Rayleigh–Bénard convection

When Bénard experiment ( Bénard effect Bénard system Bénard cells, Rayleigh - Benard experiment), a thin, homogenous fluid layer is located in a fixed container and in a gravitational field, is heated from the bottom, while the top side is kept by cooling to a lower temperature. They form geometric patterned vertically arranged convection cells (see image right). Especially in the edge region of the fluid exchange between the hot liquid from the bottom and the cooled liquid from above takes place. The cell structures are typically linear or hexagonal in plan view. In the second case is formed in the center of the structure, a flow from the center. The state is classified between a solid state stratification ( little or no temperature difference ) and a state of pure chaos (very large temperature difference ). With increasing temperature difference, the complexity of the structure is increased in such a system, according to Lorenz.

The experiment was named after Henri Bénard, the 1900 in his dissertation first described it in detail. Some of the Bénard experiment in the literature is also described as Rayleigh - Benard experiment and relates this extension at Baron Rayleigh.

The Bénard - Marangoni effect (after Carlo Marangoni ) is often confused with the one described here. In this related effect the convection is limited by other non- solid media.

Description of the experiment

A liquid expands in the warm bottom and rises due to the lower density to the top while the colder, more dense liquid sinks to the bottom in the upper region. The viscosity of the liquid limits the speed of these movements.

If the temperature difference between the bottom and surface low, outweigh the forces due to the viscosity and the heat is transported without simultaneous mass transfer by conduction from the bottom up. Above a critical temperature difference, this state is unstable, the heat transfer takes place by convection. The liquid is in motion due to the density differences between the top and bottom. Occur regularly shaped convection usually in hexagonal ( seen from above) or role pattern (viewed from the side), the Bénard cells. If above the liquid, an interface exists in a gaseous medium, the convective heat transfer is enhanced by possible variations in the surface tension at the interface. Because the surface tension decreases with the temperature, as a rule, have locations which is closer to the hot wall are a smaller surface tension than those that are further away. Therefore, an additional driving force is created which induces a flow towards colder areas. If the temperature difference between the top and bottom of the liquid to continue to put a critical value from a second period doublings. The system reaches the Feigenbaum route to chaos, it developed turbulence, showed how first Albert J. Libchaber the late 1970s.

To carry out the experiment is particularly suitable liquids with a relevant low viscosity, such as thin oil or gels. However, it has also been carried out with liquid, frozen helium. The thermal expansion coefficient of the liquid must be positive. The temperature and velocity field of this experiment must be of the Navier -Stokes equation, satisfy the heat conduction equation and the continuity equation ( conservation of mass ).

The world's largest simulation system for the experiment is the Barrel of Ilmenau, an institution of the Technical University of Ilmenau.

Importance

The Bénard experiment is a standard example of the formation of dissipative structures in convective, open systems far from thermodynamic equilibrium. Similar behavior can occur in principle in all viscous media. In addition to model experiments with thin layers of oil paint to explore ( eg in the form of hexagonal or roll-shaped cloud structures ) similar behavior in the mantle, the ocean or in the atmosphere.

The study of atmospheric convection was the starting point that led through the meteorologist Edward Lorenz in the early 1960s to the discovery of deterministic chaos. He examined the transition of thermal convection in a turbulent state within a medium. , Drawn up by Lorenz for this purpose system ( Lorenz attractor ) consists of three autonomous differential equations showed for the first time at the computer to understand chaotic oscillations within a deterministic system.

Examples:

• Granulation on the solar surface, see granulation ( astronomy).
• Thermal Vertical motion in the mantle, mantle convection see.
• Segregation of pigments with different densities in certain varnishes during drying.