Mass transfer effects on linear wave propagation in diluted bubbly liquids

Fuster, Daniel; Montel, François

doi:10.1017/jfm.2015.436

Cited by 63 publications

(68 citation statements)

References 30 publications

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“…Quantity ρ b is the density of the air‐vapor mixture in the bubble, and

D_{normalb}^{normalM}

is the mass diffusion coefficient of vapor in air. For the heat flux, Fuster and Montel () defined the difference of the conductive heat flux in the liquid and the bubble to be equal to the vaporization enthalpy Δ H vap times the total mass flux across the interface,

κ_{normall} \frac{\partial T_{normall}}{∂r} - κ_{normalb} \frac{\partial T_{normalb}}{∂r} = JΔ H_{vap} at r = R,

where κ l and κ b are the thermal conductivities, T l and T b are the temperatures, and the subscripts b and l refer to the liquid and bubble phase, respectively. In equations and , the total mass flux of water across the bubble‐liquid interface, J ( r = R ) is equal to the amount of vapor that undergoes phase change.…”

Section: Effective Fluid Propertiesmentioning

confidence: 99%

“…In equations and , the total mass flux of water across the bubble‐liquid interface, J ( r = R ) is equal to the amount of vapor that undergoes phase change. Fuster and Montel () defined this mass flux, which is driven by the evaporation and condensation at the surface of the bubble, by the Hertz‐Knudsen‐Langmuir (see Fuster & Montel, , and references therein) expression to be

J (r = R) = α_{evap} \frac{P_{eq}^{normalI} - P_{b,vapor}^{normalI}}{\sqrt{2 π R_{spec} T_{int}}} .

…”

Section: Effective Fluid Propertiesmentioning

confidence: 99%

“…Their derivations are based on the Rayleigh‐Plesset equation (e.g., Plesset & Prosperetti, ) and on the assumption that the bubbles are surrounded by a liquid expanding toward infinity. The corresponding expressions for b and ω 0 are reproduced from Fuster and Montel () in Appendix A. Fuster and Montel () then use ω 0 and b for calculating the frequency‐dependent sound speed of the liquid‐bubble mixture, following the frequency domain approach of Commander and Prosperetti (). This yields the complex sound speeds c c as a function of angular frequency ω :

\frac{1}{c_{normalc}^{2}} ≅ \frac{1}{c_{normall}^{2}} + \frac{3 β}{R_{0}^{2}} \frac{1}{ω_{0}^{2} - ω^{2} + 2 ibω},

where i is the imaginary quantity, c l is the sound speed of the pure liquid phase, and β is the volumetric bubble content.…”

Section: Effective Fluid Propertiesmentioning

confidence: 99%

“…Here it is assumed that all bubbles have the same equilibrium radius R 0 . In the case of varying radii, the volumetric bubble content becomes (Commander & Prosperetti, ; Fuster & Montel, )

β ≅ \frac{4 π}{3} n {falsefalse}_{\int}^{0} R_{0}^{3} f (R_{0}) normald R_{0},

where f ( R 0 ) is a probabilistic function for the bubble equilibrium radius and n is the number of bubbles per unit volume. Using this expression in equation , the sound speed is defined as (Commander & Prosperetti, ; Fuster & Montel, )

\frac{1}{c_{normalc}^{2}} ≅ \frac{1}{c_{normall}^{2}} + 4 πn {falsefalse}_{\int}^{0} \frac{R_{0} f (R_{0})}{ω_{0}^{2} - ω^{2} + 2 ibω} normald R_{0} .

…”

Section: Effective Fluid Propertiesmentioning

confidence: 99%

See 3 more Smart Citations

The Effect of Boiling on Seismic Properties of Water‐Saturated Fractured Rock

et al. 2017

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Seismic campaigns for exploring geothermal systems aim at detecting permeable formations in the subsurface and evaluating the energy state of the pore fluids. High‐enthalpy geothermal resources are known to contain fluids ranging from liquid water up to liquid‐vapor mixtures in regions where boiling occurs and, ultimately, to vapor‐dominated fluids, for instance, if hot parts of the reservoir get depressurized during production. In this study, we implement the properties of single‐ and two‐phase fluids into a numerical poroelastic model to compute frequency‐dependent seismic velocities and attenuation factors of a fractured rock as a function of fluid state. Fluid properties are computed while considering that thermodynamic interaction between the fluid phases takes place. This leads to frequency‐dependent fluid properties and fluid internal attenuation. As shown in a first example, if the fluid contains very small amounts of vapor, fluid internal attenuation is of similar magnitude as attenuation in fractured rock due to other mechanisms. In a second example, seismic properties of a fractured geothermal reservoir with spatially varying fluid properties are calculated. Using the resulting seismic properties as an input model, the seismic response of the reservoir is then computed while the hydrothermal structure is assumed to vary over time. The resulting seismograms demonstrate that anomalies in the seismic response due to fluid state variability are small compared to variations caused by geological background heterogeneity. However, the hydrothermal structure in the reservoir can be delineated from amplitude anomalies when the variations due to geology can be ruled out such as in time‐lapse experiments.

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“…Quantity ρ b is the density of the air‐vapor mixture in the bubble, and

D_{normalb}^{normalM}

κ_{normall} \frac{\partial T_{normall}}{∂r} - κ_{normalb} \frac{\partial T_{normalb}}{∂r} = JΔ H_{vap} at r = R,

Section: Effective Fluid Propertiesmentioning

confidence: 99%

J (r = R) = α_{evap} \frac{P_{eq}^{normalI} - P_{b,vapor}^{normalI}}{\sqrt{2 π R_{spec} T_{int}}} .

…”

Section: Effective Fluid Propertiesmentioning

confidence: 99%

\frac{1}{c_{normalc}^{2}} ≅ \frac{1}{c_{normall}^{2}} + \frac{3 β}{R_{0}^{2}} \frac{1}{ω_{0}^{2} - ω^{2} + 2 ibω},

where i is the imaginary quantity, c l is the sound speed of the pure liquid phase, and β is the volumetric bubble content.…”

Section: Effective Fluid Propertiesmentioning

confidence: 99%

“…Here it is assumed that all bubbles have the same equilibrium radius R 0 . In the case of varying radii, the volumetric bubble content becomes (Commander & Prosperetti, ; Fuster & Montel, )

β ≅ \frac{4 π}{3} n {falsefalse}_{\int}^{0} R_{0}^{3} f (R_{0}) normald R_{0},

\frac{1}{c_{normalc}^{2}} ≅ \frac{1}{c_{normall}^{2}} + 4 πn {falsefalse}_{\int}^{0} \frac{R_{0} f (R_{0})}{ω_{0}^{2} - ω^{2} + 2 ibω} normald R_{0} .

…”

Section: Effective Fluid Propertiesmentioning

confidence: 99%

See 2 more Smart Citations

The Effect of Boiling on Seismic Properties of Water‐Saturated Fractured Rock

et al. 2017

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“…The problem of small disturbance propagation in a liquid with gas-vapor bubbles in some or another formulation was studied in [20][21][22][23][24][25][26][27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Reflection of acoustic waves from the boundary or layer of two-phase medium

2018

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Abstract. The inclined incidence of the acoustic wave on a layer of gas-droplet mixture or bubbly liquid of finite thickness is theoretically investigated. In the case of the incidence of the low-frequency acoustic wave to interface between the pure gas and aerosol or to interface between pure liquid and bubbly liquid the basic laws of reflection and transmission of a wave are established. This circumstance allows us to evaluate the transmission and reflection coefficients, depending on the volume content of inclusions and the angle of incidence of the acoustic wave. In particular, for the interface between pure gas and aerosol analytical expressions of the critical angle of wave incidence at which reflection coefficient becomes zero are obtained, i.e. thus there is a complete passage of the acoustic wave through the interface. It is established that the increase of the angle of incidence of the acoustic wave on the boundary or layer of aerosol causes: first, either to increase or to decrease of the reflection coefficient at low frequencies, and second, to appearance of additional minima depending on the reflection coefficient from frequency of disturbances related to the difference of speed of sound and density of the medium.

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Bio‐inspired Porous Composite Electrode for Enhanced Mass Transfer and Electrochemical Water Purification by Modifying Local Flow Pattern

Yuan

Pei

Zhang

et al. 2023

Adv Funct Materials

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Porous electrodes offer a new opportunity for flow-through electrochemical water purification, but their irregular porous-structure makes the local flow pattern and mass transfer performance inhomogeneous, unpredictable, and uncontrollable. In this study, a bio-inspired design is reported for porous electrode by learning the micro-scale architectures of the wings of butterfly and owl based on analogy between heterogeneous mass transfer and sound absorption. Results demonstrate that combining gyroid and perforated plate can produce strong periodic vortex and inertial flow in interpenetrating channels even at laminar flow region. This enables homogeneous, predictable and controllable flow patterns and enhanced mass transfer, which can be explained by uniformity analysis and physical field synergy. Based on experimental tests on Cu electrode fabricated by selective laser melting, the composite gyroid electrode generates the limiting current density of 83% higher than random porous-structured electrode, accounting for nitrate removal as high as 95% by electrochemical denitrification. This study represents a paradigm shift to advance design for porous architectures by learning experiences of hydrodynamic behaviors from nature. In this way, it is feasible to enhance mass transfer by modifying local flow patterns on pore scale, which may have broader implications that extend to other heterogeneous reaction systems.

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Mass transfer effects on linear wave propagation in diluted bubbly liquids

Cited by 63 publications

References 30 publications

The Effect of Boiling on Seismic Properties of Water‐Saturated Fractured Rock

The Effect of Boiling on Seismic Properties of Water‐Saturated Fractured Rock

Reflection of acoustic waves from the boundary or layer of two-phase medium

Bio‐inspired Porous Composite Electrode for Enhanced Mass Transfer and Electrochemical Water Purification by Modifying Local Flow Pattern

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