Stability of similarity solutions of viscous thread pinch-off

@article{Dallaston2021StabilityOS,
  title={Stability of similarity solutions of viscous thread pinch-off},
  author={Michael C. Dallaston and Chen Zhao and James E. Sprittles and Jens Eggers},
  journal={Physical Review Fluids},
  year={2021}
}
In this paper we compute the linear stability of similarity solutions of the breakup of viscous liquid threads, in which the viscosity and inertia of the liquid are in balance with the surface tension. The stability of the similarity solution is determined using numerical continuation to find the dominant eigenvalues. Stability of the first two solutions (those with largest minimum radius) is considered. We find that the first similarity solution, which is the one seen in experiments and… 

Figures from this paper

References

SHOWING 1-10 OF 29 REFERENCES

Pinching threads, singularities and the number 0.0304...

The dynamics of capillary pinching of a fluid thread are described by similarity solutions of the Navier–Stokes equations. Eggers [Phys. Rev. Lett. 71, 3458 (1993)] recently proposed a single

ON THE BREAKUP OF VISCOUS LIQUID THREADS

A one-dimensional model evolution equation is used to describe the nonlinear dynamics that can lead to the breakup of a cylindrical thread of Newtonian fluid when capillary forces drive the motion.

Nonlinear dynamics and breakup of free-surface flows

Surface-tension-driven flows and, in particular, their tendency to decay spontaneously into drops have long fascinated naturalists, the earliest systematic experiments dating back to the beginning of

Stability of a viscous pinching thread

We consider the dynamics of a fluid thread near pinch-off, in the limit that inertial effects can be neglected. There exists an infinite hierarchy of similarity solutions corresponding to pinch-off.

Axisymmetric Surface Diffusion: Dynamics and Stability of Self-Similar Pinchoff

The dynamics of surface diffusion describes the motion of a surface with its normal velocity given by the surface Laplacian of its mean curvature. This flow conserves the volume enclosed inside the

Stability of Self-similar Solutions for Van der Waals Driven Thin Film Rupture

Recent studies of pinch-off of filaments and rupture in thin films have found infinite sets of first-type similarity solutions. Of these, the dynamically stable similarity solutions produce

Stability of viscous fingering.

  • Bensimon
  • Mathematics, Physics
    Physical review. A, General physics
  • 1986
TLDR
Numerical simulations demonstrate the existence of a finite-amplitude nonlinear instability appearing at low surface tensions in a two-dimensional Hele-Shaw cell.

Analytic theory for the linear stability of the Saffman-Taylor finger

An analytic theory is presented for the linear stability of the Saffman–Taylor finger in a Hele–Shaw cell. Eigenvalues of the stability operator are determined in the limit of zero surface tension

Capillary breakup of a liquid bridge: identifying regimes and transitions

Computations of the breakup of a liquid bridge are used to establish the limits of applicability of similarity solutions derived for different breakup regimes. These regimes are based on particular

Discrete Self-Similarity in Interfacial Hydrodynamics and the Formation of Iterated Structures.

TLDR
It is demonstrated that iterated structures appear as a consequence of discrete self-similarity, where certain patterns repeat themselves, subject to rescaling, periodically in a logarithmic time scale, creating an infinite sequence of ridges and filaments with similarity properties.