Numerical simulation of non‐viscous liquid pinch off using a coupled level set boundary integral method

Simulations of the pinch-off of an inviscid fluid column are carried out based upon a potential flow model with capillary forces. The interface location and the time evolution of the free surface boundary condition are both approximated by means of level set techniques on a fixed domain. The interface velocity is obtained via a Galerkin boundary integral solution of the 3D axisymmetric Laplace equation. A short-time analytical solution of the Raleigh-Taylor instability in a liquid column is available, and this result is compared with our numerical experiments to validate the algorithm. The method is capable of handling pinch-off and after pinch-off events, and simulations showing the time evolution of the fluid tube are presented.

[1]  Norman Chigier,et al.  Breakup of liquid sheets and jets , 1999 .

[2]  O. Basaran,et al.  Drop formation from a capillary tube: Comparison of one-dimensional and two-dimensional analyses and occurrence of satellite drops , 2002 .

[3]  Odd M. Faltinsen,et al.  A BEM‐level set domain‐decomposition strategy for non‐linear and fragmented interfacial flows , 2006 .

[4]  J. Sethian,et al.  A Fast Level Set Method for Propagating Interfaces , 1995 .

[5]  O. Basaran,et al.  Computational and experimental analysis of pinch-off and scaling. , 2002, Physical review letters.

[6]  J. Keller,et al.  Surface Tension Driven Flows , 1983 .

[7]  J. Sethian,et al.  A coupled level set projection method applied to ink jet simulation , 2003 .

[8]  James A. Sethian,et al.  Level Set Methods and Fast Marching Methods , 1999 .

[9]  J. Sethian.  Curvature and the evolution of fronts , 1985 .

[10]  P. Concus,et al.  Variational Methods for Free Surface Interfaces , 1987 .

[11]  Baba C. Vemuri,et al.  Shape Modeling with Front Propagation: A Level Set Approach , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  John R. Lister,et al.  Capillary pinch-off in inviscid fluids , 2003 .

[13]  J. Sethian,et al.  LEVEL SET METHODS FOR FLUID INTERFACES , 2003 .

[14]  J A Sethian,et al.  A fast marching level set method for monotonically advancing fronts. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[15]  Cecil Hastings,et al.  Approximations for digital computers , 1955 .

[16]  Zhiye Zhao,et al.  Boundary stress calculation—a comparison study , 1999 .

[17]  Leonard J. Gray,et al.  Boundary Integral Evaluation of Surface Derivatives , 2004, SIAM J. Sci. Comput..

[18]  E. Villermaux,et al.  Physics of liquid jets , 2008 .

[19]  David L. Chopp,et al.  Some Improvements of the Fast Marching Method , 2001, SIAM J. Sci. Comput..

[20]  L. J. Gray,et al.  Evaluation of singular and hypersingular Galerkin integrals: direct limits and symbolic computation , 1998 .

[21]  L. Rayleigh.  On The Instability Of Jets , 1878 .

[22]  J. Eggers.  Nonlinear dynamics and breakup of free-surface flows , 1997 .

[23]  J. Sethian,et al.  Wave breaking over sloping beaches using a coupled boundary integral-level set method , 2003 .

[24]  L. Gray,et al.  Galerkin boundary integral analysis for the axisymmetric Laplace equation , 2006 .

[25]  Smithsonian Institution.  Annual Report of the Board of Regents of the Smithsonian Institution , 1893 .

[26]  P. Steen,et al.  Dynamics of inviscid capillary breakup: collapse and pinchoff of a film bridge , 1997, Journal of Fluid Mechanics.

[27]  Notz,et al.  Dynamics of Drop Formation in an Electric Field. , 1999, Journal of colloid and interface science.

[28]  Edmund Taylor Whittaker,et al.  A Course of Modern Analysis , 2021 .

[29]  J. Sethian,et al.  Transport and diffusion of material quantities on propagating interfaces via level set methods , 2003 .

[30]  R. Schulkes,et al.  The evolution and bifurcation of a pendant drop , 1994, Journal of Fluid Mechanics.

[31]  James A. Sethian,et al.  The Fast Construction of Extension Velocities in Level Set Methods , 1999 .

[32]  M. Sussman,et al.  Simulation of liquid metal droplets from field emission , 2007 .

[33]  J. Sethian,et al.  A coupled level set-boundary integral method for moving boundary simulations , 2005 .

[34]  Mary P. Anderson.  The Boundary Integral Equation Method for Porous Media Flow , 1984 .

[35]  J. Sethian.  AN ANALYSIS OF FLAME PROPAGATION , 1982 .

[36]  J. Sethian,et al.  Crystal growth and dendritic solidification , 1992 .

[37]  James A. Sethian,et al.  Numerical Methods for Propagating Fronts , 1987 .

[38]  John R. Lister,et al.  SELF-SIMILAR CAPILLARY PINCHOFF OF AN INVISCID FLUID , 1997 .

[39]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .