Prediction of the Effective Thermal Conductivity of Hollow Sphere Foams

Microscale and mesoscale hollow sphere foam (HSF) materials have attracted tremendous attention in recent decades due to their potential applications. Here, we study the effective thermal conductivity (ETC) of HSFs using an equivalent model, in which hollow spheres are first treated as equivalent solid particles, and then are combined with the ETC models that have been previously developed for solid particle filled composites. Compared with the rule of mixture model and syntactic foam models, this model shows better accuracy in predicting the ETC of HSFs. The theoretical model, together with finite element simulations, is then used to guide the design of HSFs. The results show that smaller size (nanoscale), lower packing fraction, lower shell conductivity, larger shell porosity, longer binder length, and higher interfacial thermal resistance lead to significantly lower ETC, while packing pattern, sphere size distribution, pore size of the porous shell, and binder radius have relatively minor influences. Moreover, size effects are investigated to use the proposed model for microscale and nanoscale problems. Aside from the well-known Knudsen effect, the size effect induced by interfacial thermal resistance should also be considered when the sphere size is smaller than a critical length. Interestingly, the Knudsen effect in the pores of a porous shell is shown to have an insignificant influence on the ETC. This study provides deep understanding of the thermal (and electrical, equivalently) behavior of the HSFs, which will potentially aid future design of novel and multifunctional HSF materials.