Elastic solid dynamics in a coupled oscillatory Couette flow system

We report analytical solutions of a problem involving a visco-elastic solid material layer sandwiched between two fluid layers, in turn confined by two long planar walls that undergo oscillatory motion. The resulting system dynamics is rationalized, based on fluid viscosity and solid elasticity, via wave and boundary layer theory. This allows for physical interpretation of elasto-hydrodynamic coupling, potentially connecting to a broad set of biophysical phenomena and applications, from synovial joint mechanics to elastometry. Further, obtained solutions are demonstrated to be rigorous benchmarks for testing coupled incompressible fluid-hyperelastic solid and multi-phase numerical solvers, towards which we highlight challenging parameter sets. Finally, we provide an interactive online sandbox to build physical intuition, and open-source our code-base.

Automated summary

This paper presents analytical solutions to a problem involving a visco-elastic solid layer sandwiched between two fluid layers. The system dynamics are explained based on fluid viscosity and solid elasticity using wave and boundary layer theory. The findings provide a physical interpretation of elasto-hydrodynamic coupling and have potential applications in various biophysical phenomena. Additionally, the obtained solutions serve as rigorous benchmarks for testing numerical solvers for coupled incompressible fluid-hyperelastic solid and multi-phase systems.