Ultrasound is known to enhance surface bubble growth and removal in catalytic and microfluidic applications, yet the contributions of rectified diffusion and microstreaming phenomena towards mass transfer remain unclear. We quantify the effect of ultrasound on the diffusive growth of a single spherical CO$_2$ bubble growing on a substrate in supersaturated water. The time dependent bubble size, shape, oscillation amplitude and microstreaming flow field are resolved. We show and explain how ultrasound can enhance the diffusive growth of surface bubbles by up to two orders of magnitude during volumetric resonance. The proximity of the wall forces the bubble to oscillate non-spherically, thereby generating vigorous streaming during resonance that results in convection-dominated growth.
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. , J. Fluid Mech. , vol. 800, 2016 b , 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.
Dissolution and mass transfer of carbon dioxide gas into liquid barriers plays a vital role in many environmental and industrial applications. We study the downward dissolution and propagation dynamics of CO${}_{2}$ into a vertical water barrier confined to a narrow vertical glass cylinder, using both experiments and direct numerical simulations (DNS). Tracking the CO${}_{2}$ front propagation in time leads to discovery of two distinct transport regimes: A purely diffusive and an enhanced diffusive regime. Using DNS, we explain the propagation dynamics of these two transport regimes, namely by disentangling the contributions of diffusion and convection to the propagation of the CO${}_{2}$ front.
The presence of bubbles in gas-evolving electrolytic processes can heavily alter the mass transport of gaseous products and can induce severe overpotential penalties at the electrode through the action of bubble coverage (hyperpolarization) and electrolyte constriction (Ohmic shielding). However, bubble formation can also alleviate the overpotential by lowering the concentration of dissolved gas in the vicinity of the electrode. In this study, we investigate the latter by considering the growth of successive hydrogen bubbles driven by a constant current in alkaline-water electrolysis and their impact on the half-cell potential in the absence of hyperpolarization. The bubbles nucleate on a hydrophobic cavity surrounded by a ring microelectrode which remains free of bubble coverage. The dynamics of bubble growth does not adhere to one particular scaling law in time, but undergoes a smooth transition from pressure-driven towards supply-limited growth. The contributions of the different bubble-induced phenomena leading to the rich behaviour of the periodic fluctuations of the overpotential are identified throughout the different stages of the bubble lifetime, and the influence of bubble size and applied current on the concentration and Ohmic overpotential components is quantified. We find that the efficiency of gas absorption, and hence the concentration-lowering effect, increases with increasing bubble size and also with increasing current. However, the concentration-lowering effect is always eventually countered and overcome by the effect of Ohmic shielding as the bubble size outgrows and eclipses the electrode ring beneath.
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-generated bubbles is compared to that of CO2 bubbles growing on a similar surface in the presence of a supersaturated solution of carbonated water. For electrolytic bubbles and under the range of current densities considered here (5-15 A/m2), 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. This clearly contradicts the common assumption that constant current densities must yield time-invariant growth rates. Conversely, for the case of CO2 bubbles, the growth coefficient successively decreases for every subsequent bubble as a result of the persistent depletion of dissolved CO2.
Bubbles are known to hinder electrochemical processes in water-splitting electrodes. In this study, we present a novel method to promote gas evolution away from the electrode surface. We consider a ring microelectrode encircling a hydrophobic microcavity from which a succession of bubbles grows. The ring microelectrode, tested under alkaline water electrolysis conditions, does not suffer from bubble coverage. Consequently, the chronopotentiometric fluctuations of the cell are weaker than those associated with conventional microelectrodes. Herein, we provide fundamental understanding of the mass transfer processes governing the transient behaviour of the cell potential. With the help of numerical transport models, we demonstrate that bubbles forming at the cavity reduce the concentration overpotential by lowering the surrounding concentration of dissolved gas, but may also aggravate the ohmic overpotential by blocking ion-conduction pathways. The theoretical and experimental insight gained have relevant implications in the design of efficient gas-evolving electrodes.
Mass transfer of gases in liquid solvents is a fundamental process during bubble generation for specific purposes or, vice versa, removal of entrapped bubbles. In our work, we address the growth dynamics of a trapped slug bubble in a vertical glass cylinder under a water barrier after replacing the ambient air atmosphere by a CO${}_{2}$ atmosphere at the same or higher pressure. The asymmetric exchange of the gaseous solutes between the CO${}_{2}$-rich water barrier and the air-rich bubble always results in net bubble growth, which we call solute exchange. We compare and explain the experimental results with a simple numerical model, with which the underlying mass transport processes are quantified.
Microstructured electrodes have been shown to be effective as light harvesting structures for solar-driven water electrolysis. [1] However, a better understanding of the fundamental physicochemical aspects of the gas evolution particularly at the micro- and mesoscale, and bubble formation during the electrolysis is needed in order to improve the efficiencies of hydrogen production. [2] We have micromachined superhydrophobic pits on top of single pillars to control the evolution of gas bubbles. Single pillars with radius R p , ranging from 1.5 μm up to 15 μm in radius, are considerably smaller than the electrode surface ( R e >> R p , with R e the radius of the circular electrode surface). This is done to minimize bubble-bubble interaction and to optically study the interaction of bubbles on such structures. Pits entrap air upon submersion of the electrode in an electrolyte, and thus serve as predefined bubble nucleation site. During electrolysis, the bubbles grow from the pit, up to their detachment. Upon detachment, a gas pocket is left in the pit, ensuring a continuous cycle of bubble growth and detachment. Figure 1(b) shows the electrolytic growth of successive bubbles on a microstructured electrode at various current densities. It is observed that the size of detaching bubbles does not depend on the current density, but on a balance between interfacial tension and buoyancy forces. However, the time taken for bubbles to detach varies with the current density. In general, for successive electrolytic bubbles growing on electrodes, the bubble growth rate increases with time. The time evolution of the bubble radius R(t) can be described by R = βt x , where β is a growth coefficient determined by the supersaturation level of dissolved gas in the liquid phase and x a scaling exponent. [3] It is known that during electrolysis with a large electrode surface ( R e >> R d , with R d the bubble radius at detachment), diffusive bubble growth is obtained. Diffusive growth, where x = 1/2 , will be assumed for our studies. The growth coefficient is then defined as: β = d(R(t)/t 1/2 )/dt . A boundary layer of dissolved gas is formed near the electrode surface during electrolysis. We can accurately describe the phenomena associated to the boundary layer influencing the growth of bubbles by studying the growth coefficient. Successive generated bubbles experience a locally depleted gas boundary layer. When bubbles detach, they transport hydrogen away from the boundary layer. In Figure 1(c) the β value decreases at short times ( t m < 684 s, with t m the mean time of the individual bubble growth period), because the evolved hydrogen had little time to diffuse in a region of the order of the bubble size. This depletion effect is more important in early stages because, as the reaction time increases, the boundary layer develops further, resulting in faster bubble growth and larger β values. Eventually, a roughly constant value is reached with prolonged electrolysis time (not shown in the figure). Next to the bubble evolution by electrolysis as described above, we also work on CO 2 bubble evolution in supersaturated liquids on the same type of microstructured electrodes. Our ultimate aim is to understand the underlying fundamentals of bubble growth on any substrate. The obtained insight will be valuable for the design of novel surfaces in electrolysers, fuel cells, and solar-to-fuel devices. [1] R. Elbersen, W. Vijselaar, R. M. Tiggelaar, H. Gardeniers, and J. Huskens. Adv. Energy Mater . Vol. 6, Issue 3, pp. 1-6, 2016. [2] M. A. Modestino, D. F. Rivas, S. M. H. Hashemi, J. G. E. Gardeniers, and D. Psaltis, Energy Environ. Sci. Vol. 9, pp. 3381-3391, 2016. [3] N. P. Brandon and G. H. Kelsall, J. Appl. Electrochem. Vol. 15, No. 4, pp. 475-484, 1985. Acknowledgements This work was supported by the Netherlands Center for Multiscale Catalytic Energy Conversion (MCEC), an NWO Gravitation programme funded by the Ministry of Education, Culture and Science of the government of the Netherlands. Figure 1
This paper is associated with a video winner of a 2018 APS/DFD Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2018.GFM.V0054