Comparison of low amplitude oscillatory shear in experimental and computational studies of model foams

TL;DR

This study compares experimental and computational low-amplitude oscillatory shear responses of model foams, revealing distinct flow regimes and transition behaviors with good agreement between methods.

Contribution

It provides a detailed characterization of the transition from solid- to liquid-like flow in foam models using combined experiments and simulations.

Findings

Velocity profiles are linear at low frequencies

Total phase shift scales as ω^3 at low frequencies

Transition to nonlinear velocity profiles at high frequencies

Abstract

A fundamental difference between fluids and solids is their response to applied shear. Solids possess static shear moduli, while fluids do not. Complex fluids such as foams display an intermediate response to shear with nontrivial frequency-dependent shear moduli. In this manuscript, we conduct coordinated experiments and numerical simulations of model foams subjected to boundary-driven oscillatory, planar shear. Our studies are performed on bubble rafts (experiments) and the bubble model (simulations) in 2D. We focus on the low-amplitude flow regime in which T1 bubble rearrangement events do not occur, yet the system transitions from solid- to liquid-like behavior as the driving frequency is increased. In both simulations and experiments, we observe two distinct flow regimes. At low frequencies $\omega$, the velocity profile of the bubbles increases linearly with distance from the stationary wall, and there is a nonzero total phase shift between the moving boundary and interior bubbles. In this frequency regime, the total phase shift scales as a power-law $\Delta \sim \omega^n$ with $n \approx 3$. In contrast, for frequencies above a crossover frequency $\omega > \omega_{p}$, the total phase shift $\Delta$ scales linearly with the driving frequency. At even higher frequencies above a characteristic frequency $\omega_{nl} > \omega_{p}$, the velocity profile changes from linear to nonlinear. We fully characterize this transition from solid- to liquid-like flow behavior in both the simulations and experiments, and find qualitative and quantitative agreement for the characteristic frequencies.