Spontaneous Nucleation of Bubbles in a Gas-Saturated Melt under Instantaneous Decompression

Chernov, A. A.; Kedrinskii, V. K.; Davydov, M. N.

doi:10.1023/b:jamt.0000017592.35765.9c

“…With these remarks taken into account, it can be concluded that σ = 0.08 N/m. This value is close to σ = 0.076 N/m for which good agreement between numerical results and the experimental data of [3] was obtained in [11]. The difference of σ = 0.08 N/m from the value σ = 0.10-0.11 N/m obtained in [8] with the use of Eq.…”

supporting

confidence: 86%

Effect of viscosity on nucleation of bubbles in decompressed water-saturated magma

Lezhnin

¹

,

Прибатурин

²

,

Sorokin

³

2005

J Appl Mech Tech Phys

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Based on the classical nucleation theory, the effect of viscosity on bubble nucleation in water-saturated magma has been studied. A comparison with experimental data proves that viscosity has a pronounced effect on the rate of homogeneous nucleation in magma.The volcanic-eruption pattern is largely determined by nucleation and growth of gas bubbles dissolved in magma, which are predominantly formed by H 2 O and CO 2 [1]. Magma-degassing dynamics depends on the number of bubbles formed; the latter can be predicted using theoretical dependences for the nucleation rate [2,3]. Yet, these dependences ignore the effect of magma viscosity, which is known to be quite appreciable [4].The objective of the present work was to predict the rate of homogeneous nucleation in water-saturated magma on the basis of the classical nucleation theory [5] with allowance for viscosity. For the case of pure-liquid boiling, the rate of homogeneous nucleation was calculated with allowance for viscosity and thermal conductivity by Kagan [6]. The method proposed in [6] was used in the present study; to facilitate the comparison, we use the same notation.Let us briefly recall the main postulates of the classical nucleation theory [5]. We assume that the nuclei of the new phase are macroscopic and their size distribution function f (t, r) can be found from the following equation of the Fokker-Planck type:Here A is the growth rate of the nuclei, B is the diffusivity in the size space, and J is the nucleation rate. To calculate the growth rate of supercritical nuclei, we use the solution of an appropriate continual (heat-conduction or diffusion) problem. In constructing the steady-state solution of Eq. (1), the boundary condition at r → 0 is f (r) = f 0 (r), where f 0 (r) is the size distribution function of nuclei given by the thermodynamic fluctuation theory.The boundary condition at r → ∞ is J = const. It follows from these conditions that [5]where r k is the critical-nucleus radius, σ is the surface tension at the interface between the phases, k is the Boltzmann constant, and T is the temperature in the medium. Following the above-described approach, Toramaru [2] derived the following expression for the degassing conditions of water-saturated magma:

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“…As it follows from Fig. This value is close to σ = 0.076 N/m for which good agreement between numerical results and the experimental data of [3] was obtained in [11]. In performing the comparison, it should be taken into account that the experimental data obtained at moderate decompression rates (0.025 MPa/sec) could be affected by heterogeneous nucleation on the capsule walls.…”

supporting

confidence: 79%

Changes in the type of the shock-wave structure in high-velocity flows

Lezhnin

¹

,

Прибатурин

²

,

Sorokin

³

2005

J Appl Mech Tech Phys

0

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Based on the classical nucleation theory, the effect of viscosity on bubble nucleation in water-saturated magma has been studied. A comparison with experimental data proves that viscosity has a pronounced effect on the rate of homogeneous nucleation in magma.The volcanic-eruption pattern is largely determined by nucleation and growth of gas bubbles dissolved in magma, which are predominantly formed by H 2 O and CO 2 [1]. Magma-degassing dynamics depends on the number of bubbles formed; the latter can be predicted using theoretical dependences for the nucleation rate [2,3]. Yet, these dependences ignore the effect of magma viscosity, which is known to be quite appreciable [4].The objective of the present work was to predict the rate of homogeneous nucleation in water-saturated magma on the basis of the classical nucleation theory [5] with allowance for viscosity. For the case of pure-liquid boiling, the rate of homogeneous nucleation was calculated with allowance for viscosity and thermal conductivity by Kagan [6]. The method proposed in [6] was used in the present study; to facilitate the comparison, we use the same notation.Let us briefly recall the main postulates of the classical nucleation theory [5]. We assume that the nuclei of the new phase are macroscopic and their size distribution function f (t, r) can be found from the following equation of the Fokker-Planck type:

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“…The kinetics is supplemented by introducing a model of diffusion layers in the neighborhood of cavitation nuclei, which are considered as local sources of increasing gas mass contained in the nuclei due to its diffusion from the melt (Fig. 1) [1]. In essence, based on the obvious physical fact of dissolved gas diffusion (behind the decompression wave front) from magma, it becomes possible to divide, by the order of magnitude, the diffusion flow from magma into two flows: one of them is responsible only for saturation of magma with nuclei (from zones outside the diffusion layers) and the other is primarily sent to the cavitation bubbles, increasing the gas mass in them.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…It is extremely difficult to separate some processes from the whole complex of these effects and try to elucidate their role and influence because they are interdependent. From this viewpoint, introduction of the notion of a diffusion layer [1], which surrounds the cavitation nucleus in which the nucleation of other nuclei is substantially bounded, has appeared to be of principle.…”

Section: Introductionmentioning

confidence: 99%

Formation of a saturation wave front and dynamics of magma state characteristics in its zone

Kedrinskii

¹

,

Nakoryakov

²

,

Sigfusson

³

2011

J. Engin. Thermophys.

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The influence of the diffusion zone width (parameter χ), which bounds the nucleation process in the nucleus neighborhood, on the dynamics of magma melt state at the initial stage of explosive eruption is numerically analyzed in the context of the Iordanskii-Kogarko-van Vijngaarden model of multiphase media. It is shown that in the region of 5 ÷ 50, the value of χ does not affect the time of forming the front of the zone of magma saturation with nuclei, but determines their maximum density, which decreases by three orders of magnitude, from 510 10 to 810 7 m −3 , as the parameter χ grows by one order of magnitude. The most considerable losses of gas dissolved in magma are observed for χ = 5 and, consequently, as soon as 100 ms later after the beginning of decompression, there appear zones behind the wavefront, where the melt viscosity grows to hundreds of thousand Pa·s. Under the restriction of diffusion to bubbles, the decompression wave has a classical profile that is slightly perturbed by the front of saturation zone. However, in spite of the fact that the density of the number of nuclei in the cavitating magma upon removing the restriction of gas diffusion into bubbles remains the same as in the case of restriction, the effect of diffusion of additional mass of gas into bubbles changes radically the wavefield structure. Substantially increasing gas pressure in the bubbles due to diffusion with the melt viscosity growing by several orders of magnitude, which prevents bubble growth, changes appreciably the dynamics of the main characteristics of the cavitating magma state.

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Spontaneous Nucleation of Bubbles in a Gas-Saturated Melt under Instantaneous Decompression

Cited by 21 publications

References 6 publications

Effect of viscosity on nucleation of bubbles in decompressed water-saturated magma

Effect of viscosity on nucleation of bubbles in decompressed water-saturated magma

Changes in the type of the shock-wave structure in high-velocity flows

Formation of a saturation wave front and dynamics of magma state characteristics in its zone

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