Thin film extensional flow of a transversely isotropic viscous fluid

Many biological materials such as cervical mucus and collagen gel possess a fibrous microstructure. This microstructure affects the emergent mechanical properties of the material and hence the functional behavior of the system. We consider the canonical problem of stretching a thin sheet of transversely isotropic viscous fluid as a simplified version of the spinnbarkeit test for cervical mucus. We propose a solution to the model constructed by Green and Friedman by manipulating the model to a form amenable to arbitrary Lagrangian-Eulerian (ALE) techniques. The system of equations, reduced by exploiting the slender nature of the sheet, is solved numerically, and we discover that the bulk properties of the sheet are controlled by an effective viscosity dependent on the evolving angle of the fibers. In addition, we confirm a previous conjecture by demonstrating that the center line of the sheet need not be flat, and perform a short timescale analysis to capture the full behavior of the center line.

Automated summary

The fibrous microstructure of biological materials affects their mechanical properties and functional behavior. This study simulates the stretching of a fibrous membrane and finds that the macroscopic properties are controlled by an effective viscosity dependent on the evolving fiber angle. It also confirms that the center line of the membrane does not have to be flat.