Axisymmetric boundary integral formulation for a two‐fluid system

A 3D axisymmetric Galerkin boundary integral formulation for potential flow is employed to model two fluids of different densities, one fluid enclosed inside the other. The interface variables are the velocity potential and the normal velocity, and they can be solved for separately, the second linear system being symmetric. The algorithm is validated by comparing with the analytic solutions for a static interior spherical drop over a range of values for the relative densities D=ρE/ρI of exterior and interior fluids and various boundary conditions. For time‐dependent simulations utilizing a level set method for the interface tracking, the accuracy has been checked by comparing against the known oscillation frequency of the sphere. Pinch‐off profiles corresponding to an initial two‐lobe geometry drop and D = 6 are also presented. Published in 2011 by John Wiley & Sons, Ltd.

[1]  Leonard J. Gray,et al.  Numerical simulation of non‐viscous liquid pinch off using a coupled level set boundary integral method , 2007, J. Comput. Phys..

[2]  P. Taborek,et al.  Bifurcation from bubble to droplet behavior in inviscid pinch-off. , 2008, Physical review letters.

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

[4]  J. Eggers,et al.  Theory of the collapsing axisymmetric cavity. , 2006, Physical review letters.

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

[6]  Paul H. Steen,et al.  Numerical simulations of inviscid capillary pinchoff , 2004 .

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

[8]  Osman A. Basaran,et al.  Small‐scale free surface flows with breakup: Drop formation and emerging applications , 2002 .

[9]  Alex M. Andrew,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition) , 2000 .

[10]  G. Baker,et al.  Application of Adaptive Quadrature to Axi-symmetric Vortex Sheet Motion , 1998 .

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

[12]  S. Heister.  Boundary element methods for two-fluid free surface flows , 1997 .

[13]  C. Spangler.  Nonlinear modeling of jet atomization in the wind-induced regime , 1995 .

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

[15]  J. Liggett,et al.  The Boundary Integral Equation Method for Porous Media Flow , 1982 .

[16]  J A Sethian,et al.  Simulation of the droplet-to-bubble transition in a two-fluid system. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[18]  J. Sethian,et al.  FRONTS PROPAGATING WITH CURVATURE DEPENDENT SPEED: ALGORITHMS BASED ON HAMILTON-JACOB1 FORMULATIONS , 2003 .

[19]  Luiz C. Wrobel,et al.  Applications in thermo-fluids and acoustics , 2002 .

[20]  G. M.,et al.  Elliptic Integrals , 1917, Nature.