Numerical simulation of surfactant motion in flowing foams and application to biological tissues

Abstract

We present a numerical model to study the rheology of two-dimensional dry foams. In a foam flowing at high velocity, the tangential component of the velocity associated with the gradient of surfactant concentration is not negligible. We develop a dynamical model to investigate the influence of viscoelastic parameters on the film evolution. Particularly, we consider the surfactant transport and the consequent surface tension variation along each film. Moreover, experiments on a foam between two parallel plates suggest that the diffusion of curvature along the film controlled by external friction can not be neglected. Hence, we merge our surfactant transport (ST) model with the two-dimensional Viscous Froth (VF) model [45]. The VF+ST model is validated by fitting experimental data for the evolution of the length of a film after a topological rearrangement (T1). Extending the VF model, which allows us to estimate the drag coefficient, our VF+ST model predicts two additional parameters, the Gibbs elasticity and the surface viscosity. With the VF+ST model we can fit experimental data for both foam containing anionic surfactants or proteins [74]. Furthermore, we apply the VF+ST model to predict rheological parameters of a flowing two-dimensional dry foam. We implement situations in which hexagonal and disordered foams subjected to simple shear or oscillating strain. We highlight how the viscoelastic parameters of our model affect the distribution of topological rearrangements in the foam. Additionally, we calculate the shear stress which offer a qualitative description of the transition of the foam from a solid-like to a liquid-like behaviour. Hence, starting from the stress-strain curves at different shear rates we predict the elastic shear modulus and the yield stress of the foam. In case of oscillating strain we investigate how the foam behaviour changes when varying the frequency or the amplitude of the applied strain and we calculate the storage and loss moduli. Overall, we analyse the effect of the viscoelastic parameters of our model on the rheological properties of the foam. Finally, the model is applied to investigate the morphology of biological tissues. Well-known analogies between fluids and biological tissues make possible the application of our model to simulate experiments presented by Bonnet et al. [6]. They carried out an annular ablation on Drosophila pupa dorsal thorax epithelium. In agreement with the experimental results we find that after cutting the cell-cell junctions and relaxing the tissue to its configuration of mechanical equilibrium, the anisotropy in the tissue increases with the age of the Drosophila pupa. Also in this case we investigate the effect of our viscoelastic parameters on the tissue. We propose our model as a tool for further investigations on tissue morphology.
Note: The material of Chapter 2 has been published in the scientific journal Physical Review E [74].

Date of Award	2019
Original language	English
Awarding Institution	Aberystwyth University
Supervisor	Simon Cox (Supervisor) & Gennady Mishuris (Supervisor)