Chapter 7: The Experimenter

This chapter looks at different experiments performed by Albert Libchaber. I will focus on one of his experiments on convection, which I found to be quite interesting.

Libchaber was an intelligent experimenter who spent his days in laboratories. One of his early inventions, which was he used to measure a liquid’s temperature, was called “Helium in a box”. It contained a cell with liquid helium, that was about the size of a lemon seed”. Liquid helium, which was chilled to 4degrees above absolute zero, was put into this cell. There was also a tiny sapphire “bolometer” inside which measured the fluid’s temperature. The cell was embedded in a casing in order to prevent noise ad vibrations to skew his results. Linchaber used electric heating coils and Teflon gaskets to as heat conductors. The liquid helium would enter the system through a reservoir. The entire system was contained in liquid nitrogen to help stabilize temperature. His plan with the experiment was to create convection, the rising of hot gas or liquid, in the liquid helium as he made the bottom plate warmer than the top. 

 The reason Libchaber used liquid helium in his experiment is because it has low viscosity, meaning it will roll with a slight push.  To cause convection in his tiny cell he had to create a temperature difference of a thousandth of a degree between the top and bottom surfaces. Through his design, Libchaber chose dimensions that allowed enough room for only two rolls.  The heated liquid helium would rise in the center turn up and over to the right and descend on the outside edges of the cell. To record his results, he inserted two microscopic temperature probes in the sapphire, ad their output would be recorded by a pen plotter. 

His results corresponded with the Navier-Stokes equation, which relates a fluid’s velocity, pressure, density, and viscosity, is used to represent the nonlinear relationship. The equation describes the process by which when a liquid is heated from below, and the fluid moves in cylindrical rolls. Hot fluid will rise on one side, lose heat, and descend on the other side. However, when the heat is turned up further, there is instability, and the movement along the cylindrical shape is no longer uniform. At even higher temperature, the motion becomes turbulent and chaotic. These are just a few examples of where chaos exists in our world. With nonlinear systems, this chaos can be further observed and interpreted.

This is the most general form of the Navier–Stokes equat

ion :

 

 

where v is the velocity of the flow, ρ is the density of the fluid, p is the pressure, T and  represents forces acting on the body (per unit volume) acting on the fluid and D is the delta operator.