Flow of a two-dimensional liquid foam: Impact of surfactant type and boundary conditions

Abstract

In this study, we experimentally investigate the rheological and flow behavior of two-dimensional (2D) monodisperse aqueous foams, sheared between parallel plates using a custom-made rheo-optical apparatus with smooth and roughened walls. The foams were prepared using two commercially available detergents — Foam 1 and Foam 2 — while maintaining similar bubble sizes and liquid fractions. The linear viscoelastic results reveal that the Foam 1 consistently exhibits higher elastic and loss moduli than the Foam 2, regardless of boundary conditions, with roughened walls further enhancing these moduli in both foams. Additionally, the Foam 1 shows a lower viscoelastic relaxation frequency compared to the Foam 2, indicating a less mobile interface for the Foam 1. In the non-linear regime, significant differences were observed. Under smooth boundary conditions, Foam 2 exhibits yield stress behavior, whereas Foam 1 does not, despite having higher viscous stresses. The viscous stress in the Foam 1 scales with the capillary number as ${\tau }_w\propto$ Ca${}^{0.5}$, while for the Foam 2, the scaling depends on the boundary conditions: ${\tau }_w\propto$ Ca${}^{0.85}$ for smooth walls and ${\tau }_w\propto$ Ca${}^{0.65}$ for roughened walls. These variations in rheological behavior are attributed to differences in surfactant chemistry, leading to different interface mobilities, with the Foam 1 having a less mobile interface compared to the Foam 2.