The axisymmetric capillary pinch-off of a viscous fluid thread of viscosity λμ and surface tension γ immersed in a surrounding fluid of viscosity μ is studied. Similarity variables are introduced (with lengthscales decreasing like τ , the time to pinch-off, in a rapidly translating frame) and the self-similar shape is determined directly by a combination of modified Newton iteration and a standard boundary-integral method. A large range of viscosity ratios is studied ( 0.002\,≤\,λ\,≤\, 500 ) and asymmetric profiles are observed for all λ , with conical shapes far from the pinching point, in agreement with previous time-dependent studies. The stability of the steady solutions is investigated and oscillatory instability is found for λ ≥ 32 . For λ\,\, 1 an asymptotic scaling of λ1/2 is suggested for the slopes of the far-field conical shapes. These compare well with the quantitative predictions of a one-dimensional theory based on Taylor's (1964) analysis of a slender bubble.
No takes yet. Share an insight, caveat, or question.
Sierou et al. (2003) studied this question.