An experimental study of drop deformation and breakup in extensional flow at high capillary number

Abstract

An experimental study is reported of the flow-induced stretching of drops in a four-roll mill at low Reynolds number, but for capillary numbers that are large compared to the critical capillary number for onset of stretching. We mainly consider Newtonian drops in a Newtonian suspending fluid, but also present a brief study of Newtonian drops in a viscoelastic (Boger fluid) suspending fluid. The stability of the drops following cessation of flow is determined, in either case, by the ratio of their extended length to the undeformed radius. If this ratio is large enough, the drops will break into two or more parts via the capillary flow process known as end-pinching. However, for Newtonian drops in a Newtonian suspending fluid, it is shown that the critical degree of stretch for breakup increases sharply with increase of the capillary number that characterizes the stretching process. Furthermore, it is shown, in this case, that the critical stretch ratio is not unique, but that there can be a discrete range of stretch ratios above the first (or smallest) critical value where the drop is again stable before it encounters a second larger “critical” stretch ratio. This “restabilization” is associated with the transition from two to three drops in the breakup process. Newtonian drops in the viscoelastic Boger fluid are found to be slightly more stable than the same drops in a Newtonian fluid when stretched at strain rates just exceeding the critical value. By this we mean that the critical elongation ratio necessary for the drops to break upon cessation of flow is increased by about 20%. When stretched at a higher strain rate, approximately 2.15 times the critical value, large drops in the viscoelastic fluid (above 100 microns in radius for this particular suspending fluid) are destabilized relative to their counterpart in a Newtonian suspending fluid, while smaller drops are strongly stabilized.