Experimental study of the solid-liquid interface in a yield-stress fluid flow upstream of a step

Abstract

We present an experimental study investigating the transition zone between a liquid-like unyielded region and a solid-like yielded region in a yield-stress fluid. The configuration consists of a rectangular closed-channel flow disturbed by the presence of a step. Upstream of the step, a solid-liquid interface between a dead zone and a flow zone appears. In this study, we use a model fluid, namely polymer micro-gel Carbopol, which exhibits Herschel-Bulkley viscoplastic rheology. Exploiting the fluid transparency, the flow is monitored by particle image velocimetry using an internal visualization technique. The main outcome of this study is to show that, except in a thin transition layer close to the solid-liquid interface, the flow behaves as an apparent Poiseuille flow with an apparent slip condition at the base. The slip frontier is found to be almost independent of the flow rate while the corresponding slip velocity increases with the flow rate.

Augmented Lagrangian simulations study of yield-stress fluid flows in expansion-contraction and comparisons with physical experiments

“…See Appendix A.2 for details. Of note, in section 3, we will present the results in the dimensionless form, but we will use the dimensional form in section 4 to compare more easily with the results of [19].…”

“…In the case of "long" cavities as presented in Figure 8 and as in the configuration of [19], where the dead zone at the back of the cavity is disconnected, one can measure the horizontal length of the deadzone, denoted as L d (see Fig. 17, in section 4).…”

“…We are specifically interested in the numerical simulation of recent physical experiments of Chevalier et al [6] and Luu et al [19]. We provide a detailed analysis of the velocity profiles and unyielded zones.…”

“…An impressive range of Bingham numbers, aspect ratios of the geometry and shapes of the cavity (rectangular, sinusoidal wave, triangular, semi-fractal) are presented. But they did not describe in depth the velocity profiles in conjunction with the plug zone, along the lines of the physical experiments of Coussot's and Chambon's groups [6,19].…”

“…We also retrieve the existence of a so-called slip line and the Poiseuille-like behaviour above this slip line shown in [19] (see section 4). Of note, we also give the horizontal length of the dead zone at the corner of the cavity as a function of the Bingham number (section 2.3).…”