Algorithms for generating planar networks simulating hierarchical patterns of cracks formed during film drying

Hierarchical crack patterns that arise during the drying of thin films of colloidal dispersions or polymer solutions on a solid substrate are of interest both from a fundamental standpoint and in the context of the creation of transparent electrodes for optoelectronics. This paper analyzes the morphology of such patterns based on image processing of real-world samples. Graph theory is used to extract chains of edges and analyze the network topology. A method based on the hierarchy of connections is applied to classify cracks by generation. The limitations of existing classification approaches related to the discreteness of the time scale and the use of only a part of the entire pattern are discussed. Three approaches are used to generate artificial hierarchical networks: random uniform partitioning, recursive Voronoi partitioning, and a crack growth simulation model, each modified to reproduce the hierarchical structure. A comparison was made of the geometric characteristics (distribution of crack angles, edge lengths, cell areas, and circularity coefficient) and topological properties (distribution of the number of cell sides) of real and simulated networks. It was shown that the simulation model best reproduces the key features of real cracks, including the characteristic right angles of their connections.