Dynamics Of Bubble Growth Research Articles

The dynamics of vapor bubble growth in boiling owing to excess enthalpy of surrounding superheated liquid

The formula of exponential time dependence of the radius of spherical bubble is derived. The parameters of this formula are determined for the first time as a result of theoretical analysis. The known experimental data, obtained under conditions of boiling in a body of liquid, on a thin wire, and on a flat surface, are used to demonstrate the much higher accuracy of approximation of these data by the exponential dependence compared to other, most frequently employed, formulas.

Vapor bubble growth at the surface of flat and cylindrical heaters

The growth dynamics are investigated of a sole vapor bubble in a nonuniform temperature field. A two-zone model is developed of the bubble growth on the solid surface. The calculation results are in satisfactory agreement with the experimental data available for the flat and cylindrical heaters. The influence is considered of the evaporation front occurring under high overheating on the bubble growth dynamics.

Numerical studies of bubble necking in viscous liquids

The pinch-off of a gas bubble from a tiny nozzle immersed vertically in another quiescent viscous fluid due to buoyancy is numerically investigated. The dynamics of bubble growth and pinch-off are described by the full Navier-Stokes equations for both gas and liquid phases. The equations are solved with a finite-volume method based on the SIMPLE scheme, coupled with a front tracking method to locate the interface between the two phases. The effects of liquid viscosity, surface tension, and gas density on the bubble pinch-off dynamics, which are always coupled in experiments, are investigated separately through simulations. The numerical results are compared with experimental observations on the bubble pinch-off for validation purposes. The simulation results show that the radius of the necking region decreases in a power law mode with time as r approximately tau;{alpha} , where tau is the time to pinch-off and the exponent alpha varies in the range 0.5-1.0 depending strongly upon the liquid properties such as viscosity and surface tension. In addition, the surface tension can significantly affect the bubble pinch-off exponent alpha when the surface tension coefficient is smaller than 0.030 N/m with a Bond number higher than 0.72. It is also found that both higher viscosity of the liquid phase and higher surface tension may result in a delayed pinch-off process and a larger bubble. The effect of gas phase density on the pinch-off is also investigated. As reported in the literature, the gas density variation has minimal effect on the necking process because the density ratio of the gas phase to the liquid phase is small.

Damping of pressure waves in visco-elastic, saturated bubbly magma

Abstract The attenuation of pressure waves in a saturated bubbly magma is examined in a model, coupling seismic wave-propagation with bubble growth dynamics. This model is solved analytically and numerically, including effects of diffusion of volatiles, visco-elasticity and bubble number density. We show that wave attenuation is controlled mainly by the Peclet and Deborah numbers. The Peclet number is a measure of the relative importance of advection to diffusion. The Deborah number is a visco-elastic measure, describing the importance of elasticity in comparison to viscous melt deformation. We solve numerically for wave attenuation for various magma properties corresponding to a wide range of Peclet and Deborah numbers. We show that the numerical solution can be approximated quite well for frequencies above 1 Hz, by an analytical end-member solution, obtained for high Peclet and low Deborah numbers. For lower frequencies, volatile transport should be accounted for, leading to higher attenuation with respect to the analytical solution. However, if the Deborah number is increased, either by longer relaxation time or by higher frequencies, then attenuation decreases with respect to the analytical solution. Therefore, visco-elasticity leads to a significant improvement of the resonating qualities of a magma-filled conduit and widens the depth and frequency ranges where pressure waves will propagate efficiently through the conduit.

Thermodynamic crisis of boiling

The procedure of calculation of the dynamics of rapid near-wall vaporization near a metallic heater is considered. A physical model of explosive boiling-up on bubbles of fluctuation origin is used. The model is limited to regimes when the motion of bubbles can be ignored and convective flows do not have enough time to develop. It is assumed that the dry spot under a bubble thermally insulates the heater wall. The heat removal is provided by the vicinity of the wetting line (WL). An analytical calculation has become possible on the basis of the well-known exact solution to the problem of the temperature field near the wetting line. Generalization of this solution has led to two new problems. These are the problem of allowance for the difference of the dynamic wetting angle from the right angle and that of allowance for thermocapillary flows. A numerical comparison of the results of calculation of the dry area with the use of different methods of allowing for the “tightness” effect in the dynamics of bubble generation and growth has been made. The evolution of bubbles from their generation to growth limited by the heat supply has been investigated. It has been found that the transition stage in the development of bubbles from Rayleigh to thermal ones is of considerable importance in the processes of explosive boiling-up. The dynamics of change in the dry area and wetting line length prior to the stage of bubble merging into a vapor film has been calculated. A condition of passage of the heat flux through a maximum is found. The applicability of the idea of thermodynamic crisis to calculations of miniature devices is justified. The problem of constructing a model to calculate the interphase surface shape near the wetting line under a developed thermocapillary flow and considerable reactive forces of the vapor flow is formulated. The model is in good agreement with the results of experiments on pulsed superheating of liquids at a rate higher than 1 K/μs.

Dynamics of bubble growth and detachment in a viscous shear flow

The quasistatic injection of air bubbles at the wall in a viscous shear flow is experimentally investigated by high-speed video pictures and image processing. The bubble radius and center of gravity position are determined throughout the growth. Experimental results are then used to validate a force balance model during bubble growth and after detachment for small bubble Reynolds numbers. The contact angles at the bubble foot calculated from the force balance agree well with those experimentally obtained from image processing. Finally, the force balance model is used to predict the departure bubble radius versus the gas flow rate and liquid flow shear rate.

Dynamics of diffusive bubble growth and pressure recovery in a bubbly rhyolitic melt embedded in an elastic solid

We present a model of gas exsolution and bubble expansion in a melt supersaturated in response to a sudden pressure drop. In our model, the melt contains a suspension of gas bubbles of identical sizes and is encased in a penny‐shaped crack embedded in an elastic solid. The suspension is modeled as a three‐dimensional lattice of spherical cells with slight overlap, where each elementary cell consists of a gas bubble surrounded by a shell of volatile‐rich melt. The melt is then subjected to a step drop in pressure, which induces gas exsolution and bubble expansion, resulting in the compression of the melt and volumetric expansion of the crack. The dynamics of diffusion‐driven bubble growth and volumetric crack expansion span 9 decades in time. The model demonstrates that the speed of the crack response depends strongly on volatile diffusivity in the melt and bubble number density and is markedly sensitive to the ratio of crack thickness to crack radius and initial bubble radius but is relatively insensitive to melt viscosity. The net drop in gas concentration in the melt after pressure recovery represents only a small fraction of the initial concentration prior to the drop, suggesting the melt may undergo numerous pressure transients before becoming significantly depleted of gases. The magnitude of pressure and volume recovery in the crack depends sensitively on the size of the input‐pressure transient, becoming relatively larger for smaller‐size transients in a melt containing bubbles with initial radii less than 10−5 m. Amplification of the input transient may be large enough to disrupt the crack wall and induce brittle failure in the rock matrix surrounding the crack. Our results provide additional basis for the interpretation of volume changes in the magma conduit under Popocatépetl Volcano during Vulcanian degassing bursts in its eruptive activity in April–May 2000.

Bubble growth processes in magma surrounded by an elastic medium

Gas bubble growth in magma plays an important role in volcanic explosivity, and many previous studies have undertaken theoretical and experimental analyses of gas bubble expansion in melt. These previous studies commonly assume constant ambient pressure, but it is more natural to assume that the magma is stressed by the crust or volcanic edifices as the volume of gas bubbles increases. Here we present a bubble growth model that takes into account the elasticity of the surrounding medium; we use this model to examine temporal changes in the bubble growth process. Our model consists of a two-dimensional dike filled with compressible viscous melt and numerous tiny gas bubbles. We use the cell model proposed by Proussevitch et al. [Proussevitch, A., Sahagian, D. L., Anderson, A. T., 1993. Dynamics of diffusive bubble growth in magmas: isothermal case. J. Geophys. Res. 98, 22283–22307] to describe the interaction between the numerous gas bubbles and the melt. The bubble growth process is formulated by the diffusion equation of volatiles in the melt, the mass balance between bubbles and melt, and the momentum equation of the melt. We also introduce pressure balance equations between the melt and the surrounding elastic medium [Nishimura, T., 2004. Pressure recovery in magma due to bubble growth. Geophys. Res. Lett. 31]. Using the finite difference scheme, we numerically calculate temporal changes in bubble radius and melt pressure within magma subjected to sudden depressurization. Simulation results show that the elasticity of the surrounding medium strongly controls the bubble growth process. Under high effective rigidity, the final bubble radius is several times smaller than for zero rigidity, and the time required for bubble growth is an order of magnitude quicker. Temporal changes in the melt pressure are particularly dependent on the elasticity of the surrounding medium. Melt pressure effectively recovers and even exceeds the given pressure drop for conditions of high rigidity and/or small initial bubble radius. Although bubble growth in magma has previously been investigated mainly from geological samples and theoretical perspectives, our model can quantitatively evaluate pressure changes in magma that can also be detected by seismic and geodetic measurements.

Prediction of foam growth and its nucleation in free and limited expansion

The influence volume approach (IVA) is often utilized for modeling the mass transfer process dictating bubble growth dynamics in physical foaming. However, the assumed concentration profile in the IVA method is only valid when the changes in dissolved gas concentration are small (less than 5%). In addition, the validity of the IVA method is difficult to justify in chemical foaming applications because of the difficulties involved in defining the dissolved gas concentration profile. In the present work, we define two distinct stages of bubble growth for physical foaming. These two stages are termed as free and limited expansion and are controlled by the bubble nucleation rate. Bubble nucleation is assumed to occur only in the free expansion stage. In this stage, the bubble pressure drops substantially from an initially high pressure in the supersaturated state while the dissolved gas concentration changes very little. The second stage of our two-stage mass transfer model is termed the limited expansion stage and accounts for bubble growth in the late stages of foam evolution, when the pressure changes become small. However, in the limited stage of bubble growth the dissolved gas concentration drops significantly, as the available dissolved gas is depleted. To summarize our two-stage mass transfer model of foam expansion, the pressure difference between the bubble phase and the liquid phase is the primary mechanism for driving mass transfer in the early ( free) stages of foam growth and the concentration difference is the driver for bubble growth in the late ( limited) stages of growth. The first stage can be regarded as the nucleation stage and it is relatively short; while the second stage can be regarded as the bubble growth stage and is much longer. Most of the bubble volume expansion takes place in the second stage. The concentration gradient at the bubble edge, which is often ignored in other models, is analyzed in detail in this paper. The details of our novel mass transfer model are also presented.

Magma dynamics at mid-ocean ridges by noble gas kinetic fractionation: Assessment of magmatic ascent rates

Abstract Despite its impact in understanding oceanic crust formation and eruptive styles of related volcanism, magma dynamics at mid-ocean ridges are poorly known. Here, we propose a new method to assess ascent rates of mid-ocean ridge basalt (MORB) magmas, as well as their pre- and sin-eruptive dynamics. It is based on the idea that a rising magma can reach a variable degree of both CO2 supersaturation in melt and kinetic fractionation among noble gases in vesicles in relation to its ascent rate through the crust. To quantify the relationship, we have used a model of multicomponent bubble growth in MORB melts, developed by extending the single-component model of Proussevitch and Sahagian [A.A. Proussevitch, D.L. Sahagian, Dynamics and energetics of bubble growth in magmas: analytical formulation and numerical modeling, J. Geophys. Res. 103 (1998), 18223–18251.] to CO2–He–Ar gas mixtures. After proper parameterization, we have applied it to published suites of data having the required features (glasses from Pito Seamount and mid-Atlantic ridges). Our results highlight that the investigated MORB magmas display very different ranges of ascent rates: slow rises of popping rock forming-magmas that cross the crust (0.01–0.5 m/s), slightly faster rates of energetic effusions (0.1–1 m/s), up to rates of 1–10 m/s which fall on the edge between lava effusion and Hawaiian activity. Inside a single plumbing system, very dissimilar magma dynamics highlight the large differences in compressive stress of the oceanic crust on a small scale. Constraints on how the systems of ridges work, as well as the characteristics of the magmatic source, can also be obtained. Our model shows how measurements of both the dissolved gas concentration in melt and the volatile composition of vesicles in the same sample are crucial in recognizing the kinetic effects and definitively assessing magma dynamics. An effort should be made to correctly set the studied samples in the sequence of volcanic submarine deposits where they are collected. Enhanced knowledge of a number of physical properties of gas-bearing MOR magmas is also required, mainly noble gas diffusivities, to describe multicomponent bubble growth at a higher confidence level.

Approximate Solution for a Nonisothermal Gas Bubble Growth over a Spherical Heating Element

Recent experimental evidence has shown that single bubble generation on miniature heating elements is a competitive alternative to massive bulk bubble generation for the study of gas/vapor bubble growth dynamics. The inherent two-dimensionality of the problem leads to significant deviations of the bubble growth with respect to the bulk bubble growth which can be approximated by the classical one-dimensional (spherically symmetric) theory. In the present work, an approximate theory is developed, valid for a certain region of the problem parameters, which permits computation of the bubble radius evolution curves. On the basis of these results, the effect of the two-dimensionality (axial symmetry) of the problem on the bubble growth characteristics is assessed. The approximate solution developed here is of particular interest, since the complete solution using computational fluid dynamics (CFD) techniques is not practically feasible at this moment because of the large number of size and time scales involved in the problem.

Cavitation cluster dynamics in shock-wave lithotripsy: Part 1. Free field

The spatiotemporal dynamics of cavitation bubble growth and collapse in shock-wave lithotripsy in a free field was studied experimentally. The lithotripter was equipped with two independently triggerable layers of piezoceramics. The front and back layers generated positive pressure amplitudes of 30 MPa and 15 MPa, respectively, and −10 MPa negative amplitude. The time interval between the launch of the shock waves was varied from 0 and 0.1 s, covering the regimens of pulse-modification (regimen A, delay 0 to 4 μs), shock wave-cavitation cluster interaction (B, 4 μs to 64 μs) and shock wave-gas bubble interaction (C, 256 μs to 0.1 s). The time-integrated cavitation activity was most strongly influenced in regimen A and, in regimen B, the spatial distribution of bubbles was altered, whereas enhancement of cavitation activity was observed in regimen C. Quantitative measurements of the spatial- and time-integrated void fractions were obtained with a photographic and light-scattering technique. The preconditions for a reproducible experiment are explained, with the existence of two distinct types of cavitation nuclei, small particles suspended in the liquid and residuals of bubbles from prior cavitation clusters. (E-mail: c.d.ohl@tnw.utwente.nl)

Oxidation of zinc sulphide concentrate in a fluidised bed reactor - Part 1: Characterization of the fluid dynamics of the particle bed

The oxidation kinetics of a blend of zinc sulphide concentrates in a bench-scale fluidised bed reactor operated in batch regime was studied. This work involves the fluid dynamics characterisation of the bed during the reaction. Its purpose is to determine bed behaviour and to assess the experimental conditions used in the roasting experiments. The characterisation is derived from both fluid dynamics maps and an analysis based on the dynamics of gas bubble growth in the bed. Bed behaviour under any experimental condition is evaluated with the fluid dynamics maps. The transitions fixed/fluidised bed, fluidised bed/pneumatic transport and between several fluidisation regimes are obtained from curves of dimensionless gas velocity versus dimensionless particle diameters. The possibility of fluidisation in the slugging regime is verified by the dynamics of gas bubble growth in the bed.

Spark-induced consolidation of biological sludge

Subjecting a suspension of biological sludge to underwater sparks (3 kV, 50 kA) leads to its consolidation, decreases the charge density on the solids, and increases its settling rate. The cake solids increase, but by only one percentage point. High-speed video images show that the spark generates a steam bubble. The dynamics of bubble growth could be estimated through the Rayleigh model. The bubble collapses into an acoustic field, which then agglomerates the particles. Sparking does not affect the settling rate of an aqueous slurry of softwood pulp because the fibrous particles are too large to be aggregated by an acoustic pulse.

Modeling of bubble growth dynamics and nonisothermal expansion in starch‐based foams during extrusion

AbstractA mathematical model was developed to describe expansion phenomena in starch‐based foams during extrusion. The model was divided into three parts to describe the microbubble growth dynamics, to couple bubble growth with extrudate expansion, and to describe the macrotransport phenomena in the extrudate, respectively. The differential equations involved in the model were solved by finite element schemes. For validating the model, the predicted radius, density, and residual moisture of final extrudate were compared with experimental data. Standard deviations between the predicted and experimental radius, density, and residual moisture of final extrudates were 16.7%, 11.2%, and 39.3%, respectively. The model was used to predict the profiles of downstream velocity, expansion ratio, moisture content, and temperature of extrudate during expansion. © 2005 Wiley Periodicals, Inc. Adv Polym Techn 24:29–45, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/adv.20030

Dynamics of positronium bubble growth in liquid media and the energy dissipation problem

The dynamics of positronium bubble growth and dissipative energy loss accompanying this process were considered in the hydrodynamic approximation for liquid media with strongly differing values of the surface tension and viscosity. The driving force of the growth of the positronium bubble is repulsive exchange interaction between the electron inherent in the positronium atom and electrons of surrounding molecules. Intermolecular attraction (Laplace pressure) and viscous media retard bubble growth. In liquid helium and glycerol, the Ps formation time is comparable to or even longer than the parapositronium lifetime. Dissipative energy losses accompanying the bubble growth are substantially higher than the surface energy of the equilibrium bubble.

Modeling nanoporosity development in polymer films for low-k applications

The bubble growth dynamics of a polymer supersaturated with CO2 have been modeled for micron-size films after nucleation. The model equations are based on the shell model of Arefmanesh, Advani, and Michaelides in which a nucleated bubble is surrounded by a finite concentric shell of polymer supersaturated with gas. Bubbles grow by mass transfer of dissolved gas from this shell. The model is extended to allow for diffusion of dissolved gas out of the shell in addition to diffusion into the bubble. A parametric analysis is performed to examine the effects of film thickness, temperature, diffusivity at the Tg and Henry's law constant. POLYM. ENG. SCI., 45:640–651, 2005. © 2005 Society of Plastics Engineers

Experimental observations and modelling relating to foaming and bubble growth from pentane loaded polystyrene melts

This paper is concerned with microstructure and kinetics relating to bubble growth within a pentane loaded molten polystyrene sample and the work is of relevance to the commercial foaming of polymers achieved by pressure release at the exit of an extruder. Optical experiments were carried out using a Multipass Rheometer to follow the time evolution for melting pentane loaded polystyrene beads. Two protocols were followed and one resulted in the formation of a single melt phase. With subsequent pressure release, the growth kinetics of bubbles were followed together with rheological measurements. A modified Newtonian model incorporating gas diffusion was developed and compared with the experimental data. Good matching of data could be achieved using realistic values of parameters and the model was able to predict early stage growth conditions. The model, as presented, still has many simplifications, however it does form the basis for further refinement.

The dynamics of spherical bubble growth

Spherically symmetric bubble expansion in uniformly superheated infinite pools of liquid have been simulated numerically. Bubble growth curves have been generated for a range of Jakob numbers, 3⩽ Ja⩽3167, by altering the initial metastable state of the system facilitated by changes in the initial superheat and system pressure. The detailed physics of vapour bubble growth is studied through delineation of the parameters governing the changes in the growth dynamics from surface tension, to inertia dominated, to diffusion controlled, and the domains between them.

Simulation on the Ejection Performance of Thermal Bubble Inkjet Printhead for Top and Back Shooting Design

There are many parameters that influence droplet ejection performance, i.e. printing quality, of inkjet print head such as ejection velocity and directionality of ink droplet. Ink droplet with larger ejection velocity from an inkjet print head nozzle exit will be less affected by the surrounded air disturbance and keep a good directionality. The printing quality of a thermal bubble inkjet print head is also affected by bubble growth dynamics. It depends on the proper geometry and size designs of micro-fluidic ink channel within the inkjet print head such as nozzle orifice, ink firing chamber and heaters. This work used computational fluid dynamics (CFD) method to study the parameters and effects on droplet ejection performance of thermal bubble inkjet print head for both top and back shooting type of thermal bubble nucleation. The numerical scheme, volume of fluid (VOF) method, has been used to deal with the interface between surrounded air and droplet liquid.