
Top left: top view photo of Benard cells: showing their hexagonal shape. Bottom left: a diagram showing heat flow. Middle: a Benard cell internal atomic or molecular movement flow diagram, showing how the cooling mechanism. Right: a Pareto social pyramid, showing Vilfredo Pareto’s 1902 conception of “circulation of elites”, over time, in a given hierarchied social system, akin to a social Benard cell, as Fritjof Capra (1996) likes to theorize, wherein more agitated human molecules (e.g. first generation millionaires) tend to move up the spinning top social pyramid, and less agitated human molecules (e.g. silver spoon babies) tend to move down, through generations.

In science, Bénard cells (TR:56), or "Benard rings" (Schoffeniels, 1973), are ordered hexagonal convection cells or atomic-molecular structures that spontaneously form in viscous mediums, such as silicon oil or whale oil, when placed on a hot plate and heated past a bifurcation point into the turbulent flow regime.

History
The cells are named after French physicist Henri Bénard, who, in completing his PhD dissertation "Cellular Eddies in a Horizontal Liquid Layer", conducted the first experiments on them in 1900. [1] The Bénard cell phenomenon is the model for the now-famous conception of "far-from-equilibrium" invented by Belgian chemist Ilya Prigogine in the 1970s, in "ordered structures" (models for organized life) are said to "spontaneously" form, at a point far away from equilibrium (high heat flow).

These types of structures are termed dissipative structures, and are supposedly representative of things such as evolution and the formation of human societies, and thus are said to give resolution to the tendency to disorder aspects (view) of the second law.

The following, as cited by Aharon Katchalsky (1971), shows the development of Benard cells over time: [7]

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Anthropomorphic thermodynamics
In the 1970s, Bénard cells began to be popularized by Belgian chemist Ilya Prigogine, who used them as an example of “dissipative structures”, being a type of ordered structure that forms according to his entropy generation version of the second law of thermodynamics. This was soon parlayed into a thermodynamic model of the evolution of life. [2] In the reading accounts of Bénard structure formation in reference to evolution, on the logic of Prigogine, one will often find anthropomorphic accounts or descriptions of molecular behavior in the region of heat flow. In the 1996 book The Web of Life, Austrian-born American theoretical physicist Fritjof Capra tells us that: [3]

“Prigogine’s detailed analysis of Bénard cells showed that as the system moves farther away from equilibrium, it reaches a critical point of instability, at which the ordered hexagonal pattern emerges” and that, during convection, “heat is transferred by the coherent motion of large numbers of molecules.”

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Diagram of the internal heat convection structure of Benard cells from Richard Coren’s 2006 chapter “The Challenge to Evolution”; adjacent to 2010 video overview of Benard cells by Libb Thims. [6]

Gradient-dissipation theory
In the early 1990s, American ecologists Eric Schneider and James Kay built on early data from silicon oil Bénard cells experiments to postulate an entropy production, exergy consumption theory of biological order formation in the heat gradient from the sun. Specifically, using a nonequilibrium extension of the second law, of the William Thomson / Ilya Prigogine energy dissipation variety, to graphical calculations of theirs done on heat flow through silicon oil in turbulent flow regime, they argue that spontaneous organizations appear in the fluid, which act to degrade the heat flow gradient across a fluid layer. They then extend this postulate to be a pervading regulatory behavior in the whole of the biosphere.

In particular, using the 1957 experimental data from the PhD dissertation of German researcher P. L. Silveston, in 1994, Schneider and Kay start with the generalized Prigoginean thermodynamics perspective that when a system is removed far from equilibrium by subjecting it to a stress, it will often undergo a transition from a spatially uniform state to a patterned state of spatial variation, but add to it that both “entropy production and exergy destruction occur” during the heat transfer process across the fluid layer, and that the “emergence of the ordered structures (Bénard cells)”, at a Rayleigh number (a dimensionless number for a fluid associated with the transition of heat transfer from the form of conduction to convection) of about 1760, results in such a manner to act to dissipate more energy. [5] In other words, the ordered structures emerge to act more effective energy dissipaters, consuming energy in the form of increased entropy production and decrease exergy (available work) consumption.

In the early 2000s, Schneider continued his writing on this subject, but in coordination with Dorian Sagan. In their 2005 book Into the Cool - Energy Flow, Thermodynamics, and Life, for instance, they state: [4]

“In Bénard systems molecules come together, organize, and allow heat to flow more efficiently into the cool … [but] these organisms of physics do not have the capacity, as true organisms do, to seek out new gradients to support their nonequilibrium organization.”

They argue further that “neither the first law of thermodynamics nor the second law is violated during the formation of these nonliving cells”, but rather, “the quality of energy (engineers call it exergy) is degraded as self-like entities form.”

References
1. (a) Bénard, Henri. (1900). “Les Tourbillons Cellulaires Dans Une Nappe Liquide” (Cellular Eddies in a Horizontal Liquid Layer). PhD dissertation. University of Paris.
(b) Koschmieder, E. L. (1993). Bénard Cells and Taylor Vortices. Cambridge University Press.
2. Solé, Ricard V. and Goodwin, Brian. (2002). Signs of Life, (pgs. 13-29). Basic Books.
3. Capra, Fritjof. (1996). The Web of Life - A New Scientific Understanding of Living Systems, (section: “Dissipative Structures”, pgs. 86-89). New York: Anchor books.
4. Schneider, Eric D. and Sagan, Dorion. (2005). Into the Cool - Energy Flow, Thermodynamics, and Life (pgs. 112-24, 328-29). Chicago: The University of Chicago Press.
5. (a) Silveston, P.L. (1957). “Warmedurchange in Horizontalen Flassigkeitschichtem.” (Heat Changes in Horizontal Silicon Oil), PhD thesis, Techn. Hochsch. Muenchen, Germany.
(b) Schneider, E.D, Kay, J.J., 1994, "Life as a Manifestation of the Second Law of Thermodynamics", Mathematical and Computer Modelling, Vol 19, No. 6-8, pp.25-48.

6. (a) Coren, Richard L. (2006). God and Science Among the Infinities (previously titled: The World is Too Complex for God, 2001) (thermodynamics, pgs. 49, 62-68). BookSurge.

(b) Thims, Libb. (2010). “Benard Cells” (Ѻ), HumanChemistry101, Oct 6.
7. (a) Gmitro, John I and Scriven, L.E. (1966). “A Physicochemical Basis for Pattern and Rhythm”, in: Intracellular Transport (editor: Katherine Warren). Symposia of the International Society for Cell Biology, Volume 5 (pg. 223). Academic Press.
(b) Katchalsky, Aharon. (1971). “Thermodynamics of Flow and Biological Organization” (abs)(Ѻ), Zygon, 6(2):99-125.

External links
● Benard cells – Wikipedia.