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Tiny Bubbles

July 3, 2023

My grandchildren enjoy making backyard bubbles during the summer months, reminding me of all the ways that bubbles have entered adult life. Members of my generation will remember the 1967 hit, Tiny Bubbles, by Hawaiian singer, Don Ho (1930-2007), while an earlier generation will remember Lawrence Welk's bubble machine that wafted streams of large bubbles across the bandstand as visual reinforcement of his television show's "Champagne Music" tagline.

As I wrote in one of last year's articles (Eternal Bubbles, October 24, 2022), a good recipe for a bubble-making solution is as follows:

• 2/3 cup of dishwashing liquid

• 2/3 tablespoon of glycerine (also known as glycerol)

• 1 gallon of water

The purpose of the glycerine is to slow the evaporation of water from the bubble, thereby increasing its lifetime.

A large soap bubble reflecting a streetscape in Ljubljana, Slovenia.

Soap bubbles containing glycerine have a longer lifetime, since the glycerine molecules have a low vapor pressure, and they're hydrogen-bonded to the water molecules. For those reasons, they slow water evaporation.

(Wikimedia Commons image by P.L. Bechly.)

Bubble properties go beyond their mere entertainment value, and they have been the topic of many scientific studies. As I wrote in a previous article (Cavitation, October 16, 2017), bubbles can damage tough metallic components by a process called cavitation. Mechanical forces acting on a liquid can create bubbles through a rapid decrease in pressure; and, when this is followed by a a rapid change to higher pressure, these bubble will implode to generate an intense shock wave.

While the term, cavitation, wasn't used until 1893,[1] Leonhard Euler (1707-1783) was the first to discuss cavitation in his 1754 paper, "Théorie plus complette des machines qui sont mises en mouvement par la réaction de l'eau (A more complete theory of machines that are set in motion by reaction with water).[2] The physics of cavitation was investigated in 1917 by Rayleigh, who analyzed the implosion of a void in a large mass of liquid.[3] This study led to the Rayleigh–Plesset equation, which is an ordinary differential equation describing the dynamics of cavitation for spherical bubbles. Since the bubbles are nucleated on a surface, their shape is actually more like a hemisphere; so, this might be the most apt reference to a spherical cow model.

If you don't look too closely, a cow is topologically equivalent to a sphere.

I do a spherical cow calculation before I attempt an experiment, since my equipment might not be capable of the particular measurement task.

(Wikimedia Commons image, original by Keenan Crane, modified.)

Soap bubbles lose water by evaporation; so, it's not surprising that bubbles cool on their march to oblivion. At the end of 2022, solid state physicists from the Université Paris-Saclay (Orsay, France) examined cooling of soap bubbles and found that their surrounding soap film can be up to 8°C cooler than the environment.[4-5]

In their experiments the French physicists used a fluid mixture of dishwashing liquid, water, and glycerol, similar to the recipe above, and they examined evaporation under different conditions of glycerol concentration and relative humidity.[4-5] Not surprisingly, higher glycerol content, which results in a lower water evaporation rate, generated bubble having higher temperatures.[5] Eight degrees is a significant cooling, and the study authors write that this cooling needs to be considered in studies of soap film dynamics, and in the stability of bubbly industrial and consumer products.[4-5]

A Guinness widget for canned beer, and a figure from the original widget patent.

Left, a Guinness widget for canned beer, and figure 5 from the original widget patent. When the can is opened, nitrogen bubbles are released from this device to give a desired foamy beer head.

(Left, a Wikimedia Commons image by Duk. Right, fig. 5 of US Patent no. 4,832,968, "Beverage package and a method of packaging a beverage containing gas in solution," by Alan J. Forage and William J. Byrne, May 23, 1989.[6] Click for larger image.)

A stream of air bubbles in solution is an excellent source of agitation. I once etched prototype copper printed circuit boards in an aqueous solution of ferric chloride with an air plenum that provided agitation bubbles produced by air streaming through holes. Air bubbles in water are a common way to clean materials. Millimeter-sized air bubbles aimed at an inclined surface will slide across it and exert a shear stress that causes contaminants on the surface to be removed.[7] The important parameter of this process is the tangential speed of the bubble with respect to the surface, divided by the thickness of the thin layer of liquid separating the bubble and the solid surface.[7]

Engineers from Cornell University (Ithaca, New York) have recently published results of their experiments on this process with a goal of finding the optimal impact angle for best cleaning of contaminated surfaces.[7-8] In their experiments, they coated some glass microscope slides with mixtures of milk- and flour-based proteins, and with others, a biofilm of the E. coli bacterium.[8] These were subjected to six minute bubble streams at various angles face-down in a water tank.[8] Cleaning efficacy was measured by the ratio of transparency to that of uncontaminated slides.[8]

While the researchers found that bubbles were effective at cleaning at all angles, the effectiveness of cleaning gradually increased from 5° to 20°, giving an increase of transparency from 70% to about 90%.[8] Larger angles gave less cleaning, with transparency decreasing to about 38% at 40°.[8] The highest cleaning efficacy for polydisperse bubbles in the range of 0.3-2 millimeters and an average radius of 0.6 millimeters was at an angle of about 22.5°.[7]

The research team created a simulation of a single air bubble impacting with a clean surface that showed that the shear force of the bubble reaches a maximum at 22.5° and then declined at higher angles.[7-8] The simulation showed that increasing the inclination angle gives a higher bubble speed along the surface, increases the shear force.[8] Increased angle, however, decreases the bubble buoyant force, and this reduces the time that bubbles are pressed against the surface.[8] These competing principles lead to the optimal cleaning angle of about 22.5°.[8]

One commonly observed bubble phenomenon is the rising columns of bubbles in a glass of carbonated soft drink or sparkling wine. This phenomenon was analyzed in a recent paper in Physical Review Fluids by fluid mechanics researchers from Brown University (Providence, Rhode Island) and the University of Toulouse (Toulouse, France).[9-11] In some such drinks, stable, straight line bubble chains rise from nucleation sites, while in other drinks such as soda and beer, the bubbles diverge into cones (see figure).[9,11] The research team's experiments and simulations show that the type of bubble chain behavior depends on bubble size and the chemistry of the liquid.[10]

The shape of a bubble stream changes as the rate of bubble injection increases

The shape of a bubble stream changes as the rate of bubble injection into a pure liquid increases to that of Champagne.

(Brown University image by Roberto Zenit. Click for larger image.)

In this study, experiments were performed on Charles de Cazanove Champagne, San Pellegrino sparkling water, Tecate beer,and a Spanish-style brut.[10-11] A small rectangular plexiglass container was filled with these fluids, and a syringe needle at the bottom was used to inject gas at various rates to create different kinds of bubble chains.[11] Added surfactants led to more stable bubble chains, while increased bubble size made the bubble chains more stable, even without surfactants. Most carbonated drinks have small bubbles and few surfactants.[11] Champagne, while having small bubbles, also has a high concentration of surfactants; so, the bubble stream is straight and stable.[10]

Bubbles in a glass of Champagne, extracted from a Wikimedia Commons video by Subhashish Panigrahi.)

Among the fluid properties the research team measured in their experiments were liquid density, bubble radii, bubble paths, and the fatty acid composition.[10] Their experiments, confirmed by computer simulation, showed that for small bubbles, or for larger bubbles in liquids with low surfactant concentration, the bubbles shed vortices to form a pattern in which a leading bubble induces lateral forces on the trailing bubble, thereby de-stabilizing the chain and developing a zig-zag path, and the bubble stream becomes a cone.[10-11] The results of their experiments indicate that Champagne and other sparkling wines in which bubble diameter is small have stable bubble streams because they contain ingredients that act as surfactants that reduce the interface tension between the liquid and the gas bubbles.[11]

As Roberto Zenit, a Brown University professor of engineering and one of the paper's authors, explains, "The theory is that in Champagne these contaminants that act as surfactants are the good stuff... These protein molecules that give flavor and uniqueness to the liquid are what makes the bubbles chains they produce stable."[11] Some beers also contain surfactant-like molecules, and the bubble streams in these will likewise rise in straight chains.[11] Carbonated water, however, has no such surfactants, and its bubbles will form into a cone.[11]

These research findings are important to understanding such bubbling systems as ocean seeps, in which methane and carbon dioxide bubble from the ocean floor, and bubble-induced mixing in aeration tanks at wastewater treatment facilities.[10-11]

References:

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