|
|
|
|
|
Bnard CellsBnard cells are obtained in a simple experiment that Bnard, a French physicist, conducted in 1900. They are the convection cells that appear spontaneously in a liquid layer when heat is applied from the outside. The experiment illustrates the theory of dissipative structures in a way that anybody can understand. The experimental set-up uses a layer of liquid, e.g. water, between 2 parallel planes. The height of the layer is small compared to the horizontal dimension. Equilibrium and thermal conduction At first, the temperature of the bottom plane is the same as the top plane. The liquid will go towards an equilibrium, where its temperature is the same as the one outside. Once there, the liquid is perfectly uniform : an observer in it would see the same environment in any spot, and in any direction. This equilibrium is also asymptotically stable: after a local, temporary perturbation of the outside temperature, it will go back to its uniform state, in line with the second law of thermodynamics. Then, the temperature of the bottom plane is increased slightly : a permanent flow of energy will occur through the liquid. The system will begin to have a structure of thermal conductivity: the temperature, and the density and pression with it, will vary linearly between the bottom and top plane. This system is modelled very well in Statistical mechanics. Far from equilibrium: convection and turbulence If we progressively increase the temperature of the bottom plane, there will be a temperature at which something dramatic happens in the liquid : convection cells will appear. The microscopic random movement spontaneously became ordered on a macroscopic level, with a characteristic correlation length. The rotation of the cells is stable and will alternate from clock-wise to counter-clockwise as we move along horizontally: there is a spontaneous symmetry breaking. A small perturbation will not be able to change the rotation of the cells, but a larger one could very well do it: the cells exhibit hysteresis, i.e. they have a memory of their history. Moreover, the deterministic law at the microscopic level produces a non-deterministic arrangement of the cells: if you reproduce the experiment many times, a particular position in the experiment will be in a clockwise cell in some cases, and a counter-clockwise cell in others. Microscopic perturbations of the boundary condition is enough to produce a macroscopic effect: this is the Butterfly effect. The temperature at which convection appears is thus a bifurcation point: hence, the system can be analyzed with bifurcation diagrams. The bifurctation temperature depends on the viscosity and thermal conductivity of the liquid, and on the physical dimensions of the experiment. If we further increase the temperature of the bottom pane, the structure becomes more complex in space and time: the turbulent flow becomes chaotic.
|
 |
|
| Copyright 2005-2009 OnPedia.com. All Rights Reserved |
|
|