The deformation and breakup of a power-law non-Newtonian slender drop in a Newtonian liquid in simple shear and axisymmetric extensional creeping flows has been theoretically studied. The steady-state problem is governed by three dimensionless parameters: the capillary number (Ca), the viscosity ratio (l) and the power-law index (n). There are similarities between both flows such as: (a) slender drops exist only if n £ 1. These drops have pointed ends; (b) for the same flow strength (G), Newtonian drops are more elongated than shear thinning drops; and (c) for the same viscosity ratio, shear thinning drops are more difficult to break than Newtonian drops. Differences between the two flows include: (a) in an extensional flow, different shapes of inviscid drops were found, depending on the value of n, while for the shear case, only one type of inviscid drop exists; (b) in an extensional flow, no stationary drop exists beyond a maximum value of G (the breakup point), while in shear flow stationary drops (stable or unstable) can be found for every value of G; and (c) for the same viscosity ratio, extensional flow is more effective than shear flow in drop breakup, since it requires smaller capillary numbers. Finally, in an extensional flow, we show that a small amount of inertia to the external flow, can dramatically change the deformation and breakup mechanism of the slender drop.
