Similarity Solutions for Capillary Pinch-Off in Fluids of Differing Viscosity

Self-similar profiles associated with capillary instability of a fluid thread of viscosity $\lambda \eta$ in surrounding fluid of viscosity $\eta$ are obtained for $\frac{1}{16}\le \lambda \le 16$ via a simplified numerical scheme. Universal similarity scaling is preserved despite an asymptotically large velocity in the pinching neck driven by nonlocal dynamics. The numerical results agree well with experimental measurements by Cohen et al. [preceding Letter, Phys. Rev. Lett. 83, 1147 (1999)]. For all $\lambda$, the self-similar profile is asymmetric and conical far from the minimum. The steep cone slope increases monotonically with $\lambda$; the shallow cone slope is maximized around $\lambda =\frac{1}{4}$.