Geoffrey M. Evans

Bubble nucleation from gas cavities : a review

Abstract This review is concerned with the nucleation of bubbles in solutions supersaturated with a gas, in particular the bubble nucleation that occurs at specific sites, as a cycle. A classification system for the kinds of nucleation that occur is defined and discussed in order to place this specific form of nucleation into a better defined context. It is noted that in the absence of pre-existing gas cavities, bubble nucleation requires exceedingly high levels of supersaturation. It is argued that the nucleation observed in most instances, which is often at low levels of supersaturation of 5 or less, is invariably associated with the existence of metastable gas cavities in the walls of the container or the solution bulk, prior to the system being made supersaturated. Here, the nucleation energy barrier for each gas cavity is very much lower than for the classical case, given that less interfacial free energy is needed for the cavity to grow to the critical size when the system is made supersaturated. Once a system contains gas cavities with radii of curvature greater than the critical nucleation radius, bubbles are produced in a steady fashion without the need to scale a nucleation energy barrier. This non-classical form of nucleation is the main focus of the paper. Issues concerning the formation of these gas filled cavities, and their stability are examined.

Predicting gas–liquid flow in a mechanically stirred tank

Abstract Computational fluid dynamics (CFD) provides a method for investigating the highly complex fluid flow in mechanically stirred tanks. Although there are quite a number of papers in the literature describing CFD methods for modelling stirred tanks, most only consider single-phase flow. However, multiphase mixtures occur very frequently in the process industries, and these are more complex situations for which modelling is not as well developed. This paper reports on progress in developing CFD simulations of gas–liquid mixing in a baffled stirred tank. The model is three-dimensional and the impeller region is explicitly included using a Multiple Frames of Reference method to account for the relative movement between impeller and baffles. Fluid flow is calculated with a turbulent two-fluid model using a finite-volume method. Several alternative treatments of the multiphase equations are possible, including various expressions for drag and dispersion forces, and a number of these have been tested. Variation in bubble size due to coalescence and break-up is also modelled. The CFD simulation method has been used to model a gas-sparged tank equipped with a Rushton turbine, and simulation results are compared with experimental data. Results to date show the correct pattern of gas distribution and the correct trends in local bubble size in the tank. Further work is needed to improve the quantitative agreement with experimental data.

PREDICTION OF THE BUBBLE SIZE GENERATED BY A PLUNGING LIQUID JET BUBBLE COLUMN

Abstract In this paper a model is presented to predict the maximum bubble size generated within the mixing zone at the top of a plunging liquid jet bubble column. The model uses a critical Weber number, where the energy dissipation rate per unit volume is derived from the theory of liquid-jet gas ejectors. The length of the mixing zone, and hence its volume, was determined experimentally from the vertical axial pressure profile along the wall of the column. The model was tested experimentally for a range of column and jet diameters, jet velocities, and liquid physical properties, and it was found that the measured maximum bubble diameter was in good agreement with the model predictions based on a critical Weber number of 1.2. It was also found that the bubble diameter distribution was fitted by a log-normal distribution, with a Sauter-mean-to- maximum-diameter ratio of 0.61 which is consistent with reported literature values.

The cycle of bubble production from a gas cavity in a supersaturated solution

Abstract Bubble nucleation, classified according to the review by Jones et al. (Adv. Colloid Interface Sci. 80 (1999) 27–50) as type IV non-classical, was examined in this study. Trains of bubbles were produced in carbonated water solutions at low levels of supersaturation, typically less than about 2, at specific sites on the surface of the vessel in contact with the liquid. Closer examination at a given site revealed a cycle of bubble formation, growth and detachment, defined by the growth time, t g , required for the bubble to grow to its detachment diameter, and the nucleation time, t n , required for a new bubble to appear following detachment. A relationship, representing the cycle of bubble production, was obtained by combining the bubble growth time, calculated using Scrivens model (Scriven, Chem. Eng. Sci. 10(1/2) (1959) 1–13), with the bubble nucleation time. That is, 1 t g = N t n + 1 t g * where N is a dimensionless number characterising the bubble nucleation time, and t g * is the growth time of the last possible bubble. Experiments conducted at a number of sites, and at different temperatures, produced results consistent with the above relationship. Most of the experiments were conducted with the contact angle at 65°, and these generally resulted in a bubble detachment diameter of about 600 μm, and a value of N ∼0.3. It was concluded that the nucleation time was dependent on the diameter of the detaching bubble. This dependence was explained by considering the volume of liquid, partially depleted of carbon dioxide, in the boundary layer of the bubble. Some of this partially depleted liquid should leave with the departing bubble, and the rest should remain above the gas cavity, thus slowing down the rate of bubble growth in the cavity. A consideration of the critical condition for bubble detachment indicated that the bubble remained rooted at the cavity mouth during its growth. It was shown, using the growth time of the last possible bubble, that the critical radius of curvature of the meniscus in the cavity was about 3.3 μm at 16°C. The radius was also found to increase significantly with temperature, suggesting that the position of the meniscus inside the cavity moved when the system temperature was changed, and that the cavity was essentially conical.

Free jet expansion and gas entrainment characteristics of a plunging liquid jet

Abstract The change in effective jet diameter is measured as a function of free jet length for vertical liquid jets passing through air. The data are incorporated into a model to predict the rate of gas entrainment for a liquid jet plunging into a confined column of liquid. In the model it was assumed that the total gas entrainment rate included gas contained within (1) the effective diameter of the free jet at the plunge point and (2) an annular film adjacent to the surface of the jet, where the outer boundary of the film was defined to be the separating streamline between the entrained and unentrained components of the moving gas boundary layer. It was further assumed that the radial location of the separating streamline was independent of both liquid and gas flow rates and system geometry. Excellent agreement between model predictions and gas entrainment measurements were obtained once a number of experimental parameters were determined.

Performance of confined plunging liquid jet bubble column as a gas–liquid reactor

The volumetric mass transfer coefficient in a confined plunging liquid jet (CPLJ) bubble column absorber was determined during a steady-state absorption of CO 2 in sodium carbonate and bicarbonate solution with an addition of hypochlorite catalyst. Special care was paid while choosing the suitable reaction rate to account for the two different zones in the absorber (mixing zone and pipe flow zone) where the volumetric mass transfer coefficients differ by an order of magnitude. The determined mass transfer coefficients reached 0.6 s -1 and appeared to be 50% lower than those determined during physical absorption of CO 2 . Energetic efficiency of the examined CPLJ contactor was also calculated.

A floating self-propelling liquid marble containing aqueous ethanol solutions

A liquid marble is a droplet coated with hydrophobic particles. A floating liquid marble is a unique reactor platform for digital microfluidics. The autonomous motion of a liquid marble is of great interest for this application because of the associated chaotic mixing inside the marble. A floating object can move by itself if a gradient of surface tension is generated in the vicinity of the object. This phenomenon is known as the Marangoni solutocapillary effect. We utilized a liquid marble containing a volatile substance such as ethanol to generate the solutocapillary effect. This paper reports a qualitative study on the operation conditions of liquid marbles containing aqueous ethanol solutions in autonomous motion due to the Marangoni solutocapillary effect. We also derive the scaling laws relating the dynamic parameters of the motion to the physical properties of the system such as the effective surface tension of the marble, the viscosity and the density of the supporting liquid, the coefficient of diffusion of the ethanol vapour, the geometrical parameters of the marble, the speed, the trajectory and the lifetime of the autonomous motion. A self-driven liquid marble has the potential to serve as an effective digital microfluidic reactor for biological and biochemical applications.

Effect of Environmental Humidity on Static Foam Stability

The quality of foaming products (such as beer and shampoo) and the performance of industrial processes that harness foam (such as the froth flotation of minerals or the foam fractionation of proteins) depend upon foam stability. In this study, experiments are performed to study the effect of environmental humidity on the collapse of static foams. The dependency of the rate at which a foam collapses upon humidity is demonstrated, and we propose a hypothesis for bubble bursting due to Marangoni instability induced by nonuniform evaporation to help explain the dependency. This hypothesis is supported by direct experimental observations of the bursting process of isolated bubbles by high speed video recording and the thinning of isolated foam films under different values of humidity and temperature by microinterferometric methods.

A simple numerical solution to the Ward-Tordai equation for the adsorption of non-ionic surfactants

A simple numerical scheme for solving the equation of Ward and Tordai (1946) for the diffusion-controlled adsorption of non-ionic surfactants to interfaces is proposed and pseudo-code, as well as C++ source code, is provided. The scheme utilises the trapezium rule of numerical integration and the accuracy and robustness of the method is enhanced by the bisection method of root-finding. The scheme is efficient and flexible in that it can be used with any adsorption isotherm and is readily modified for solving the problem of adsorption onto a convex interface. This scheme is not suggested for the adsorption onto a concave interface and the confusions that have previously arisen in relation to this problem are discussed.

Effect of vessel scaleup on the hydrodynamics of a self-aerating concave blade impeller

Abstract A theoretical model has been developed to predict the pressure at the gas outlet of a gas-inducing impeller and to determine the minimum speed at which gas induction occurs, for a given impeller design and submersion depth. The model also predicts the flow rate of gas induced at higher impeller speeds, by balancing the pressure reduction due to flow over the blades, against pressure losses associated with the flow of gas and bubble formation. Pressure measurements for an impeller moving in single-phase (prior to gas induction) were used to determine independently the model constants for a concave impeller. These constants were identified as a blade slip factor and a pressure coefficient and were shown to be independent of Reynolds number (in the turbulent regime) and constant over the range of submersion depths used in practice. The model predictions for the minimum induction speed were in good agreement with experiments for a concave impeller at a number of angles of attack and in various vessel geometries. Gas flow rate measurements at higher impeller speeds indicated that the pressure driving force was a function of the detached bubble radius, and providing this dependence was known, the model could be used to predict the rate of gas induction.