Jet drop production from bubbles with neighbors

TL;DR

The paper demonstrates that neighboring bubbles in surface rafts drastically modify jet drop formation during cavity collapse, producing smaller, faster, and more numerous drops than isolated bubbles. Using a dual-view, high-speed experimental setup and image-based raft detection, the authors show that increasing the number of neighbors up to six disrupts axisymmetry, induces polygonal cavity shapes, and enhances dissipation, effectively lowering the apparent Laplace-number regime. They quantify these effects across single and multiple bursting events and develop a Monte-Carlo estimator to predict raft-wide drop distributions from raft statistics, revealing a substantial broadening and downward shift in drop sizes relative to isolation. The findings imply that real-world systems with bubble rafts, such as ocean surfaces or sparkling beverages, exhibit significantly altered aerosolization and mass-transfer characteristics due to collective jetting dynamics, with potential implications for air-sea exchange models and microplastic/aerosol loading. The work also provides a framework to extend predictions to broad raft-size distributions and varying interfacial contamination. $R_b$, $N_n$, $R_{d_1}$, $V_{d_1}$, La, Bo, ext{and related quantities}$ are central to the analysis, and the code for downstream drop-distribution calculations is publicly available.

Abstract

Bubbles bursting at the surface of the ocean produce drops that heavily influence ocean-atmosphere interactions. One of the mechanisms through which drops are formed is called jet drop production, where the collapse of the bubble cavity leads to the formation of a fast upwards jet that breaks to form drops. While isolated bubble bursting has been extensively studied, bubbles are often found in rafts (for instance in the ocean surface or a sparkling wine glass) and the understanding of collective effects remains more limited. We investigate experimentally how jet drop formation is modified by the presence of neighboring bubbles during the collapse. With the help of multiple high speed views of the collapsing bubble, we show how a change of cavity shape during collapse leads to the selection of smaller, faster, and more numerous drops. The size of the emitted drops is monotonically reduced with increasing number of neighboring bubbles (up to six for hexagonal packing) with the size reduction reaching a factor 5. The drop size distribution associated with bubbles arranged in rafts of various sizes is therefore much wider than in the case of isolated bubbles, and with a peak shifted to smaller sizes.

Figures (15)

• Figure 1: (a) Schematic of the experimental setup used to simultaneously measure surface bubbles and jet drops. A nearly monodisperse distribution of surface bubbles is generated by injecting air at the bottom of a water tank with a syringe pump. As air is released, bubbles rise to the surface where, under sufficient surfactant contamination, they persist and form bubble rafts. Surface bubbles are detected from top-view images and the jet drops detection relies on side-view high speed imaging. (b) Example of the synchronized dual-view of a bursting event. The main view shows a tilted ejected jet destabilizing into drops (red). The times since the bursting of the cap are given in terms of the capillary timescale: $t_c=\sqrt{\rho R_b^3/\gamma} \approx 3.8$ ms. The inset in the top left panel shows the top view just before bursting with the bursting bubble highlighted in red and the neighbors in blue. The inset in the bottom right panel shows the raft on the next top view frame, with the bursting bubble having disappeared from the raft.
• Figure 2: Variations of the jetting process as the number of neighbors is increased. Each panel (a) to (d) shows the top view just before the bubble bursts (top row, bursting bubble in red and neighbors in blue), and the side view as the first drop is ejected (bottom row). As the number of neighbors is increased, the jet can be seen getting thinner and tilting towards the side free of bubbles. (e) Example of bubble bursting with six neighbors and producing a very large number of droplets. Note that the scale is smaller in this case. The inset shows the top view just before (top) and after (bottom) bursting.
• Figure 3: Evolution of the normalized radius of the first drop, $R_{d_1}/R_{d_1}(N_n=0)$ as a function of the number of adjacent neighbors $N_n$, for various contamination levels $c$ and surface bubble sizes $\left< R_b \right>$. Each datapoint corresponds to several repetitions with a given number of neighbors. The marker shows the mean, and the errorbar length is one standard deviation, with a minimal value corresponding to 4 pixels. Data points shown with transparency indicate cases where fewer than four measurements were available to compute the mean. The black line corresponds to the average of all cases.
• Figure 4: (a) Relation between the first drop's radius and velocity, both normalized by the case with no neighbors. The data shown regroups all cases of the study, and the color indicates the number of neighbors. The dashed line represents combined scalings from the literature (i.e. $V_{d_1} \propto R_{d_1}^{-3/5}$), which is consistent with the present data (Eq. \ref{['eq:velrad']}). (b) Evolution of the number of drops ejected with the number of neighbors. Colors represent different cases identically to Fig. \ref{['fig:first_drop_rad']}. Markers show the mean, and the errorbar length is one standard deviation. Data points shown with transparency indicate cases where fewer than four measurements were available to compute the mean. The dotted line is the trend line $N_d = 4 / 3 N_n$.
• Figure 5: Chronophotography of side-view images showing cavity collapse dynamics for different neighboring configurations, all recorded at an SDS concentration of $c = 27.2~\mu\mathrm{mol}/\mathrm{L}$. A schematic of the top view is displayed for each case, with the red bubble bursting. Time of acquisitions are normalized by the capillary time $t_c = 3.8$ ms. In the presence of neighboring bubbles, the axisymmetry of the cavity collapse is broken, and the cavity profiles differs from the isolated case in particular on the side with neighbors.