Critical bubble bursting in real water. Effect of surface-active contaminants

TL;DR

The paper addresses how surface-active contaminants influence bubble bursting at a free surface under critical conditions defined by $Bo \approx 0$ and $La \approx La^*$. It employs experiments with DMSO/water mixtures and two surfactants to quantify changes in the first-emitted jet droplet, including $R_d$, $V_d$, and the total spray, while linking these changes to surfactant adsorption and surface-tension variations via Langmuir/Gibbs isotherms. The key finding is that surfactant accumulation at the cavity bottom during collapse induces Marangoni stresses that slow the jet interface and delay free-surface reversal, while also increasing the overall mass and energy transferred to the spray; these effects persist even for very weak contaminants and can be described by a power-law in surfactant strength and concentration. The results imply that natural seawater contamination can markedly alter aerosol production from bursting bubbles and related transport of chemicals and biological materials into the atmosphere, with potential implications for climate-related aerosol dynamics and public health.

Abstract

We study the bursting of a bubble on a liquid free surface under critical conditions, i.e., those leading to the minimum (maximum) size (velocity) of the first-emitted jet droplet. Our experiments show that a tiny amount of surfactant considerably increases (decreases) the droplet radius (velocity). The volume of the first-emitted droplet increases by a factor of 20 for a concentration that produces an insignificant reduction in the bubble surface tension. The total liquid volume ejected by the bubble increases with the surfactant concentration. Surfactant accumulates at the bubble base due to cavity bottom shrinkage and surfactant convection. The resulting reduction in surface tension narrows the region of free surface reversal. Despite this effect, the size of the emitted droplet increases due to the Marangoni stress acting on the jet surface. Marangoni stress slows down the interface of the liquid jet, delaying the detachment of the droplet. More liquid flows into the droplet, increasing the mass and energy transfer to the resulting spray. A significant increase in the droplet size is also observed with a weak surfactant. This indicates that natural water contamination can substantially alter the bursting of bubbles under critical conditions. Our results may explain the size of the particles emitted by bubble bursting in seawater.

Figures (5)

• Figure 1: Radius $R_d$ and velocity $V_d$ of the first emitted droplet as a function of the Laplace number for surfactant-free experiments. The droplet radius and velocity are measured in terms of the viscous-capillary length $L_{\mu}=\mu^2/(\rho\sigma)$ and velocity $V_{\mu}=\sigma/\mu$. The triangles are our experimental data for $\text{Bo}=0.007-0.018$. The squares, circles, and diamonds are the results of BBWFYB18, BDSP20, and DGLDZPS18, respectively.
• Figure 2: (a) Bubble bursting in the presence of surfactant. (b) Surface tension $\sigma$ as a function of the surfactant concentration $c/c_{\hbox{\scriptsize{cmc}}}$ for DMSO/water mixtures (50/50 wt). The arrows indicate the surfactant concentrations considered in this study. The solid line is a fit to the experimental data using the Langmuir equation of state for Tween 80 (see the Supplemental Material). (c) Surface tension $\sigma$ as a function of the surfactant coverage $\Gamma$ calculated from the fit for Tween 80. The horizontal arrows indicate the estimated increase in the surface coverage during the bubble bursting, as explained in the text.
• Figure 3: (a) Images of the cavity collapse without surfactant and with Tween 80 at $c/c_{\hbox{\scriptsize{cmc}}}=0.0233$ ($\Gamma_{\hbox{\scriptsize{eq}}}=0.26$) both for $\text{La}\simeq \text{La}^*$ and $\text{Bo}\simeq 0.01$. (b) Zoom in on the bubble bottom region close to the free surface reversal. The labels indicate the time to the film rupture (a) and free surface reversal (b) divided by the inertio-capillary time $t_0$. The orange arrows indicate the free surface reversal instant. The red arrows in (b) point at a previous capillary wave. The black arrow in (b) indicates the free surface curvature $\kappa_1=-d^2r/dz^2/[1+(dr/dz)^2]^{3/2}$ partially eliminated by the surfactant. (c) Cavity bottom width $w$ and upward velocity $V_B$ as a function of time to the free surface reversal. (d) Curvature $\kappa_1$ and total curvature $\kappa=\kappa_1+\kappa_2$ ($\kappa_2=[r\sqrt{1+(dr/dz)^2}]^{-1}$) along the lateral free surface (excluding the corner and bottom of the cavity) for $(t-t_r)/t_0=-0.07$ calculated with a subpixel resolution technique M24. The bubble was 225 $\mu$m in radius.
• Figure 4: Dimensionless radius $R_d/R_b$ and velocity $V_d/V_\mu$ ($V_\mu=\sigma_c/\mu$) of the first-emitted jet droplet as a function of the Laplace number La without surfactant (green symbols), with Tween 80 (red symbols), and with SDS (blue symbols). The error bars indicate the standard deviation.
• Figure 5: Number $N$ of jet droplets (a), total emitted surface $S_t$ (b), volume $V_t$ (c), and kinetic energy $E_{k,t}$ (d). The results are expressed in terms of the bubble surface $S_b=4\pi R_b^2$, volume $V_b=4/3\pi R_b^3$, and interfacial energy $E_{s,b}=\sigma_c S_b$. The dashed line in b) corresponds to $S_t/S_b=\Gamma_{\hbox{\scriptsize{eq}}}$.