Path instabilities of a freely rising or falling sphere

Abstract

Path instabilities of a sphere rising or falling in a quiescent Newtonian fluid have been studied experimentally. The rich palette of possible instabilities is dependent upon two dimensionless quantities, namely the Galileo number (Ga) and the particle/fluid mass density ratio (ρ¯). In recent literature, several (Ga,ρ¯) regime maps have been proposed to characterize path instabilities, based on both numerical and experimental studies, with substantial disagreements among them. The present study attempts to shed light on path instabilities for which previous studies disagree. A detailed experimental investigation has been conducted for 219 different combinations of Ga and ρ¯, grouped around four values of ρ¯ (∼ 0.87, 1.12, 3.19 and 3.9) and Ga in the range of ∼ 100 to 700. Our results agree well with literature for the low Ga range in which a particle takes a steady vertical or steady oblique path and for which all previous studies agree with each other. For the higher and more controversial Ga range, we discuss consensus and disagreements with previous studies. Some regimes, which were only recently observed in numerical simulations, have been observed experimentally for the first time. Also, intriguing bi-stable regimes (i.e., coexistence of two stable asymptotic states) have been observed. For all four investigated density ratios, an update of the regime map is proposed. Finally, for both the rising and falling spheres, the drag coefficient as function of terminal settling Reynolds number has been determined, which for the investigated density ratios does not differ significantly from that of flow past a fixed sphere.