Non-Equilibrium Force


red ball  Consider forces between two spheres at different temperatures:

yellow ball "Non-equilibrium Casimir forces: Spheres and sphere-plate,"

M. Krüger, T. Emig,G. Bimonte and M. Kardar, Europhys. Lett. 95, 21002 (2011) (1 micron Si O2 spheres, force on #2)

yellow ball Whereas the equilibrium force (attractive) falls off as 1/d6, the non-equilibrium force decays as 1/d2. ( * )

yellow ball The non-equilibrium force can be attractive and repulsive.  ( * )

yellow ball Unlike in thermal equilibrium, there are points of stable levitation.  ( * )

yellow ball Forces are not equal and opposite, with points of equal force in the same direction!  ( * )

red ball  Example of non-equilibrium Casimir levitation:

yellow ball A hot microsphere can levitate on top of a cold plate.

yellow ball If it cools down (including heat transfer) the sphere will fall down.