Thin film extensional flow of a transversely isotropic viscous fluid

TL;DR

This paper investigates the extensional flow of a transversely isotropic viscous fluid in thin films, revealing how fiber orientation influences effective viscosity and sheet deformation, with novel numerical solutions and analysis.

Contribution

It introduces a new numerical approach to model thin film extensional flow of fibrous viscous fluids, incorporating fiber orientation effects and confirming non-flat center-line behavior.

Findings

Effective viscosity depends on fiber angle.

Center-line of the sheet can be non-flat.

Numerical solutions reveal fiber micro-structure impacts flow.

Abstract

Many biological materials such as cervical mucus and collagen gel possess a fibrous micro-structure. This micro-structure affects the emergent mechanical properties of the material, and hence the functional behaviour 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 novel solution to the model constructed by Green & Friedman by manipulating the model to a form amenable to arbitrary Lagrangian-Eulerian techniques. The system of equations, reduced by exploiting the slender nature of the sheet, are 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 fibres. In addition, we confirm a previous conjecture by demonstrating that the centre-line of the sheet need not be flat, and perform a short timescale analysis to capture the full behaviour of the centre-line.