Objective   Metal particle pigmented coatings play a vital role in the thermal control of spacecraft. The ratio of absorptivity to emissivity of coating is one of the important properties of thermal control performance. Besides the conventional factors of particle material, size, volume fraction, morphology and coating thickness, particle orientation is also an important factor in the regulation of radiative properties of the coating. It is important to study the regulation method of the ratio of absorptivity to emissivity of the coating for the design of thermal control coating. The orientation of the particles can be adjusted by operating parameters or alignment agents. The effect of particle orientation on the ratio of absorptivity to emissivity of coating is not thoroughly explored yet. Moreover, the scattering in two-flux theory is usually assumed to be isotropic in the literature. Therefore, it is necessary to investigate the regulation of the ratio of absorptivity to emissivity of the coating by flake orientation.

  Methods   As the commonly applied heat dissipation coating, the composite coating pigmented with large-size aluminum flakes was studied. The flakes were assumed to be randomly distributed and identically oriented. Due to the limitation of computer resources, it is infeasible to calculate the radiative properties of randomly distributed non-spherical large particles through strict solution of electromagnetic theory. The radiative properties of aluminum flake at different orientation angles were calculated by geometrical optics considering diffraction, and then the radiative transfer of the coating was solved by two-flux theory considering anisotropic scattering. The geometrical optics and the two-flux theory are suitable for the rapid calculation and analysis of the radiative properties of composite coating pigmented with large-size particles. The effects of orientation angle of aluminum flake, volume fraction and coating thickness were investigated.

  Results and Discussions   The spectral radiative properties of aluminum flake at different orientation angles were calculated by geometrical optics considering diffraction (Fig.5), which indicated the variation of absorption cross-section, scattering cross-section, and the asymmetry factor of aluminum flake with orientation angle. The spectral absorptivity (Fig.7) and spectral emissivity (Fig.8) of coatings at different orientation angles were calculated by the two-flux theory considering anisotropic scattering, which revealed the trends at different volume fractions and orientation angles. The regulation of the ratio of absorptivity to emissivity of the coating by flake orientation was investigated. The dependence of average absorptivity, average emissivity, and ratio of absorptivity to emissivity of the coating on the flake orientation angle and volume fraction was illustrated (Fig.9). And the dependence of radiative properties of the coating on the coating thickness was also studied (Fig.10). The ratio of absorptivity to emissivity can be effectively regulated by particle orientation, volume fraction, or coating thickness.

  Conclusions   The regulation of the ratio of absorptivity to emissivity of the thermal coating by flake orientation was systematically studied by modeling the coating pigmented with randomly distributed and identically oriented aluminum flakes. The results show that with the increase of orientation angle, the absorption cross-section and scattering cross-section of aluminum flake decrease, and the asymmetry factor increases. The ratio of absorptivity to emissivity of coating can be regulated in the range of 0.48-1.69 by adjusting the flake orientation. The average absorptivity and emissivity of the coating increase significantly when the orientation angle of aluminum flakes exceeds 45°, and increase first and then decrease with the increase of the volume fraction of aluminum flake. The ratio of absorptivity to emissivity reaches a minimum value at the orientation angle of around 45°. And the ratio decreases with the increase of the volume fraction of aluminum flakes. The coating thickness has greater effects on the average emissivity and the ratio of absorptivity to emissivity when the orientation angle of aluminum flake is larger. The ratio of absorptivity to emissivity decreases with the increase of coating thickness. The spectral absorptivity and spectral emissivity of the coating are small and vary little with orientation angle when the orientation angle of aluminum flake is less than 45°, and increase obviously when the orientation angle is greater than 45°, and then decrease with the continued increase of orientation angle. This work demonstrates that the ratio of absorptivity to emissivity can be effectively regulated by adjusting the particle orientation, providing a new method for the design and preparation of thermal control coating.