Near-field radiative energy transfer between sphere-sphere and sphere-flat surfaces

From Thermal-FluidsPedia

(Difference between revisions)
Jump to: navigation, search
m
Line 1: Line 1:
-
Near-field thermal radiation between two spheres was first reported by Volokitin and Persson [1] by assuming them as dipoles. When there are two spherical nanoparticles whose dielectric constants are ''&epsilon;<sub>1</sub>''  and ''&epsilon;<sub>2</sub>'' , the spectral power dissipated in particle 2 by the electromagnetic field induced by particle 1 can be written using the dipolar approximation as
+
Near-field thermal radiation between two spheres was first reported by Volokitin and Persson [1] by assuming them as dipoles. When there are two spherical nanoparticles whose dielectric constants are ''&epsilon;<sub>1</sub>''  and ''&epsilon;<sub>2</sub>'' , the spectral power dissipated in particle 2 by the electromagnetic field induced by particle 1 can be written using the dipolar approximation as  
 +
 
 +
<div style="text-align: right;">
 +
<div style="float: left; width: 1115px;">[[File:Sphereee.jpg|center|EQ1]]</div>
 +
(1)
 +
</div>
 +
 
 +
 
 +
 
 +
where x<sub>2</sub> is the position of the particle 2 and <big><math>{\alpha _2} = {4 \pi R^3 (\epsilon_2 -1) / (\epsilon_2 +2)} </math></big> is the polarizability of a sphere of radius ''R'' having the relative permittivity of &epsilon;<sub>2</sub>. The electric field incident on the particle 2, E<sub>inc</sub>(x<sub>2</sub>,''ω''), is created by the thermal fluctuating dipole of particle 1 at Temperature ''T<sub>1</sub>'' :
 +
<div style="text-align: right;">
 +
<div style="float: left; width: 1115px;">[[File:Sphere2.jpg|center|EQ2]]</div>
 +
(2)
 +
</div>
 +
 
 +
 
 +
where <math>\rm \overline {\overline G}_e (x_2,x_1,\omega)</math> is the electric dyadic Green’s function between two dipoles in vacuum and expressed as [2]
 +
 
 +
<div style="text-align: right;">
 +
<div style="float: left; width: 1115px;">[[File:Sphereuc.jpg|center|EQ3]]</div>
 +
(3)
 +
</div>
 +
 
 +
 
 +
 
 +
 
 +
where

Revision as of 08:09, 3 March 2012

Near-field thermal radiation between two spheres was first reported by Volokitin and Persson [1] by assuming them as dipoles. When there are two spherical nanoparticles whose dielectric constants are ε1 and ε2 , the spectral power dissipated in particle 2 by the electromagnetic field induced by particle 1 can be written using the dipolar approximation as

EQ1

(1)


where x2 is the position of the particle 2 and α2 = 4πR32 − 1) / (ε2 + 2) is the polarizability of a sphere of radius R having the relative permittivity of ε2. The electric field incident on the particle 2, Einc(x2,ω), is created by the thermal fluctuating dipole of particle 1 at Temperature T1 :

EQ2

(2)


where \rm \overline {\overline G}_e (x_2,x_1,\omega) is the electric dyadic Green’s function between two dipoles in vacuum and expressed as [2]

EQ3

(3)



where