In an unconfined space, the sizes of the bubbles are unpredictable, but the situation changes when they bubble into liquid in a tube instead. Up to a certain point, the size and shape of the tube doesn't matter, nor do the characteristics of the orifice the gas comes through. Instead the bubbles, like the droplets from a faucet, are uniformly sized and spaced.
Pahlavan says, "Our work is really a tale of two surprising observations; the first surprising observation came around 15 years ago, when another group investigating formation of bubbles in large liquid tanks observed that the pinch-off process is nonuniversal" and depends on the details of the experimental setup. This observation is "surprising," he says, because intuitively it might seem that bubbles able to move freely through the liquid would be less affected by their initial conditions than those that are hemmed in.
But the opposite turned out to be true. It turns out that interactions between the tube and the forming bubble, as a line of contact between the air and the liquid advances along the inside of the tube, play an important role.
This "effectively erases the memory of the system, of the details of the initial conditions, and therefore restores the universality to the pinch-off of a bubble," he says. While such research may seem esoteric, its findings have potential applications in a variety of practical settings, Pahlavan says.
A few examples are inkjet printing, medical imaging, and making particulate materials. The new understanding is also important for some natural processes. These interactions between the fluids and the surrounding grains are often neglected in analyzing such processes. But the behavior of such geological systems is often determined by processes at the grain-scale, which means that the kind of microscale analysis done in this work could be helpful in understanding even such very large-scale situations.
The bubble formation in such geological formations can be a blessing or a curse, depending on the context, Juanes says, but either way it's important to understand. For carbon sequestration, for example, the hope is to pump carbon dioxide, separated out from power plant emissions, into deep formations to prevent the gas from getting out into the atmosphere.
In this case, the formation of bubbles in tiny pore spaces in the rock is an advantage, because the bubbles tend to block the flow and keep the gas anchored in position, preventing it from leaking back out. But for the same reason, bubble formation in a natural gas well can be a problem, because it can also block the flow, inhibiting the ability to extract the desired natural gas. Materials provided by Massachusetts Institute of Technology. Then the newly-formed bubbles grow according to the scheme 14 , as illustrated schematically in Fig.
In the first stage of evolution, bubbles spread over a distance of the order of the tube radius, and at this stage of bubble evolution, the total number density of air molecules in bubbles is of the order of the number density of molecules in atmospheric air. In the second stage of evolution, bubbles formed in the first stage spread throughout the water volume. As a result, the rate of bubble generation matches the rate of the floating up process for bubbles, including accounting for their growth due to the coagulation process.
Scheme of injection of submicron air bubbles into water: 1 container, 2 water, 3 flux of air bubbles, 4 porous material, 5 compressed air, 6 valve, 7 plunger, 8 region of high air density. In order to understand the real character of bubble evolution, we evaluate parameters of this evolution under conditions of experiment [ 3 ]. The flow velocity V varies in the experiment [ 3 ] from 0. From this we find that the rate of insertion of air molecules into water through a porous material is.
The number density of air molecules in bubbles near the entrance into the water is given by. As we discussed above, we divide the evolution of bubbles in water into two stages. In the first stage, the flow of water forming bubbles does not include new water additions, i. In the second stage of bubble evolution, they mix with water in the container.
This leads to a decrease in the total number density of air molecules in the container, and we assume that bubbles mix with water of the container uniformly. We assume that the number density of air molecules in bubbles does not vary so long as the flowing bubbles do not encounter container walls. This yields an average bubble radius from 0.
Correspondingly, the average number density N w of air molecules in bubbles over all the container is. As bubbles evolve in a water reservoir, they grow by coagulation and leave when they reach the water-air boundary. But because motion of water has a turbulent character under experimental conditions [ 3 ], departure of bubbles is determined primarily by parameters of turbulent motion, rather than simply by the rate of the smooth floating up of bubbles.
In considering the above regime of the kinetics of bubbles of micron and submicron size, we were guided by experimental conditions [ 3 ] in which a gas is injected into a liquid through a porous material with nano-size pores.
There, the gas enters the liquid in the form of jets whose radii correspond to pore sizes, and then the jets are destroyed due to the Rayleigh—Plesset instability [ 14 , 15 ] and transform into micron-size bubbles which then join to bubbles of larger sizes. In particular, within the framework of experiment [ 3 ], bubbles that form in water after association of injected bubbles contain a few of hundreds of the initially injected bubbles.
Let us consider one more example, in which bubbles propagate along a tube in a liquid flow. In this example we will be guided by the blood flow [ 16 — 18 ].
It should be noted that if contrast agents or drugs are injected in blood, they dissolve in blood water, and just this mixture is used in clinical applications [ 19 — 21 ]. Therefore an injected medicine must not react with walls of a blood vessel in this case. In the case under consideration an injected substance may react with a blood vessel, and it is necessary to transport the medicine through a blood vessel without contacts with walls.
Let us inject this medicine in the center of a blood flow in the form of micron-size bubbles or droplets and they travel over the vessel cross section as a result of diffusion or floating-up. For example, these bubbles may contain ozone or another oxidizer, and these substances lose chemical activity if bubbles contact the walls of a blood vessel. Below we determine the lifetime of bubbles in a blood flow under these conditions.
Comparing the propagation of a bubble in water due to floating-up and diffusion, one obtains that transport due to floating-up takes place for distances L. Hence, the floating-up mechanism is realized for bubble transport of micron-size bubbles through a blood vessel. If this criterion holds true, the bubble displacement in blood flow through a venous duct is small compared with its radius.
Along with this criterion, there is a requirement of a restricted number density of bubbles, so that a doubling time of a bubble size as a result of their association must exceed their residence time in the flow. In addition, one can take instead of bubbles micron-size droplets. These bubbles and droplets may be used not only for transport of some substances through a blood vessel, but they can be catalysts to remove harmful compounds from the blood.
Above we analyze conditions where transport of bubbles through a blood vessel excludes their interaction with vessel walls. Another problem of their interaction with red corpuscules will require a special analysis of its own. Disperse systems under consideration consist of a liquid and gaseous bubbles. If a gas is inserted into a liquid and its amount exceeds the maximum level of solubility of that gas, the excess gas forms bubbles in the liquid through time. Processes in such a system with micron-size bubbles include diffusion and floating-up of bubbles, as well as association of contacting bubbles.
The above rates of these processes allow us to describe the kinetics of growth for a disperse system of such a type. We consider disperse systems located in a container with an open surface containing the gas above the interface. Because of the long time of bubble floating-up under laboratory conditions, bubbles grow in the liquid and their size is independent of initial conditions when they reach the interface. This fact simplifies the problem and allows us to connect a size of floating-up bubbles with the gas concentration in the liquid and the path to the interface.
The above analysis allows one to choose optimal conditions for any process involving micron-size bubbles or droplets for a certain disperse system.
In analyzing the behavior of a gas inside a liquid, we show that thermodynamic equilibrium in this system takes place between dissolved molecules and the liquid, while excess molecules leave the liquid. In the regime under consideration an outgoing time is relatively long, and the number density of dissolved molecules is small compared to undissolved ones, and this gas-liquid system is a nonequilibrium one.
In the end, undissolved molecules leave the liquid through its boundary, and most of the time in the course of this process, undissolved molecules are in the liquid in the form of bubbles. Then the rate of exit of undissolved gas molecules in the liquid is summed from kinetics of bubble growth as a result of their association and floating up under the action of the gravitation force.
We use here the classical theory of growth kinetics of aerosols in a gas [ 8 — 10 ] which is constructed on the basis of the Smoluchowski equation [ 6 ] and was applied to growth of liquid clusters in a gas [ 11 , 12 ] in the diffusion regime of the cluster growth process. Using the analogy of the above growth processes with bubble growth in a liquid, we apply formulas for kinetics of aerosol and cluster growth in this case.
As a bubble grows, its floating velocity increases, and accounting for both processes allows us to determine the bubble life time in a liquid with an open upper surface. The evaluations are made for the growth and floating up of the oxygen bubbles in water. This process takes place when oxygen results for the photosysntesis process in a water reservoir.
It should be noted that this model may be used also for the analysis of bubble evolution of liquid flows if they propagate through a tube. This may be used for injection of drugs or contrast agents in blood that propagates through a blood vessel [ 16 — 18 ]. In such applications, usually the injected substance is mixed with a blood or is dissolved in it [ 19 — 21 ]. The above approach allows one to deliver a substance in the form of bubbles or droplets, and the above theory gives conditions to escape interaction of injected bubbles with vessel walls.
This provides a list of possible medical applications. BMS was the initiator of this study. Both authors read and approved the final manuscript. Boris M. Smirnov, Email: moc. Stephen Berry, Email: ude. National Center for Biotechnology Information , U. Journal List Chem Cent J v. Chem Cent J. Published online Sep Smirnov and R. Stephen Berry. Author information Article notes Copyright and License information Disclaimer. Corresponding author. Received Mar 31; Accepted Sep 9.
Abstract Background Evolution of a gas injected in a liquid is analyzed using the example of the behavior of oxygen molecules in water in which bubbles of gas molecules grow slowly by attachment of gas molecules to bubbles, the bubbles then associate and finally flow up to the liquid—gas interface and pass into the gas phase.
Results Two methods are considered for gas injection in a liquid, insertion of individual molecules and injection of small gas bubbles via gas penetration through a porous material. Conclusions It is shown that measurement of the size distribution function of micron-size bubbles in various regions of the water container allows one to establish the flow current lines on the basis of the theory of bubble growth. Graphical abstract:. Open in a separate window.
Keywords: Bubbles in liquid, Oxygen in water, Floating-up of bubbles, Growth of bubbles. Background If gas molecules are located in a simple liquid, they may be found in three states.
Introduction In this paper we consider the character of evolution of a gas which penetrates through a porous medium into an open, liquid-filled reservoir. Oxygen in water In considering the equilibrium between a gas in a liquid we will be guided by oxygen molecules in water, or by air molecules if we assume the behavior of nitrogen molecules to be analogous to that of oxygen molecules. Thermodynamics of liquid with gas inside it We below consider evolution of the system consisting of a liquid which borders with a gas and an equilibrium is established in the liquid—gas system through the interface.
Floating-up of bubbles in liquid Thus we see that if the amount of a gas in a liquid exceeds the solubility limit of the gas molecules in the liquid, all the excess of this gas forms bubbles in the liquid, provided the amount of liquid is sufficient to contain those bubbles. Bubble growth in liquid When bubbles are located in a liquid, they move there and may be in contact as it is shown in Fig.
Growth of air bubbles in a water container We now apply the above results to certain systems. Liquid flow with bubbles in tube Let us consider one more example, in which bubbles propagate along a tube in a liquid flow.
Conclusion Disperse systems under consideration consist of a liquid and gaseous bubbles. Sign up for our email newsletter. Already a subscriber? Sign in. Thanks for reading Scientific American. Create your free account or Sign in to continue. See Subscription Options.
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