Effects of interface kinetics, capillarity and solute diffusion on bubble growth rates in highly supersaturated liquids

Rosner, Daniel E.; Epstein, Michael

doi:10.1016/0009-2509(72)80142-8

Cited by 121 publications

(80 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As noted by Rosner and Epstein (1972), a full model would include consideration of nucleation, kinetics of gas adsorption, transport of the gas, and mechanical response of the sediments. Nucleation should only be a question when preexisting gas cavities are scarce, a situation we do not believe exists in clay-rich sediments with their abundant and complex surface area and past history of aerial exposure; consequently, nucleation kinetics are ignored (Jones et al 1999).…”

Section: The Modelmentioning

confidence: 99%

Rate of growth of isolated bubbles in sediments with a diagenetic source of methane

Boudreau

Gardiner

Johnson

2001

Limnology & Oceanography

View full text Add to dashboard Cite

Observation of bubbles in estuarine and coastal sediments indicates that bubbles at or below 10 cm depth grow on seasonal time scales (May-October). In order to determine the controls on this growth rate, we have constructed a diffusion-reaction model that accounts for the dynamics of methane formation, its diffusion through pore waters, its incorporation into a bubble, and the consequent growth of the bubble. The model produces an explicit equation for the radius of a growing bubble, R(t), with time using mean parameter values and under the assumption that the mechanics of the sediment response to growth can be neglected:where is the porosity, D is the tortuosity-corrected diffusivity, c g is the concentration of gas in the bubble, S is the rate of methanogenesis near the bubble, R 1 is the half-separation distance between bubbles (R 1 k R), c 1 is the ambient CH 4 concentration, c 0 is the pore-water CH 4 concentration at R, t is time, and R 0 is the initial bubble radius, if not zero. The effects of the source S and supersaturation (c 1 Ϫ c 0 ), thus, appear as separate contributing terms, and this formula can then be applied even in those cases where apparently c 1 ഠ c 0 . The model is applied to three sediments where bubbles have been previously studied, i.e., Cape Lookout Bight (USA), White Oak River (USA) and Eckernförde Bay (Germany). In all three cases, using the site-specific time-averaged parameter values, the model predicts seasonal growth rates, consistent with the observations. Furthermore, the source term dominates the rate of growth at the first of these two sites, whereas diffusion from the ambient supersaturation dominates at the German location. Real bubbles may follow a more complicated growth history than predicted by the above equation because of the mechanical properties of sediments; nevertheless, the overall growth times are concordant with ultimate diffusion control. The effects of rectified diffusion, that is, the pumping of gas into a bubble by pressure oscillations, e.g., from waves and tides, were also examined. Existing models for that process suggest that it is negligible, due to the low frequency of these types of oscillations.

show abstract

Section: The Modelmentioning

confidence: 99%

Rate of growth of isolated bubbles in sediments with a diagenetic source of methane

Boudreau

Gardiner

Johnson

2001

Limnology & Oceanography

View full text Add to dashboard Cite

show abstract

“…Because there are many variables involved in bubble growth, it is computationally efficient to define a set of nondimensional equations to described the system. In some previous analyses [Rosner and Epstein, 1972;$zekely and Fang, 1973], nondimensionalization was performed in order to obtain analytical solutions of simple formulations using asymptotic approximations which discount many variables but allow for analytical solution. In contrast, the purpose of nondimensionalization in our analysis is to provide a useful transformation of the original analytical equations for numerical solution in order to reduce the order of differential equations, improve convergence, reduce the number of iterations, and increase precision.…”

Section: Decompressionmentioning

confidence: 99%

Dynamics and energetics of bubble growth in magmas: Analytical formulation and numerical modeling

Proussevitch¹,

Sahagian²

1998

J. Geophys. Res.

216

154

View full text Add to dashboard Cite

Abstract. We have developed a model of diffusive and decompressive growth of a bubble in a finite region of melt which accounts for the energetics of volatile degassing and melt deformation as well as the interactions between magmatic system parameters such as viscosity, volatile concentration, and diffusivity. On the basis of our formulation we constructed a numerical model of bubble growth in volcanic systems. We conducted a parametric study in which a saturated magma is instantaneously decompressed to one bar and the sensitivity of the system to variations in various parameters is examined. Variations of each of seven parameters over practical ranges of magmatic conditions can change bubble growth rates by 2-4 orders of magnitude. Our numerical formulation allows determination of the relative importance of each parameter controlling bubble growth for a given or evolving set of magmatic conditions. An analysis of the modeling results reveals that the commonly invoked parabolic law for bubble growth dynamics R -t 1/2 is not applicable to magma degassing at low pressures or high water oversaturation but that a logarithmic relationship R -log(t) is more appropriate during active bubble growth under certain conditions. A second aspect of our study involved a constant decompression bubble growth model in which an initially saturated magma was subjected to a constant rate of decompression. Model results for degassing of initially water-saturated rhyolitic magma with a constant decompression rate show that oversaturation at the vent depends on the initial depth of magma ascent. On the basis of decompression history, explosive eruptions of silicic magmas are expected for magmas rising from chambers deeper than 2 km for ascent rates > 1-5 m s-1.

show abstract

“…The new bubble pressure and radius are calculated by Eqs. (13) and (14). Table 3 shows a list of parameter to perform the numerical simulation.…”

Section: Numerical Simulationmentioning

confidence: 99%

“…Detailed derivation is found in the reference. 14) ........ (9) where PD0 and R0 are the bubble pressure and radius of nucleus. Notice that the Eq.…”

Section: Bubble Growthmentioning

confidence: 99%

“…[14][15][16][17] In this study, the bubble growth model was based on the Rosner and Epstein integration model. 14) They coupled the force balance equation of pressure difference between gas pressure and pressure of matrix and mass transfer of single bubble. Equation (2) where ng is a number of gas molecules in molar unit, is gas constant, D is diffusion coefficient, c concentration of gas dissolved in matrix.…”

Section: Bubble Growthmentioning

confidence: 99%

See 1 more Smart Citation

A Simplified Bubble Nucleation, Growth and Coalescence Model for Coke Production Process

Taki

Hayashizaki

Fukada³

2014

ISIJ Int.

View full text Add to dashboard Cite

Coke production process, which involves gas generation, cross-linking, gas foaming as well as solidification phenomena, is extremely complex and is difficult to model them without simplification. In this study, a simple phenomenological model was developed based on a gas foaming simulation model of polymer foaming, which enabled us to simulate the number density of bubbles and their distributed size. The model was extended to account their kinetics of bubble nucleation, growth and coalescence in nonisothermal chemical reactions of gas generation and cross-linking. The bubbles size and morphology obtained from the numerical simulation of two different coals agreed with the pictures of the experiment qualitatively. Five different coals were investigated to understand the relationship between the kinetic and final morphology of coke.

show abstract

Effects of interface kinetics, capillarity and solute diffusion on bubble growth rates in highly supersaturated liquids

Cited by 121 publications

References 19 publications

Rate of growth of isolated bubbles in sediments with a diagenetic source of methane

Rate of growth of isolated bubbles in sediments with a diagenetic source of methane

Dynamics and energetics of bubble growth in magmas: Analytical formulation and numerical modeling

A Simplified Bubble Nucleation, Growth and Coalescence Model for Coke Production Process

Contact Info

Product

Resources

About