Looking under the skirt of a bubble

For viscous liquids and large bubble, a thin layer of fluid, commonly referred to as a “skirt”, can be observed issuing from the rim of bubbles. First reported for drops by Thomson and Newall (1885), the appearance of skirts requires a sufficiently viscous continuous phase. A criterion for the skirt formation can be obtained considering that the balance between the surface tension contribution and the normal viscous stress becomes impossible (Bhaga 1976). Different theories have been proposed for the skirt thickness (Guthrie and Bradshaw 1969, Wairegi 1974, Ray & Properetti 2014). The significant differences between experimental observations and proposed theories have motivated this work. We present direct numerical simulations of skirt bubble and investigate in detail the flow field in the skirt in order to discuss the skirt formation and the assumptions made in the theoretical derivations. Our results confirm that the flow can be considered as parallel in the skirt and that the velocity on the inner side is much smaller than the bubble velocity in agreement with Wairegi’s measurements. The simulations also outlines that the liquid velocity on the outer side of the skirt differs from the bubble rising velocity resulting in a reduction of the skirt thickness.