behavior in Isopropyl Alcohol Added Cleaning Solution

2012 ◽  
Vol 195 ◽  
pp. 169-172
Author(s):  
Bong Kyun Kang ◽  
Ji Hyun Jeong ◽  
Min Su Kim ◽  
Hong Seong Sohn ◽  
Ahmed A. Busnaina ◽  
...  
Keyword(s):  
Growth Rate ◽  
Physical Properties ◽  
Bubble Growth ◽  
Bubble Collapse ◽  
Particle Removal ◽  
Factors Affecting ◽  
Ultrasound Field ◽  
Cavitation Threshold ◽  
The Difference ◽  
Cavitation Behavior

As the semiconductor manufacturing technology for ultra-high integration devices continue to shrink beyond 32 nm, stringent measures have to be taken to get damage free patterns during the cleaning process. The patterns are no longer cleaned with the megasonic (MS) irradiation in the advanced device node because of severe pattern damages caused by cleaning. Recently, several investigations are carried out to control the cavitation effects of megasonic to reduce the pattern damages. The mechanism of damage caused by an unstable acoustic bubble motion was mainly attributed to the high sound pressure associated with violent bubble collapse [1]. In order to characterize the dominant factors affecting the cavitation, MS cleaning was conducted with various dissolved gas concentrations in water. It was reported that the cavitation phenomena relating to particle removal efficiency (PRE) and pattern damage were considerably changed with the addition of a specific gas [2]. This changing behavior may be due to the difference in the physical properties of dissolved gases associated with acoustic bubble growth rate as a function of their concentration. In particular, cavitation effects induced during MS cleaning was controlled by adjusting the acoustic bubble growth rate. Also the change of bubble growth rate is well explained by both rectified diffusion for single bubble and bubble coalescence for multi-bubble, respectively. Similarly, it is well-known that surface active solute (SAS) in the ultrasound field plays an important role in controlling the cavitation effects. A detailed explanation of the acoustic bubble growth rate, cavitation threshold and their relationship with various types of SAS and concentration of biomedical and chemical reactions perspective have been reported elsewhere [3,4]. Their studies demonstrated that the change of cavitation effects depends not only on the chain length of alcohol in the solution but also on the physical properties such as surface tension and viscosity of SAS solutions.

The quasi-static growth of CO2 bubbles

2014 ◽  
Vol 741 ◽  
Author(s):  
Oscar R. Enríquez ◽  
Chao Sun ◽  
Detlef Lohse ◽  
Andrea Prosperetti ◽  
Devaraj van der Meer
Keyword(s):  
Boundary Layer ◽  
Growth Rate ◽  
Early Phase ◽  
Bubble Growth ◽  
Bubble Radius ◽  
Combined Effects ◽  
Gas Bubble ◽  
Final Phase ◽  
Concentration Boundary ◽  
Bubble Detachment

AbstractWe study experimentally the growth of an isolated gas bubble in a slightly supersaturated water–CO2 solution at 6 atm pressure. In contrast to what was found in previous experiments at higher supersaturation, the time evolution of the bubble radius differs noticeably from existing theoretical solutions. We trace the differences back to several combined effects of the concentration boundary layer around the bubble, which we disentangle in this work. In the early phase, the interaction with the surface on which the bubble grows slows down the process. In contrast, in the final phase, before bubble detachment, the growth rate is enhanced by the onset of density-driven convection. We also show that the bubble growth is affected by prior growth and detachment events, though they are up to 15 min apart.

Quantification of a Single Gas Bubble Growth in Solvent(s)–CO2–Heavy Oil Systems With Consideration of Multicomponent Diffusion Under Nonequilibrium Conditions

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Yu Shi ◽  
Daoyong Yang
Keyword(s):  
Growth Rate ◽  
Heavy Oil ◽  
Bubble Growth ◽  
Bubble Radius ◽  
Motion Equation ◽  
Liquid Volume ◽  
Gas Bubble ◽  
Viscous Term ◽  
Proposed Model ◽  
Nonequilibrium Conditions

A mechanistic model has been developed and validated to quantify a single gas bubble growth with considering multicomponent gas diffusion in solvent(s)–CO2–heavy oil systems under nonequilibrium conditions. Experimentally, constant-composition expansion (CCE) experiments are conducted for C3H8–CO2–heavy oil systems under equilibrium and nonequilibrium conditions, respectively. Theoretically, the classic continuity equation, motion equation, diffusion–convection equation, real gas equation, and Peng–Robinson equation of state (PR EOS) are integrated into an equation matrix to dynamically predict gas bubble growth. Also, the viscous term of motion equation on the gas phase pressure is included due mainly to the viscous nature of heavy oil. The newly proposed model has been validated by using the experimentally measured gas bubble radius as a function of time with good accuracy. Combining with the experimental measurements, the critical nucleus radius and gas bubble growth are quantitatively predicted with the newly proposed model. Effects of mass transfer, supersaturation pressure, mole concentration of each component, liquid cell radius, and pressure decline rate on the gas bubble growth are examined and analyzed. In general, gas bubble growth rate is found to increase with an increase of each of the aforementioned five parameters though the contribution of individual component in a gas mixture to the bubble growth rate is different. A one-step pressure drop and the unlimited liquid volume surrounding a gas bubble are considered to be the necessary conditions to generate the linear relationship between gas bubble radius and the square root of time.

Existence of Universal Phase Diagrams for Describing General Pore Shape Resulting From an Entrapped Bubble During Solidification

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
P. S. Wei ◽  
C. C. Chang
Keyword(s):  
Climate Change ◽  
Contact Angle ◽  
Phase Diagrams ◽  
Pore Formation ◽  
Solidification Rate ◽  
Pore Shape ◽  
Coordinate Systems ◽  
General Development ◽  
Base Radius ◽  
Dimensionless Coordinate

This study shows that there exist a pair of universal and unique phase diagrams to describe general development of the pore shape in solid, resulting from a bubble captured by a solidification front. Like thermodynamics, phase diagrams have advantages to generally identify the states and design processes of a system. Pore formation and its shape in solids influence not only microstructure of materials but also contemporary issues of biology, engineering, foods, geophysics, and climate change, etc. In this study, a pair of phase diagrams is thus found to be under dimensionless coordinate systems of dimensionless apex radius, contact angle, and base radius of the bubble cap, as well as solidification rate, contact angle, and growth rate of base radius. The computed results of the development of the pore shape agree with experimental data. The pore shape in solid thus can be optimistically predicted and controlled by choosing a desired path on phase diagrams.

Prediction Model for Bubble Contact Circle Diameter on Heating Wall

2010 ◽  
Author(s):  
De-qi Chen ◽  
Liang-ming Pan
Keyword(s):  
Experimental Data ◽  
Growth Rate ◽  
Bubble Growth ◽  
Bubble Radius ◽  
Growth Time ◽  
Heating Wall ◽  
Contact Circle ◽  
Proper Values ◽  
Circle Diameter ◽  
Contact Diameter

Phenomenal and theoretical analysis about the evolution of bubble contact circle diameter during bubble growing is presented in current paper; and it is found that bubble contact diameter is dependent on bubble growth rate and bubble radius strongly. By analyzing experimental data from open literature, the relation between dimensionless bubble contact diameter, kw, and dimensionless bubble growth time, t+, is obtained; based on this, a model relative to dimensionless bubble growth rate, dR+/dt+, and dimensionless bubble radius, R+, is proposed for prediction of bubble contact diameter. With proper values for coefficients, aw and nw, this model can well predict experimental data of bubble circle contact diameter in published literatures, with an error within ±20%.

Pore Formation in Solid

2012 ◽  
Vol 28 (1) ◽  
pp. 1-6
Author(s):  
P. S. Wei ◽  
S. Y. Hsiao ◽  
S. S. Hsieh
Keyword(s):  
Solidification Front ◽  
Pore Formation ◽  
Three Dimensional ◽  
Pore Shape ◽  
Critical Factors ◽  
Dissolved Gas ◽  
Factors Affecting ◽  
Working Parameters ◽  
Realistic Prediction ◽  
Perturbation Solutions

ABSTRACTThe shapes of a growing or decaying bubble entrapped by a solidification front are predicted in this work. The bubble results from supersaturation of a dissolved gas in the liquid ahead of the solidification front. Pore formation and its shape in solid are one of the most critical factors affecting properties, microstructure, and stresses in materials. In this study, the bubble and pore shapes entrapped in solid can be described by a three-dimensional phase diagram, obtained from perturbation solutions of Young-Laplace equation governing the tiny bubble shape in the literature. The predicted growth and entrapment of a microbubble as a pore in solid are found to agree with experimental data. This work thus provides a realistic prediction of the general growth of the pore shape as a function of different working parameters.

Gestation length, birth weight and growth rates of pure-bred indigenous goats and their crosses in Kenya

1988 ◽  
Vol 111 (2) ◽  
pp. 363-368 ◽  
Author(s):  
F. Ruvuna ◽  
T. C. Cartwright ◽  
H. Blackburn ◽  
M. Okeyo ◽  
S. Chema
Keyword(s):  
Growth Rate ◽  
Birth Weight ◽  
Statistical Analysis ◽  
Least Squares ◽  
Growth Rates ◽  
Gestation Length ◽  
East African ◽  
Factors Affecting ◽  
Cross Breeding ◽  
Indigenous Goats

SummaryData on gestation period of 701 indigenous East African and Galla does and pre- and postweaning growth of 810 pure-bred and cross-bred kids were analysed by least squares statistical analysis. Breeds of kids were East African, Galla, Toggenburg × East African, Toggenburg × Galla, Anglo-Nubian × East African and Anglo-Nubian × Galla. Average gestation length was 149 days and was significantly (P < 0·05) affected by type of birth of the kid, year–month of kidding, and age of dam. Does carrying twins had shorter gestation length than does carrying singles. Sex and breed of kid did not have significant effect on gestation length.Significant (P < 0·05) factors affecting birth weight, weight at 30, 60, 90, 120, 150, 210 and 270 days of age, and preweaning growth rate were breed and sex of kid, type of birth, year–month and age of dam. Male kids grew faster and were heavier than females. Kids born single were heavier and grew faster than twin-born kids. Kids from dams less than 3 years old weighed less than kids from older dams. Cross-bred kids had higher preweaning growth rates than indigenous pure-bred kids. The Anglo-Nubian × Galla cross was heaviest while the East African ranked lowest. The results point to importance of cross-breeding with temperate breeds to increase growth rates of indigenous goats. Comparison of Toggenburg and Anglo-Nubian sires for cross-breeding showed both buck breeds produced kids with roughly equal growth rates. Evaluation of indigenous Galla and East African dams for cross-breeding showed Galla dams produced heavier kids than East African but preweaning growth rates were not significantly different.

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