
Model  Author  Structure representation  Method  Comments 

Empirical  Lu et al. [60] Wang et al. [67]  Ignored  Volume average as a function of density or porosity  Cannot be applied for aerogels with different microstructures 

Analytical 
Wei et al. [10] Lu et al. [65] Wei et al. [10]  Cubic array of nanospherical structure  Standard equivalent circuit method  Cannot represent the randomness and complexity of aerogels 
JunJie et al. [66]  3D random DLCA structure  Standard equivalent circuit with improved analytical parallelseries model  Does not require any empirical parameters as input 

Numerical  Spagnol et al. [68] Zhao et al. [12]  Von Koch snowflake fractal structure and random DLCA structure  Finite volume method based on the mesh division  3D calculations are time consuming 
