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. Contributor Information Boris M. References 1. Accessed 10 Dec Kittel C. Thermal physics. New York: Wiley; Kukizaki M, Goto M.
Size control of nanobubbles generated from Shirasu-porous-glass membranes. J Membr Sci. Fluid dynamics. Oxford: Pergamon Press; Lide DR ed — Handbook of chemistry and physics, 86 edn.
CRC Press, London. Smoluchowski MV. Zs Phys Chem. Levich VG. Physical-chemical hydrodynamics. Moscow: Fizmatgiz; Fuchs NA. The mechanics of aerosols. The dynamics of aerocolloidal systems. Friedlander SK Smoke, dust and haze. In: Fundamental of aerosol dynamics. Oxford Univ. Press, New York. Smirnov BM. Clusters and small particles in gases and plasmas.
New York: Springer; Cluster processes in gases and plasmas. Berlin: Wiley; Pergamon Press, Oxford. Rayleigh L. On the pressure developed in a liquid during the collapse of a spheriical cavity. Philos Mag. Plesset M. The dynamics of cavitation bubbles. J Appl Mech. Oka S. Cardiovascular hemorheology. Cambridge: Camb. Press; Woerlee GM. Kinetics and dynamics of intravenous anesthetics. Dordrecht: Kluwer; Saltzman WM. Sign in. Thanks for reading Scientific American.
Create your free account or Sign in to continue. See Subscription Options. Discover World-Changing Science. Get smart. 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. Original written by David L. Note: Content may be edited for style and length.
Science News. Journal Reference : Amir A. Pahlavan, Howard A. Stone, Gareth H. McKinley, Ruben Juanes. Restoring universality to the pinch-off of a bubble. ScienceDaily, 17 June Massachusetts Institute of Technology. Mystery of how gas bubbles form in liquid solved. Retrieved November 10, from www. As the bubbles burst, the released carbon dioxide gas imparts the beverage's desirable tang.
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