Experimental study of a buoyancy-driven instability of a miscible horizontal displacement in a Hele-Shaw cell

Abstract

When a given fluid displaces another less viscous miscible one in a horizontal HeleShaw cell, the displacement is stable from the viscous point of view. Nevertheless, thin stripes perpendicular to the moving interface can be observed in the mixing zone between the fluids both in rectilinear and radial displacements. This instability is due to buoyancy effects within the gap of the cell which develop because of an unstable density stratification associated with the underlying concentration profile. To characterize this buoyancy-driven instability and the related striped pattern, we perform a parametric experimental study of viscously stable miscible displacements in a horizontal Hele-Shaw cell with radial injection. We analyze the influence of the flow rate, the thickness of the gap, and the relative physical fluid properties on the development and characteristics of the instability. C ⃝ 2014 AIP Publishing LLC.

Schlieren imaging of viscous fingering in a horizontal Hele-Shaw cell

“…Chief among them is the decay of the displacement front velocity with time in the radial displacement. The images clearly demonstrate both the well-known viscous fingering instability of the displacement front, and narrowly spaced radial streaks behind the front that are associated with the gravitational instability mode investigated by Haudin et al (2014), Talon et al (2013), and John et al (2013). Figure 10 shows a close-up image of water displacing 20 % glycerol-water solution.…”

“…Field of view: 9 cm x 9 cm Fig. 8 Schematic of a less viscous fluid displacing a more viscous one (possibly of different density) in a horizontal HS cell taken from the stability analysis of Talon et al (2013) results in the formation of thin little stripes developing in the invading fluid and perpendicular to the front, as seen using a dye in a viscously stable case (Haudin et al 2014). These stripes result from streamwise, counter-rotating vortices, such as can be seen in Figs.…”

“…What is pertinent here is how Schlieren is capable of imaging the smaller features associated with the radial streaks internal to the primary fingers. Using dye imaging on a viscously stable displacement, Haudin et al (2014) have shown that the small fingers in the 55 % glycerol system are attributable to a gravitational instability due to layering induced by the Poiseuille profile. These are readily observed at the periphery of the 55 and 65 % flows.…”

“…Visualization is typically done by injecting a dyed fluid into a transparent fluid and recording the spatiotemporal evolution of the dye distribution with a camera (Fernandez et al 2002;Haudin et al 2014;Homsy 1987;Maes et al 2010;Riolfo et al 2012). However, particularly for low flow rates (small Péclet numbers), there is no guarantee that imaging the dye is equivalent to imaging the undyed fluid.…”

Calcium Carbonate Mineralization in a Confined Geometry

“…They originate from buoyancy-driven convection due to a density gradient. 13 The radial symmetry is, however, preserved, but the precipitate starts to be flushed away from the injection point by the flow; F is thus slightly smaller than 1. Increasing further the flow rate destabilizes the pattern perimeter in fingers, which breaks the radial symmetry ( Figure 2c7).…”