Non-equilibrium fluctuation-induced interactions between spheres: heat radiation and non-equilibrium Casimir forces
This test validates the scuff-neq application module of the scuff-em code suite by using it to compute (a) the temperature-dependent rate of heat radiation from individual spheres, (b) radiative heat-transfer rates and non-equilibrium Casimir forces between spheres at various separation distances.
Analytical solution
Analytical formulas for single-sphere heat radiation and sphere-sphere heat-transfer rates and non-equilibrium Casimir forces were obtained by M. Krueger and are discussed in this paper:
The formulas are a bit complicated to reproduce here, but here is a simple julia code that implements them:
This code may be used to
scuff-em solution
Values of the flux quantity $\phi^{\text{\small heat radiation and between two dielectric spheres may be computed using scuff-cas3d as follows:
% scuff-neq --geometry SiO2Sphere_501.scuffgeo --OmegaFile OmegaFile
% scuff-neq --geometry SiO2Spheres_501.scuffgeo --OmegaFile OmegaFile
Here the two .scuffgeo
files
(PECSpheres_501.scuffgeo
and E10Spheres_501.scuffgeo
]
describe the two geometric configurations
(two PEC spheres and two dielectric spheres of radius m
separated by an initial center-center distance of =3 m) while
Spheres.trans
specifies the list of center-center
separation distances at which we compute the energy and force.
(Both geometries refer to the same surface mesh file for the
sphere, Sphere_327.msh
.
The above calculations produce output files named
PECSpheres_327.out
and
E10Spheres_327.out
. Plotting against
the theoretical predictions of Emig et. al (referenced above)
yields good agreement:
.
Here's the gnuplot script I used to produce this
plot: Plotter.gp
.