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.

scholarly journals Gas depletion through single gas bubble diffusive growth and its effect on subsequent bubbles

2017 ◽  
Vol 831 ◽  
pp. 474-490 ◽  
Author(s):  
Álvaro Moreno Soto ◽  
Andrea Prosperetti ◽  
Detlef Lohse ◽  
Devaraj van der Meer
Keyword(s):  
Bubble Growth ◽  
Quantitative Data ◽  
Liquid Solution ◽  
Nucleation Site ◽  
Simplified Model ◽  
Gas Bubble ◽  
Dissolved Gas ◽  
Bubble Detachment ◽  
Diffusive Growth ◽  
Pure Diffusion

When a gas bubble grows by diffusion in a gas–liquid solution, it affects the distribution of gas in its surroundings. If the density of the solution is sensitive to the local amount of dissolved gas, there is the potential for the onset of natural convection, which will affect the bubble growth rate. The experimental study of the successive quasi-static growth of many bubbles from the same nucleation site described in this paper illustrates some consequences of this effect. The enhanced growth due to convection causes a local depletion of dissolved gas in the neighbourhood of each bubble beyond that due to pure diffusion. The quantitative data of sequential bubble growth provided in the paper show that the radius-versus-time curves of subsequent bubbles differ from each other due to this phenomenon. A simplified model accounting for the local depletion is able to collapse the experimental curves and to predict the progressively increasing bubble detachment times.

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.

The boundary layer on a spherical gas bubble

1963 ◽  
Vol 16 (2) ◽  
pp. 161-176 ◽  
Author(s):  
D. W. Moore
Keyword(s):  
Boundary Layer ◽  
Potential Flow ◽  
Bubble Radius ◽  
Terminal Velocity ◽  
Gas Bubble ◽  
Fractional Powers ◽  
Small Viscosity ◽  
Flow Round ◽  
Bubble Rising ◽  
Rear Stagnation Point

The equations governing the boundary layer on a spherical gas bubble rising steadily through liquid of small viscosity are derived. These equations are linear are linear and are solved in closed form. The boundary layer separates at the rear stagnation point of the bubble to form a thin wake, whose structure is determined. Thus the drag force can be calculated from the momentum defect. The value obtained is 12πaaUμ, where a is the bubble radius and U the terminal velocity, and this agrees with the result of Levich (1949) who argued from the viscous dissipation in the potential flow round the bubble. The next term in an expansion of the drag in descending fractional powers of R is found and the results compared with experiment.

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%.

Similarity problems of the theory of unsteady concentration boundary layer

1983 ◽  
Vol 48 (10) ◽  
pp. 2751-2766
Author(s):  
Ondřej Wein ◽  
N. D. Kovalevskaya
Keyword(s):  
Boundary Layer ◽  
Approximate Method ◽  
Steady Flow ◽  
Broad Class ◽  
Concentration Boundary Layer ◽  
Concentration Change ◽  
Concentration Boundary ◽  
Flow Problems

Using a new approximate method, transient course of the local and mean diffusion fluxes following a step concentration change on the wall has been obtained for a broad class of steady flow problems.

Understanding gas bubble trauma in an era of hydropower expansion: how do fish compensate at depth?

2020 ◽  
Vol 77 (3) ◽  
pp. 556-563 ◽  
Author(s):  
Naomi K. Pleizier ◽  
Charlotte Nelson ◽  
Steven J. Cooke ◽  
Colin J. Brauner
Keyword(s):  
Bubble Growth ◽  
Gas Bubble ◽  
Hydroelectric Dams ◽  
Dissolved Gas ◽  
Empirical Relationships ◽  
Lethal Effects ◽  
Exposed Fish ◽  
Total Dissolved Gas ◽  
Rainbow Trout Oncorhynchus Mykiss ◽  
The Relationship

Hydrostatic pressure is known to protect fish from damage by total dissolved gas (TDG) supersaturation, but empirical relationships are lacking. In this study we demonstrate the relationship between depth, TDG, and gas bubble trauma (GBT). Hydroelectric dams generate TDG supersaturation that causes bubble growth in the tissues of aquatic animals, resulting in sublethal and lethal effects. We exposed fish to 100%, 115%, 120%, and 130% TDG at 16 and 63 cm of depth and recorded time to 50% loss of equilibrium and sublethal symptoms. Our linear model of the log-transformed time to 50% LOE (R2 = 0.94) was improved by including depth. Based on our model, a depth of 47 cm compensated for the effects of 4.1% (±1.3% SE) TDG supersaturation. Our experiment reveals that once the surface threshold for GBT from TDG supersaturation is known, depth protects rainbow trout (Oncorhynchus mykiss) from GBT by 9.7% TDG supersaturation per metre depth. Our results can be used to estimate the impacts of TDG on fish downstream of dams and to develop improved guidelines for TDG.

scholarly journals The impact of non-pharmaceutical interventions on COVID-19 epidemic growth in the 37 OECD member states

2021 ◽  
Author(s):  
Francisco Pozo-Martin ◽  
Heide Weishaar ◽  
Florin Cristea ◽  
Johanna Hanefeld ◽  
Thurid Bahr ◽  
...  
Keyword(s):  
Growth Rate ◽  
Early Phase ◽  
Policy Decision ◽  
Multilevel Modelling ◽  
Daily Growth ◽  
Public Places ◽  
Member States ◽  
Unit Increase ◽  
Policy Decision Making ◽  
The Impact

AbstractWe estimated the impact of a comprehensive set of non-pharmeceutical interventions on the COVID-19 epidemic growth rate across the 37 member states of the Organisation for Economic Co-operation and Development during the early phase of the COVID-19 pandemic and between October and December 2020. For this task, we conducted a data-driven, longitudinal analysis using a multilevel modelling approach with both maximum likelihood and Bayesian estimation. We found that during the early phase of the epidemic: implementing restrictions on gatherings of more than 100 people, between 11 and 100 people, and 10 people or less was associated with a respective average reduction of 2.58%, 2.78% and 2.81% in the daily growth rate in weekly confirmed cases; requiring closing for some sectors or for all but essential workplaces with an average reduction of 1.51% and 1.78%; requiring closing of some school levels or all school levels with an average reduction of 1.12% or 1.65%; recommending mask wearing with an average reduction of 0.45%, requiring mask wearing country-wide in specific public spaces or in specific geographical areas within the country with an average reduction of 0.44%, requiring mask-wearing country-wide in all public places or all public places where social distancing is not possible with an average reduction of 0.96%; and number of tests per thousand population with an average reduction of 0.02% per unit increase. Between October and December 2020 work closing requirements and testing policy were significant predictors of the epidemic growth rate. These findings provide evidence to support policy decision-making regarding which NPIs to implement to control the spread of the COVID-19 pandemic.

scholarly journals Vegetative Reproduction Is More Advantageous Than Sexual Reproduction in a Canopy-Forming Clonal Macroalga under Ocean Warming Accompanied by Oligotrophication and Intensive Herbivory

Plants ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 1522
Author(s):  
Hikaru Endo ◽  
Toru Sugie ◽  
Yukiko Yonemori ◽  
Yuki Nishikido ◽  
Hikari Moriyama ◽  
...  
Keyword(s):  
Growth Rate ◽  
High Temperature ◽  
Nutrient Availability ◽  
Vegetative Reproduction ◽  
Ocean Warming ◽  
Regeneration Ability ◽  
Combined Effects ◽  
Regeneration Rate ◽  
Fish Herbivory ◽  
C 30

Ocean warming and the associated changes in fish herbivory have caused polarward distributional shifts in the majority of canopy-forming macroalgae that are dominant in temperate Japan, but have little effect on the alga Sargassum fusiforme. The regeneration ability of new shoots from holdfasts in this species may be advantageous in highly grazed environments. However, little is known about the factors regulating this in Sargassum species. Moreover, holdfast tolerance to high-temperature and nutrient-poor conditions during summer has rarely been evaluated. In the present study, S. fusiforme holdfast responses to the combined effects of temperature and nutrient availability were compared to those of sexually reproduced propagules. The combined effects of holdfast fragmentation and irradiance on regeneration were also evaluated. Propagule growth rate values changed from positive to negative under the combination of elevated temperature (20 °C–30 °C) and reduced nutrient availability, whereas holdfasts exhibited a positive growth rate even at 32 °C in nutrient-poor conditions. The regeneration rate increased with holdfast fragmentation (1 mm segments), but was unaffected by decreased irradiance. These results suggest that S. fusiforme holdfasts have a higher tolerance to high-temperature and nutrient-poor conditions during summer than propagules, and regenerate new shoots even if 1-mm segments remain in shaded refuges for fish herbivory avoidance.

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