Homogenization of a submerged two-level bristle structure for modeling in biotechnology

The effective macroscopic model describing reciprocal motion of viscous weakly compressible fluid and two-level hierarchical fine bristle-like elastic structure is derived from microstructure via the Allaire-Briane homogenization method. This new model naturally generalizes the well-known system constructed by K.-H. Hoffmann, N. Botkin and V. Starovoitov for description of fine periodic elastic structures in fluids (2005). In applications, the established model can be used, for example, in description of airflow near surface of plant's leaf, in simulation of epithelium surfaces of blood vessels, and in design of biotechnological devices operating in liquids.