Many-body Interaction And Heat Diffusion Of Near-field Radiative Heat Transfer In Dense Particulate System

Dispersed particulate systems widely exist in the nature and industrial process,and are key research objects in the field of raidative heat transfer.According to whether the classical radiative transfer theory is applicable,the dispersed particulate systems can be classified into two types,i.e.,dilute particulate system and dense particulate system.There are mature theories for the radiative heat transfer in the dilute particle systems.However,due to the existence of a variety of complex physical processes in dense particulate systems,relevant radiative heat transfer analysis theories still need to be developed.From the applicative aspect,dense particulate system is widely used in the industrial processes,ranging from working fluid for the solar thermal utilization to powder bed for the selective laser sintering three-dimensional（3D）printing.Due to the involved high temperature working condition,thermal radiation becomes the key of the involved heat transfer process.Studies have shown the radiative heat flux can exceed the Planck’s black-body limit by several orders of magnitude due to near-field effects（evanescent wave tunneling and thermal coherent effect,etc.）when the averaged clearance between particles inside the dense particulate system is close to or less than the characteristic thermal wavelength.In a dense nanoparticle system,nanoparticles lie in the near field of each other,which leads to significant multiple scattering of the thermally excited evanescent wave,hence,the many-body interaction（MBI）will play a key role in enhancing or inhibiting radiative heat transfer.On the one hand,to date,the effect of MBI on the near-field radiative heat transfer（NFRHT）is still remaining to be investigated systematically.On the other hand,due to the unaffordable computation burden,the existing theoretical frameworks can not be applied directly when considering NFRHT in the dense particulate system composed of a great number of nanoparticles.Hence,it is necessary to develop a new effective medium theory for radiative heat transfer in dense particulate system taking MBI into consideration.In this work,the first-principle exact theory in the thermal radiation field,i.e.,fluctuational electrodynamics,is considered as the basic theorectical framework,which takes the photon tunneling and MBI effects into consideration.Effects of MBI on the NFRHT for both random and lattice nanoparticle ensemble are analyzed systematically.From the thermal radiation first principle fluctuational electrodynamics,a new norm-diffusion theory for NFRHT in dense particulate system is derived.The effect of MBI on the NFRHT between random nanoparticle ensembles（e.g.,metallic nanoparticle fractal clusters）is analyzed.The coupled electric and magnetic dipole（CEMD）approach is used to investigate the effect of MBI on NFRHT between two Ag nanoparticle fractal clusters,which is a typical kind of natural existing structures,e.g.,black carbon aerosols distributed in the atmosphere.It is found that it is the magnetically polarized eddy-current Joule dissipation that plays a dominant role in determining the NFRHT between Ag nanoparticle clusters,rather that the electrically polarized placement current dissipation.At room temperature,MBI in the metallic is unobvious,which is quite different from that in dielectric nanoparticle systems.There is a strong inhibitive MBI on NFRHT in the dielectric nanoparticle system,while the MBI in the metallic nanoparticle system is negligible.When the separation between two clusters is small enough,the radiative thermal conductance between the two clusters increases with increasing fractal dimension and the relative orientation has a significant effect on the thermal conductance between the clusters with low fractal dimension.When the separation is large enough,effect of fractal dimension and relative orientation of cluster on radiative thermal conductance is negligible.The effect of MBI on the NFRHT between lattice nanoparticle ensembles is analyzed.NFRHT in typical random nanoparticle ensembles（e.g.,one-dimensional（1D）linear nanoparticle chain,two-dimensional（2D）square-lattice nanoparticle ensemble and 2D nanoparticle grating）are anlyzed by means of the CEMD method.Dielectric Si C,metallic Ag and phase-change VO₂ nanoparticles are considered.Due to the possible structural resonances in the lattices,the characteristics of NFRHT between the lattice nanoparticle ensembles are expected to be obviously different from that of the random nanoparticle ensembles.Through analysis on the physics of heat transfer between two square-lattice particulate system,four asymptotic regimes are proposed,including（a）rarefied regime,（b）dense regime,（c）non-MBI regime and（d）MBI regime.In rarefied regime,NFRHT is determined only by the nanoparticle pairs in proximity.In dense regime,the contribution to NFRHT of nanoparticles inside each ensemble are nearly equal to each other.In non-MBI regime,the MBI is negligible.In MBI regime,the effect of MBI on NFRHT is strong.MBI in the nanoparticle ensembles can be evaluated by the separation between nanoparticles and whether the nanoparticle supports resonance in the infrared Planckian window or not.The stronger the coupling is,the more significant the effect of MBI on NFRHT is.When the coupling in the main and proximate chain is strong,the exsitence of the proximate chains will significantly inhibit the NFRHT in the main chain.When twisting the finite 2D nanoparticle gratings,the oscillating dependence of thermal conductance on the twisted angle is observed.Investigation on the near-field thermal energy from nanoparticle emitters with mutual interaction and thermally excited electromagnetic energy density can help the understanding of MBI on NFRHT in the dense particulate system.Based on the coupled dipole approximation,a general formula of the Poynting vector to evaluate the near-field radiative thermal energy comprehensively considering electric and magnetic dipole contribution together is established,which is applicable for both dielectric and metallic nanoparticle ensemble.When calculating near-field radiative thermal energy,the metallic nanoparticle（e.g.,Ag with radius 20 nm）can be treated as a magnetic dipole and neglect the electric dipole safely,as electric dipole contribution is much larger that of the magnetic dipole by 4 orders of magnitudes.However,the dielectric nanoparticle（e.g.,Si C with radius 20 nm）can be treated as a single electric dipole without magnetic dipole,as magnetic dipole contribution is much larger that of the electric dipole by 2 orders of magnitudes.As for the local energy density,the Si C proximate chain can significantly inhibit the energy density thermally excited by Si C main chain,while effect of existence of Ag proximate chain on the energy density thermally excited by the Si C or Ag main chains can be neglected safely,which is attributed to that MBI on NFRHT is strong for Si C nanoparitcles as Si C nanoparticle optical response matches well with the Planck window.For NFRHT in macroscale dense particulate system,due to the unaffordable computation burden,the existing theoretical frameworks can not be applied directly.By assuming the validity of classical heat diffusion equation and Fourier’s law for such macroscale dense particulate system,the radiative effective thermal conductivity（ETC）can be accepted to characterize the near-field radiative heat diffusion characteristics in the nanoparticle system.The many-body radiative heat transfer theory is applied to calculate the ETC,and analyze the effect of MBI,phase change and host medium relative permittivity on the ETC of the phase-change VO₂ nanoparticle chain.It is noted that the ETC of the insulator-phase VO₂ nanoparticle chain below phase transition temperature can be as high as 50 times of that for the metallic-phase above transition temperature.The strong coupling in the insulator-phase VO₂ nanoparticle chain accounts for its high ETC as compared to the low ETC for the chain at the metallic phase,where there is a mismatch between the characteristic thermal frequency and particle polarizability resonance frequency.The strong MBI is in favor of the ETC.The ETC increases with increasing the host medium relative permittivity.The host medium relative permittivity significantly affects the inter-particles couplings,which accounts for the permittivity-dependent ETC for the VO₂ nanoparticle chains.For different materials,the mechanism behind the permittivity-dependent inter-particles couplings is different from each other.For the materials without infrared resonacne（e.g.,metal）,increasing host medium relative permittivity will result in a better match between the characteristic thermal frequency and particle polarizability resonance frequency.For the materials with infrared resonacne（e.g.,insulator）,increasing host medium relative permittivity will increase the coupling mode propagation length and therefore enhance ETC.Due to the near-field effects in radiative heat transfer in dense particulate system,the hypothesis of classical heat diffusion equation and Fourier law may cease to be valid.There is lack of work on derivation of heat diffusion equation for dense particulate system starting from thermal radiation first principle fluctuational electrodynamics.The energy balance equation of nanoparticles at particle scale is established based on many-body radiative heat transfer theory.Combined with the local temperature continuity hypothesis,a rigorous theoretical derivation is carried out,and the diffusion-type governing equation with temperature as the governing variable at continuum scale is derived,and a formula of radiative ETC tensor is obtained naturally.The developed temperature governing equation is quite different from the classical heat diffusion equation.For the asymmetric system,in addition to the radiative heat diffusion term,a new radiative heat convection term appears in the new developed heat-diffusion equation,characterizing the asymmetric heat transfer caused by the asymmetry of structure.For the symmetric system,the radiative heat convection term vanishes and the derived heat-diffusion equation reduces to the classical heat diffusion equation.It is proved theoretically that the assumption of the validity of Fourier’s law is inaccurate.The convection-like heat transfer behavior caused by asymmetry of structure via thermal photons is predicted theoretically.For metalic and dielectric nanoparticle chains,through comparing the results from the developed theory and the exact results from the fluctuational electrodynamics,the developed theory is demonstrated applicable for describing NFRHT in arbitrary systems accurately.The derived formulas for radiative thermal conductivity are general and efficient for multi-dimensional nanoparticle systems.Based on the analysis on NFRHT by developed theory,the heat transfer channels increase with increasing the dimensionality of the system,which results in an increasing of radiative thermal conductivity with increasing system dimensionality.