Numerical modeling of effective thermal conductivity of hollow silica nanosphere packings

● Numerically calculating thermal conductivity of hollow silica nanosphere packings. ● Considering two-level hierarchical structure of hollow silica nanosphere packings. ● Analyzing the effect of geometric structure, contact ratio, and gas pressure. Hollow silica nanosphere packings (HSNSPs) can significantly suppress heat conduction through solid and gas phases due to the voids, small interparticle contact areas, and nanosized pores, showing promising potentials towards energy-efficient building applications. The HSNSPs display a two-level structure, where the solid silica nanoparticles form the shells of hollow spheres, and the accretion of hollow spheres form the porous powder packing structures. Investigating thermal transport in HSNSPs helps to understand the fundamental thermal transport processes and to guide the design of their geometric structures. Herein, we developed a numerical model based on the two-level structure of HSNSPs to explore their effective thermal conductivities. The developed numerical model considers the geometric parameters such as sphere size, shell thickness, interparticle contact resistance, and the gas pressure inside and outside the hollow spheres. The developed numerical model was validated by the measured thermal conductivities of HSNSPs fabricated via the sacrificial template method. The results show that the effective thermal conductivity of HSNSPs can be reduced by decreasing sphere diameter, contact area and shell thickness. The influence of ratio of contact diameter to sphere diameter on the effective thermal conductivity becomes weaker as the hollow sphere size decreases ( e.g. , < 200 nm). Besides, we also show that reducing gas pressure outside the hollow spheres can effectively decrease the thermal conductivity of HSNSPs. This work provides a guideline for the structural design and optimization of HSNSPs.