History effects on the gas exchange between a bubble and a liquid

Chu, Shigan; Prosperetti, Andréa

doi:10.1103/physrevfluids.1.064202

Cited by 13 publications

(15 citation statements)

References 19 publications

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“…For multicomponent bubbles, the variation in time of the species interfacial concentration, C s,i (t), is usually inevitable. As recently shown by Chu and Prosperetti [31], the history effect can be taken into account by the inclusion of a computationally costly history integral term in all the ODEs in Eq. (18).…”

Section: Bubble Dissolution Modelmentioning

confidence: 99%

“…Apart from the effect of advection, the (positive) error is mainly attributed to the extension of the quasistationary approximation to the interfacial concentrations of the species, since these are treated as constant in the obtention of the expression for the concentration gradient [28]. In other words, the error comes from not taking into account the so-called history effect [30,31]. The history effect can be summarized as the contribution of the preceding time history of the interfacial concentration on the current rate of growth or dissolution.…”

Section: Bubble Dissolution Modelmentioning

confidence: 99%

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Diffusion of dissolved CO2 in water propagating from a cylindrical bubble in a horizontal Hele-Shaw cell

et al. 2017

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The dissolution of a gas bubble in a confined geometry is a problem of interest in technological applications such as microfluidics or carbon sequestration, as well as in many natural flows of interest in geophysics. While the dissolution of spherical or sessile bubbles has received considerable attention in the literature, the case of a two-dimensional bubble in a Hele-Shaw cell, which constitutes perhaps the simplest possible confined configuration, has been comparatively less studied. Here, we use planar laser-induced fluorescence to experimentally investigate the diffusion-driven transport of dissolved CO 2 that propagates from a cylindrical mm-sized bubble in air-saturated water confined in a horizontal Hele-Shaw cell. We observe that the radial trajectory of an isoconcentration front, r f (t), evolves in time as approximately r f − R 0 ∝ √ t,where R 0 denotes the initial bubble radius. We then characterize the unsteady CO 2 concentration field via two simple analytical models, which are then validated against a numerical simulation. The first model treats the bubble as an instantaneous line source of CO 2 , whereas the second assumes a constant interfacial concentration. Finally, we provide an analogous Epstein-Plesset equation with the intent of predicting the dissolution rate of a cylindrical bubble.

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Section: Bubble Dissolution Modelmentioning

confidence: 99%

Section: Bubble Dissolution Modelmentioning

confidence: 99%

Diffusion of dissolved CO2 in water propagating from a cylindrical bubble in a horizontal Hele-Shaw cell

et al. 2017

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“…The convection term can be obtained from the radially-symmetric continuity equation in cylindrical coordinates with constant density [4]. A similar approach is used for the analysis of melting of nanoparticles [6] and bubble growth and oscillations [7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Phase Change with Density Variation and Cylindrical Symmetry: Application to Selective Laser Melting

Fyrillas

Ioannou

Papadakis

et al. 2019

JMMP

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In this paper we introduce an analytical approach for predicting the melting radius during powder melting in selective laser melting (SLM) with minimum computation duration. The purpose of this work is to evaluate the suggested analytical expression in determining the melt pool geometry for SLM processes, by considering heat transfer and phase change effects with density variation and cylindrical symmetry. This allows for rendering first findings of the melt pool numerical prediction during SLM using a quasi-real-time calculation, which will contribute significantly in the process design and control, especially when applying novel powders. We consider the heat transfer problem associated with a heat source of power Q' (W/m) per unit length, activated along the span of a semi-infinite fusible material. As soon as the line heat source is activated, melting commences along the line of the heat source and propagates cylindrically outwards. The temperature field is also cylindrically symmetric. At small times (i.e., neglecting gravity and Marangoni effects), when the density of the solid material is less than that of the molten material (i.e., in the case of metallic powders), an annulus is created of which the outer interface separates the molten material from the solid. In this work we include the effect of convection on the melting process, which is shown to be relatively important. We also justify that the assumption of constant but different properties between the two material phases (liquid and solid) does not introduce significant errors in the calculations. A more important result; however, is that, if we assume constant energy input per unit length, there is an optimum power of the heat source that would result to a maximum amount of molten material when the heat source is deactivated. The model described above can be suitably applied in the case of selective laser melting (SLM) when one considers the heat energy transferred to the metallic powder bed during scanning. Using a characteristic time and length for the process, we can model the energy transfer by the laser as a heat source per unit length. The model was applied in a set of five experimental data, and it was demonstrated that it has the potential to quantitatively describe the SLM process.

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“…Bubbles may also interact with nearby surfaces or they may contain more than one chemical species (Shim et al 2014;Peñas-López et al 2015). Another effect that contributes to the diffusion-driven dynamics of a bubble is the so-called history effect, discussed in Part 1 and more recently in Chu & Prosperetti (2016b). It has been shown that any recent history of growth and/or dissolution (triggered by past changes in ambient pressure) experienced by a particular bubble may leave, at least for some time, a non-negligible print on the current state of the concentration profile surrounding such bubble.…”

Section: Introductionmentioning

confidence: 99%

“…The species composition inside the bubble will thus change over time, which amounts to time-dependent partial pressures and hence time-dependent interfacial concentrations. It is possible to artificially discern the contribution of the history effect numerically, as was done by Chu & Prosperetti (2016b) for the case of a dissolving two-gas bubble. Isolating the history effect experimentally, on the other hand, is anticipated to be much harder.…”

Section: Introductionmentioning

confidence: 99%

The history effect on bubble growth and dissolution. Part 2. Experiments and simulations of a spherical bubble attached to a horizontal flat plate

et al. 2017

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The accurate description of the growth or dissolution dynamics of a soluble gas bubble in a super-or undersaturated solution requires taking into account a number of physical effects that contribute to the instantaneous mass transfer rate. One of these effects is the so-called history effect. It refers to the contribution of the local concentration boundary layer around the bubble that has developed from past mass transfer events between the bubble and liquid surroundings. In Part 1 of this work (Peñas-López et al. 2016b), a theoretical treatment of this effect was given for a spherical, isolated bubble. Here, Part 2 provides an experimental and numerical study of the history effect regarding a spherical bubble attached to a horizontal flat plate and in the presence of gravity. The simulation technique developed in this paper is based on a streamfunction-vorticity formulation that may be applied to other flows where bubbles or drops exchange mass in the presence of a gravity field. Using this numerical tool, simulations are performed for the same conditions used in the experiments, in which the bubble is exposed to subsequent growth and dissolution stages, using step-wise variations in the ambient pressure. Besides proving the relevance of the history effect, the simulations highlight the importance that boundary-induced advection has to accurately describe bubble growth and shrinkage, i.e. the bubble radius evolution. In addition, natural convection has a significant influence that shows up in the velocity field even at short times, though, given the supersaturation conditions studied here, the bubble evolution is expected to be mainly diffusive.

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History effects on the gas exchange between a bubble and a liquid

Cited by 13 publications

References 19 publications

Diffusion of dissolved CO2 in water propagating from a cylindrical bubble in a horizontal Hele-Shaw cell

Diffusion of dissolved CO2 in water propagating from a cylindrical bubble in a horizontal Hele-Shaw cell

Phase Change with Density Variation and Cylindrical Symmetry: Application to Selective Laser Melting

The history effect on bubble growth and dissolution. Part 2. Experiments and simulations of a spherical bubble attached to a horizontal flat plate

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