Near-field radiative heat transfer between irregularly shaped dielectric particles modeled with the discrete system Green's function method

Near-field radiative heat transfer (NFRHT) between irregularly shaped dielectric particles made of ${\mathrm{SiO}}_2$ and morphology characterized by Gaussian random spheres is studied. Particles are modeled using the discrete system Green's function (DSGF) approach, which is a volume integral numerical method based on fluctuational electrodynamics. This method is applicable to finite, three-dimensional objects, and all system interactions are defined independent of thermal excitation by a generalized system Green's function. The DSGF method is deemed suitable to model NFRHT between irregularly shaped particles after verification against the analytical solution for chains of two and three ${\mathrm{SiO}}_2$ spheres. The NFRHT results reveal that geometric irregularity in particles leads to a reduction of the total conductance from that of comparable perfect spheres at vacuum separation distances smaller than the particle size, a regime in which NFRHT is a surface phenomenon. At vacuum separation distances larger than the particle size, NFRHT becomes a volumetric process, and the total conductance between irregularly shaped particles converges to that of comparable perfect spheres. Spectral analysis reveals, however, that particle irregularity leads to damping and broadening of resonances at all separation distances, thereby highlighting the importance of the DSGF method for spectral engineering in the near field. The reduced spectral coherence when particle size is larger than the vacuum separation distance is attributed to coupling of surface phonon-polaritons within the randomly generated, distorted particle features. For particle size smaller than the vacuum separation distance, resonance broadening and damping are linked with the multiple localized surface phonon modes supported by the composite spherical harmonic morphologies of the Gaussian random spheres. This paper has direct implications for thermal management of packed particle systems, with applications in radiative property control, electronics, energy conversion, and nanomanufacturing.

Figure 1

System of thermal objects of arbitrary number, geometry, size, and material occupying a total volume $V_{\mathrm{therm}}$. The thermal objects may be of nonuniform temperature $T\left(\mathbf{r}\right)$ and nonuniform dielectric function $\varepsilon \left(\mathbf{r},\omega \right)$. The thermal objects are embedded in a lossless background reference medium of volume $V_{\mathrm{ref}}$ that is characterized by a real-valued dielectric function ${\varepsilon }_{\mathrm{ref}}\left(\omega \right)$.

Figure 2

Schematics of (a) two ${\mathrm{SiO}}_2$ spheres and (b) a linear chain of three ${\mathrm{SiO}}_2$ spheres embedded in vacuum. Two different sphere sizes are considered: $R=50$ and $500\mathrm{nm}$. The vacuum separation distance varies from $10\mathrm{nm}\le d\le 10\mu \mathrm{m}$. The symbol $d_c$ represents the center-of-mass separation distance.

Figure 3

Comparison of the total conductance at $T=300$ K between two ${\mathrm{SiO}}_2$ spheres calculated analytically [54] and by the discrete system Green's function (DSGF) method. Spheres of radii (a) $R=50\mathrm{nm}$ and (b) $R=500\mathrm{nm}$ are modeled for variable vacuum separation distance, $10\mathrm{nm}\le d\le 10\mu \mathrm{m}$. 50-nm-radius spheres are discretized into $N_{\mathrm{sphere}}=2176$ subvolumes per sphere for all vacuum separation distances. 500-nm-radius spheres are discretized into $N_{\mathrm{sphere}}=5616$ subvolumes per sphere for $d\le 100\mathrm{nm}$ and into $N_{\mathrm{sphere}}=2176$ subvolumes per sphere for $d>100\mathrm{nm}$. The relative error between the DSGF and analytical solution is calculated as $\frac{G_{t,12}^{\mathrm{DSGF}}-G_{t,12}^{\mathrm{analytical}}}{G_{t,12}^{\mathrm{analytical}}}$.

Figure 4

Comparison of the total conductance at $T=300$ K between two 50-nm-radius ${\mathrm{SiO}}_2$ spheres calculated analytically [54] and by the discrete system Green's function (DSGF) method when one subvolume per sphere is used in the discretization. Vacuum separation distance is varied as $10\mathrm{nm}\le d\le 10\mu \mathrm{m}$. The relative error between the DSGF and analytical solution is calculated as $\frac{G_{t,12}^{\mathrm{DSGF}}-G_{t,12}^{\mathrm{analytical}}}{G_{t,12}^{\mathrm{analytical}}}$.

Figure 5

Comparison of the total conductance at $T=300$ K between three ${\mathrm{SiO}}_2$ spheres calculated analytically [54] and by the discrete system Green's function (DSGF) method. Linear chains of spheres of radii (a) $R=50\mathrm{nm}$ and (b) $R=500\mathrm{nm}$ are modeled for variable vacuum separation distance, $10\mathrm{nm}\le d\le 10\mu \mathrm{m}$. 50-nm-radius spheres are discretized into $N_{\mathrm{sphere}}=2176$ subvolumes per sphere for all vacuum separation distances. 500-nm-radius spheres are discretized into $N_{\mathrm{sphere}}=5616$ subvolumes per sphere for $d\le 100\mathrm{nm}$ and into $N_{\mathrm{sphere}}=2176$ subvolumes per sphere for $d>100\mathrm{nm}$. The relative error between the DSGF and analytical solution is calculated as $\frac{G_{t,12}^{\mathrm{DSGF}}-G_{t,12}^{\mathrm{analytical}}}{G_{t,12}^{\mathrm{analytical}}}$ and $\frac{G_{t,13}^{\mathrm{DSGF}}-G_{t,13}^{\mathrm{analytical}}}{G_{t,13}^{\mathrm{analytical}}}$.

Figure 6

Gaussian random sphere representation of irregularly shaped particles. The relative standard deviation of the radius is varied to define mildly ($\sigma =0.2$) and highly ($\sigma =0.8$) distorted particles. Particle morphology is kept constant with increasing particle distortion.

Figure 7

Normalized total conductance as a function of the center-of-mass separation distance for mildly distorted ($\sigma =0.2, R_{\mathrm{eq},1}=49.3\mathrm{nm}, R_{\mathrm{eq},2}=44.5\mathrm{nm}, N=16605$ total subvolumes) and highly distorted ($\sigma =0.8, R_{\mathrm{eq},1}=45.8\mathrm{nm}, R_{\mathrm{eq},2}=37.9\mathrm{nm}, N=10948$ total subvolumes) particles, where $R_{\mathrm{eq}}$ is the equivalent radius of a perfect sphere with the same volume as the irregularly shaped particle. The total conductance between irregularly shaped particles is normalized with respect to the conductance of comparable perfect spheres with equivalent volume and center-of-mass separation distance.

Figure 8

Spatial distribution of power dissipation within each subvolume for two highly distorted particles ($\sigma =0.8, R_{\mathrm{eq},1}=45.8\mathrm{nm}, R_{\mathrm{eq},2}=37.9\mathrm{nm}, N=10948$ total subvolumes) at center-of-mass separation distances (a) $d_{\mathrm{c}}=110\mathrm{nm}$ and (b) $d_c=337\mathrm{nm}$ (arrows denote which particles are interacting). Negative values represent heat loss, and positive values represent heat gain. The high-temperature particle (blue color scheme since thermal energy is lost) is set at $T=300\mathrm{K}$, and the low-temperature particle (red color scheme since thermal energy is gained) is set at $T=0\mathrm{K}$. For $d_c=110\mathrm{nm}$, 80% of all power dissipation occurs at adjacent surfaces within 34% of the volume of particle 1 and 53% of the volume of particle 2. For $d_c=337\mathrm{nm}$, 80% of all power dissipation occurs within 67% of the volume of particle 1 and 71% of the volume of particle 2.

Figure 9

Spectral conductance at $T=300$ K for two highly distorted particles ($\sigma =0.8, R_{\mathrm{eq},1}=45.8\mathrm{nm}, R_{\mathrm{eq},2}=37.9\mathrm{nm}, N=10948$ total subvolumes) at center-of-mass separation distances (a) $d_{\mathrm{c}}=110\mathrm{nm}$ and (b) $d_c=337\mathrm{nm}$. Results are compared against the spectral conductance for two perfect spheres with the same volume and center-of-mass separation distance as the irregularly shaped particles.