Local dynamics during pinch-off of liquid threads of power law fluids: Scaling analysis and self-similarity

Pinch-off dynamics of liquid threads of power law fluids surrounded by a passive ambient fluid are studied theoretically by fully two-dimensional (2-D) computations and one-dimensional (1-D) ones based on the slender-jet approximation for 01Oh>1, the 2-D computations reveal that a thinning thread transitions from the VP to the IVP regime when n>2/3n>2/3 in accordance with the 1-D results but a thinning thread transitions from the VP to the PF regime when 0.542/3n>2/3 in accordance with the 1-D results but a thinning thread remains in the PF regime until breakup when n<2/3n<2/3. Moreover, when Oh≪1Oh≪1 and n>2/3n>2/3, the 2-D computations show that the interface overturns first before the thread transitions from the PF to the IVP regime. When Oh<1Oh<1 and n>2/3n>2/3, the transition between the PF and the IVP regimes is shown to occur when the minimum thread radius hmin⁡∼Oh2/(3n−2)hmin⁡∼Oh2/(3n−2). Scaling exponents and self-similar thread shapes and axial velocity profiles obtained from the 2-D computations are shown to be in excellent agreement with the 1-D results when thread shapes at breakup are slender.