Chaotic bubbles within

physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

and

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

, occur in cases when there are any dynamic processes that generate bubbles that are nonlinear. Many exhibit mathematically chaotic patterns consistent with

chaos theory Chaos theory is an interdisciplinary area of Scientific method, scientific study and branch of mathematics. It focuses on underlying patterns and Deterministic system, deterministic Scientific law, laws of dynamical systems that are highly sens ...

. In most systems, they arise out of a forcing

pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and eve ...

that encounters some kind of resistance or shear factor, but the details vary depending on the particular context. The most widely known example is bubbles in various forms of

liquid Liquid is a state of matter with a definite volume but no fixed shape. Liquids adapt to the shape of their container and are nearly incompressible, maintaining their volume even under pressure. The density of a liquid is usually close to th ...

. Although there may have been an earlier use of the term, it was used in 1987 specifically in connection with a model of the motion of a single bubble in a fluid subject to periodically driven pressure oscillations (Smereka, Birnir, and Banerjee, 1987). For an overview of models of single-bubble dynamics see Feng and Leal (1997). There is extensive literature on nonlinear

analysis Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...

of the dynamics of bubbles in liquids, with important contributions from Werner Lauterborn (1976). Lauterborn and Cramer (1981) also applied chaos theory to

acoustics Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician ...

, in which bubble dynamics play a crucial part. This includes analysis of chaotic dynamics in an acoustic cavitation bubble field in a liquid (Lauterborn, Holzfuss, and Bilio, 1994). The study of the role of

shear stress Shear stress (often denoted by , Greek alphabet, Greek: tau) is the component of stress (physics), stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross secti ...

es in non-Newtonian fluids has been done by Li, Mouline, Choplin, and Midoux (1997). A somewhat related field, the study of controlling such chaotic bubble dynamics ( control of chaos), converts them to periodic oscillations, and has an important application to gas–solids in fluidized bed reactors, also applicable to the ammoxidation of

propylene Propylene, also known as propene, is an unsaturated organic compound with the chemical formula . It has one double bond, and is the second simplest member of the alkene class of hydrocarbons. It is a colorless gas with a faint petroleum-like o ...

to acrylonitrile (Kaart, Schouten, and van den Bleek, 1999). Sarnobat et al.) study the behavior of electrostatic fields on chaotic bubbling in attempt to control the chaos into a lower order periodicity.

References

Further reading