Abstract: 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 (Penas-Lopez et al., J. Fluid Mech., vol. 800, 2016b, pp. 180–212), 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 stepwise 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, although given the supersaturation conditions studied here, the bubble evolution is expected to be mainly diffusive.
Abstract: Microscopic bubble dissolution is driven by the diffusion of gas within the surrounding liquid. Asymptotic analysis is used to characterize collective shielding effects in bubble lattices, the resulting bubble lifetime and dissolution dynamics.
TL;DR: The current results show that the dynamical evolution of bubbles is influenced by comprehensive effects combining chemical catalysis and physical mass transfer, and the size of the bubbles at the moment of detachment is determined by the balance between buoyancy and surface tension and by the detailed geometry at the bubble’s contact line.
Abstract: Whereas bubble growth out of gas-oversatured solutions has been quite well understood, including the formation and stability of surface nanobubbles, this is not the case for bubbles forming on catalytic surfaces due to catalytic reactions, though it has important implications for gas evolution reactions and self-propulsion of micro/nanomotors fueled by bubble release. In this work we have filled this gap by experimentally and theoretically examining the growth and detachment dynamics of oxygen bubbles from hydrogen peroxide decomposition catalyzed by gold. We measured the bubble radius R(t) as a function of time by confocal microscopy and find R(t) ∝ t1/2. This diffusive growth behavior demonstrates that the bubbles grow from an oxygen-oversaturated environment. For several consecutive bubbles detaching from the same position in a short period of time, a well-repeated growing behavior is obtained from which we conclude the absence of noticeable depletion effect of oxygen from previous bubbles or increasing oversaturation from the gas production. In contrast, for two bubbles far apart either in space or in time, substantial discrepancies in their growth rates are observed, which we attribute to the variation in the local gas oversaturation. The current results show that the dynamical evolution of bubbles is influenced by comprehensive effects combining chemical catalysis and physical mass transfer. Finally, we find that the size of the bubbles at the moment of detachment is determined by the balance between buoyancy and surface tension and by the detailed geometry at the bubble's contact line.
TL;DR: It is observed that H2 bubble successions at large gas-evolving substrates first experience a stagnation regime, followed by a fast increase in the growth coefficient before a steady state is reached, which clearly contradicts the common assumption that constant current densities must yield time-invariant growth rates.
Abstract: Control over the bubble growth rates forming on the electrodes of water-splitting cells or chemical reactors is critical with respect to the attainment of higher energy efficiencies within these devices. This study focuses on the diffusion-driven growth dynamics of a succession of H2 bubbles generated at a flat silicon electrode substrate. Controlled nucleation is achieved by means of a single nucleation site consisting of a hydrophobic micropit etched within a micrometer-sized pillar. In our experimental configuration of constant-current electrolysis, we identify gas depletion from (i) previous bubbles in the succession, (ii) unwanted bubbles forming on the sidewalls, and (iii) the mere presence of the circular cavity where the electrode is being held. The impact of these effects on bubble growth is discussed with support from numerical simulations. The time evolution of the dimensionless bubble growth coefficient, which is a measure of the overall growth rate of a particular bubble, of electrolysis-gene...
Abstract: When a gas bubble grows by diffusion in a gas-liquid solution, it affects the distribution of gas in its surroundings. If the density of the solution is sensitive to the local amount of dissolved gas, there is the potential for the onset of natural convection, which will affect the bubble growth rate. The experimental study of the successive quasi-static growth of many bubbles from the same nucleation site described in this paper illustrates some consequences of this effect. The enhanced growth due to convection causes a local depletion of dissolved gas in the neighbourhood of each bubble beyond that due to pure diffusion. The quantitative data of sequential bubble growth provided in the paper show that the radius-versus-time curves of subsequent bubbles differ from each other due to this phenomenon. A simplified model accounting for the local depletion is able to collapse the experimental curves and to predict the progressively increasing bubble detachment times.
Abstract: The formation of gas bubbles at gas cavities located in walls bounding the flow occurs in many technical applications, but is usually hard to observe. Even though, the presence of a fluid flow undoubtedly affects the formation of bubbles, there are very few studies that take this fact into account. In the present paper new experimental results on bubble formation (diffusion-driven nucleation) from surface nuclei in a shear flow are presented. The observed gas-filled cavities are micrometre-sized blind holes etched in silicon substrates. We measure the frequency of bubble generation (nucleation rate), the size of the detaching bubbles and analyse the growth of the surface nuclei. The experimental findings support an extended understanding of bubble formation as a self-excited cyclic process and can serve as validation data for analytical and numerical models.
Abstract: Some simple similarity solutions are presented for the flow of a viscous fluid near a sharp corner between two planes on which a variety of boundary conditions may be imposed. The general flow near a corner between plane boundaries at rest is then considered, and it is shown that when either or both of the boundaries is a rigid wall and when the angle between the planes is less than a certain critical angle, any flow sufficiently near the corner must consist of a sequence of eddies of decreasing size and rapidly decreasing intensity. The ratios of dimensions and intensities of successive eddies are determined for the full range of angles for which the eddies exist. The limiting case of zero angle corresponds to the flow at some distance from a two-dimensional disturbance in a fluid between parallel boundaries. The general flow near a corner between two plane free surfaces is also determined; eddies do not appear in this case. The asymptotic flow at a large distance from a corner due to an arbitrary disturbance near the corner is mathematically similar to the above, and has comparable properties. When the fluid is electrically conducting, similarity solutions may be obtained when the only applied magnetic field is that due to a line current along the intersection of the two planes; it is shown that the effect of such a current is to widen the range of corner angles for which eddies must appear.
Abstract: With the neglect of the translational motion of the bubble, approximate solutions may be found for the rate of solution by diffusion of a gas bubble in an undersaturated liquid‐gas solution; approximate solutions are also presented for the rate of growth of a bubble in an oversaturated liquid‐gas solution. The effect of surface tension on the diffusion process is also considered.
Abstract: The equations governing spherically symmetric phase growth in an infinite medium are first formulated for the general case and are then simplified to describe growth controlled by the transport of heat and matter. All assumptions and restrictions are recounted. Exact solutions of the equations are obtained for conditions typical of bubble growth in the nucleate boiling of (a) pure materials, and (b) binary mixtures. The effect of radial convection resulting from unequal phase densities is established and the regions of applicability of previously reported approximate solutions are determined.
Abstract: This paper deals chiefly with calculations and experiments on the flow past circular cylinders, but the arithmetical methods of solution of the equations of steady viscous flow proposed and used in Section I, are applicable to other equations and may be of interest.