Linear and Non-Linear Rheology of Single and Double Cross-Linked Biopolymer Networks under Viscous Shear Flow

TL;DR

This study uses a modified numerical model based on Slender Body theory to analyze the complex rheological behavior of biopolymer networks under shear flow, revealing nonlinear effects and structural influences.

Contribution

It introduces a modified numerical simulation approach to study the nonlinear rheology of single and double-cross-linked biopolymer networks, highlighting the impact of morphology and flow conditions.

Findings

Double peaks in nonlinear regime are not due to crosslinkers but fiber alignment changes.

Stress-strain behavior of double networks cannot be predicted by superimposing single network results at high strain.

Nonlinearity effects are significantly influenced by initial network morphology, not flow conditions.

Abstract

In this research study, a numerical tool, which is based on a version of Slender Body theory, has been used and also modified to simulate the mechanical behaviour of single- and double-cross-linked biopolymer networks (hydrogel) under oscillatory shear flow. The hydrodynamic interactions among fibres of intertwined networks were considered. Then, the stress and Fourier coefficients (i.e. shear moduli) were evaluated for both linear and nonlinear regimes. It was found that the double peaks (two-step yielding) of two double network at 100% maximum strain amplitude (nonlinear regime) cannot happen due to changes in fibre alignments and seed numbers, although the crosslinkers between two subnetworks present, which was previously reported in the literature. In fact, we also observed two peaks for single network in nonlinear regime. Furthermore, it was shown that the stress-strain curve of double network is not predicted by just superimposing the results from the corresponding single networks at 5% maximum strain amplitude (linear regime), but this prediction can be provided at 100% maximum strain amplitude (nonlinear regime). The Fourier coefficients and corresponding amplitude (an indication of nonlinearity effects) for double network were quite considerable from zero to fifth modes in nonlinear regime, despite enough zero and first modes in linear regime. It was also shown that the nonlinearity effects can be related to the morphology of the initial structure, i.e. the seed number rather than the flow condition for the single network. These results can help scientists to better design enhance fibrous materials used in wound healing or tissue engineering.