Sea spray is the main source of aerosols above the ocean. One of the pathways for sea spray production is through bubble bursting which ejects myriads of droplets. We present a detailed description of the velocity of jets formed by bubble bursting, obtained through extensive comparison between experimental results and numerical simulations for a wide range of physical parameters. We discuss the importance of the shape of the cavity on the jet velocity and the regime of parameters for which drop ejection is observed. We present a phenomenological formula that predicts the jet velocity for the full range of parameters and compare it to a theoretical prediction based on curvature reversal. The results are then discussed in light of their fundamental applications in the understanding of the phenomena.

Dynamics of jets produced by bursting bubbles

Ultrasound is extensively used in medical imaging, being safe and inexpensive and operating in real time. Its scope of applications has been widely broadened by the use of ultrasound contrast agents (UCAs) in the form of microscopic bubbles coated by a biocompatible shell. Their increased use has motivated a large amount of research to understand and characterize their physical properties as well as their interaction with the ultrasound field and their surrounding environment. Here we review the theoretical models that have been proposed to study and predict the behavior of UCAs. We begin with a brief introduction on the development of UCAs. We then present the basics of free-gas-bubble dynamics upon which UCA modeling is based. We review extensively the linear and non-linear models for shell elasticity and viscosity and present models for non-spherical and asymmetric bubble oscillations, especially in the presence of surrounding walls or tissue. Then, higher-order effects such as microstreaming, shedding and acoustic radiation forces are considered. We conclude this review with promising directions for the modeling and development of novel agents.

Ultrasound Contrast Agent Modeling: A Review.

Bubble interactions and bursting behaviors near a free surface

Here we provide a theoretical framework describing the generation of the fast jet ejected vertically out of a liquid when a bubble, resting on a liquid–gas interface, bursts. The self-consistent physical mechanism presented here explains the emergence of the liquid jet as a consequence of the collapse of the gas cavity driven by the low capillary pressures that appear suddenly around its base when the cap, the thin film separating the bubble from the ambient gas, pinches. The resulting pressure gradient deforms the bubble which, at the moment of jet ejection, adopts the shape of a truncated cone. The dynamics near the lower base of the cone, and thus the jet ejection process, is determined by the wavelength , the jet is ejected after a bubble is pinched off; in this regime, viscosity delays the formation of the jet, which is thereafter emitted at a velocity which is inversely proportional to the liquid viscosity.

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Capillary waves control the ejection of bubble bursting jets

We present experimental results of film drainage on top of gas bubbles pushed by gravity towards the free surface of highly viscous Newtonian liquid with a uniform interface tension. The temporal evolution of the thickness of the film between a single bubble and the air/liquid interface is investigated via interference method. Experiments under various physical conditions (range of viscosities and surface tension of the liquid, and bubble sizes) evidence the influence of the deformation of the thin film on the thinning rate and confirm the slow down of film drainage with Bond number as previously reported by numerical work of Pigeonneau and Sellier [Phys. Fluids 23, 092102 (2011)]10.1063/1.3629815. Considering the liquid flow in the cap squeezed by buoyancy force of the bubble, we provide an approximation of thinning rate as a function of Bond number that agrees with experimental and numerical data. Qualitatively, the smaller the area of the thin film compare to the surface of the bubble, the faster the d...

/pdf/film-drainage-of-viscous-liquids-on-top-of-bare-bubble-36kv52bh2w.pdf

Film drainage of viscous liquids on top of bare bubble: Influence of the Bond number

We present scaling laws for the jet velocity resulting from bubble collapse at a liquid surface which bring out the effects of gravity and viscosity. The present experiments conducted in the range of Bond numbers and Ohnesorge numbers were motivated by the discrepancy between previous experimental results and numerical simulations. We show here that the actual dependence of on is determined by the gravity dependency of the bubble immersion (cavity) depth which has no power-law variation. The power-law variation of the jet Weber number, , suggested by Ghabache et al. (Phys. Fluids, vol. 26 (12), 2014, 121701) is only a good approximation in a limited range of values ( ). Viscosity enters the jet velocity scaling in two ways: (i) through damping of precursor capillary waves which merge at the bubble base and weaken the pressure impulse, and (ii) through direct viscous damping of the jet formation and dynamics. These damping processes are expressed by a dependence of the jet velocity on Ohnesorge number from which critical values of are obtained for capillary wave damping, the onset of jet weakening, the absence of jetting and the absence of jet breakup into droplets.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/410A6CC24FF182C394E2D9612525A42B/S0022112017002142a.pdf/div-class-title-on-the-scaling-of-jetting-from-bubble-collapse-at-a-liquid-surface-div.pdf

On the scaling of jetting from bubble collapse at a liquid surface

For a floating bubble, in the range of Bond numbers based on an equivalent spherical radius, 0 < Boe < 1, we present analytical expressions for various shape parameters of the bubble as functions of Boe. Expressions are obtained for the radius of the rim Rr, the radius of the thin film cap Rc, the height of the top of the cap from the rim hcap, the height of the rim above the free surface hr, and the depth of the bubble cavity from the free surface Zc. To obtain these expressions, we solve equations formulated in terms of these shape parameters for the meniscus outside the bubble, the force balance of the bubble, the pressure balance at the centre line of the bubble, and geometrical constraints, after neglecting the deformation of the bubble cavity for Boe < 1. The obtained expressions are shown to match well with our experimental measurements of the shape of the bubble. In addition to these expressions, we also present simpler approximations that can be used accurately as scaling laws for these shape parameters up to Boe < 0.5.

Shape parameters of a floating bubble

For millimetre to micron sized bubbles, floating at the free surface of different low viscosity fluids with different surface tensions, and then collapsing, we study the ensuing expansion of the outer radius of the hole (ro) at the free surface, as well as its velocity of expansion (uo). Since the thin film cap of the bubble disintegrates before the hole in it reaches the static rim, the hole expansion at intermediate times occurs as if it initiates at the bubble’s static rim of radius Rr; the evolution of ro then results to be a strong function of gravity, since Rr depends strongly on the bubble radius R. A scaling analysis, which includes the increase in the tip radius due to mass accumulation and the resulting change in the retraction force, along with the gravity effects by considering the hole radius in excess of its initial static radius, re = ro − Rr, results in a novel scaling law re/R∼(t/tc)4/7, where tc=ρR3/σ is the capillary time scale; this scaling law is shown to capture the evolution of the hole radii in the present study. The dimensionless velocities of hole expansion, namely, the Weber numbers of hole expansion, Weo=ρuo2R/σ, scale as Weo∼(t/tc)−6/7, independent of gravity effects, matching the observations. We also show that these Weber numbers, which reduce with time, begin with a constant initial Weber number of 64, while the viscous limit of the present phenomena occurs when the bubble Ohnesorge number Oh=μ/σρR≃0.24.

Hole expansion from a bubble at a liquid surface

Impact of freely falling liquid containers and subsequent jetting

Herein, we report various physico-chemical approaches to probe the nature of the interface between few layers graphene (FLG) and carboxylated nitrile rubber (XNBR) nanocomposites prepared through efficient blending of XNBR latex with an aqueous dispersion of FLG. The extent of physical interaction between FLG and XNBR was investigated using Lorentz-Park and Cunneen-Russell models. The chemical interface between FLG and sulfur crosslinked XNBR was studied using model reactions between sulfur and graphene in presence of zinc 2-mercaptobenzothiazole (ZMBT). We propose that an edge sulfurated FLG is formed, which could chemically bond with XNBR during the vulcanization process. Density Functional Theory (DFT) was employed to unravel the mechanistic insights, which support this hypothesis and suggest a kinetically favorable sulfuration of both XNBR and FLG. The formation of a chemical bond between edge-FLG and XNBR through the proposed intermediacy of sulfurated FLG leads to the observed improvement in mechanical properties of the nanocomposites. 

https://www.nature.com/articles/s41598-022-08071-w.pdf

Sangeeth Krishnan

Papers

On the scaling of jetting from bubble collapse at a liquid surface

Shape parameters of a floating bubble

Hole expansion from a bubble at a liquid surface

Impact of freely falling liquid containers and subsequent jetting

In-situ interfacial compatibilization via edge-sulfurated few layer graphene during the formation of crosslinked graphene-rubber nanocomposites