Constant pressure gas-driven displacement of a shear-thinning liquid in a partially filled radial Hele-Shaw cell: Thin films, bursting and instability

•We study drop bursting in a radial Hele-Shaw cell.•We show the area expansion rate is exponential.•Film thickness is estimated by using conservation of volume.•Instability growth rate compared for Newtonian and shear-thinning fluids.•Universal relationships appear for bursting time and expansion rate.

In this manuscript we present experimental data and quantitative analysis for the fingering instability along the interface of finite volume of Newtonian (mineral oil) and dilute shear-thinning non-Newtonian (high molecular weight polyisobutylene in mineral oil) fluids. The instability is generated by air penetrating the liquid in a radial Hele-Shaw cell geometry. The novel feature of the experiment is that the gas is driven at constant pressure generating an exponential gas area expansion independent of the presence of the instability. Furthermore, we show that the instability growth along the interface is proportional to teωξtteωξt, or in other terms the instability growth rate is constant when the gas area expansion is considered. There are clear differences and similarities in the fingering growth rate, bursting time and film thickness properties when comparing Newtonian and shear-thinning non-Newtonian fluids. It is surprising that similarities occur despite side branching for the shear-thinning liquids at higher pressures.

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