Simulation of droplet formation and coalescence using lattice Boltzmann-based single-phase model.

A lattice Boltzmann method-based single-phase free surface model is developed to study the interfacial dynamics of coalescence, droplet formation and detachment phenomena related to surface tension and wetting effects. Compared with the conventional multiphase models, the lattice Boltzmann-based single-phase model has a higher computational efficiency since it is not necessary to simulate the motion of the gas phase. A perturbation, which is given in the same fashion as the perturbation step in Gunstensen's color model, is added to the distribution functions of the interface cells for incorporating the surface tension into the single-phase model. The assignment of different mass gradients along the fluid-wall interface is used to model the wetting properties of the solid surface. Implementations of the model are demonstrated for simulating the processes of the droplet coalescence, the droplet formation and detachment from ceiling and from nozzles with different shapes and different wall wetting properties.

[1]  R. Verberg,et al.  Modeling the flow of complex fluids through heterogeneous channels , 2005 .

[2]  S. Osher,et al.  A Level Set Formulation of Eulerian Interface Capturing Methods for Incompressible Fluid Flows , 1996 .

[3]  Alexander Z. Zinchenko,et al.  Cusping, capture, and breakup of interacting drops by a curvatureless boundary-integral algorithm , 1999, Journal of Fluid Mechanics.

[4]  V. Cristini,et al.  Theory and numerical simulation of droplet dynamics in complex flows--a review. , 2004, Lab on a chip.

[5]  Alexandros Kalarakis,et al.  Galilean-invariant lattice-Boltzmann simulation of liquid-vapor interface dynamics. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Shan,et al.  Lattice Boltzmann model for simulating flows with multiple phases and components. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  S. Osher,et al.  Level set methods: an overview and some recent results , 2001 .

[8]  Julia M. Yeomans,et al.  A Lattice Boltzmann Model of Binary Fluid Mixture , 1995, comp-gas/9511001.

[9]  T. Etoh,et al.  The coalescence speed of a pendent and a sessile drop , 2005, Journal of Fluid Mechanics.

[10]  Shiyi Chen,et al.  A Novel Thermal Model for the Lattice Boltzmann Method in Incompressible Limit , 1998 .

[11]  S. Osher,et al.  Capturing the Behavior of Bubbles and Drops Using the Variational Level Set Approach , 1998 .

[12]  Irina Ginzburg,et al.  A free-surface lattice Boltzmann method for modelling the filling of expanding cavities by Bingham fluids , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[13]  Chih-Ming Ho,et al.  Scaling law in liquid drop coalescence driven by surface tension , 2004 .

[14]  Three-dimensional lattice-Boltzmann model of van der Waals fluids. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Shan,et al.  Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[16]  A lattice Boltzmann based single-phase method for modeling surface tension and wetting , 2007 .

[17]  Yeomans,et al.  Lattice Boltzmann simulations of liquid-gas and binary fluid systems. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[18]  S. Zaleski,et al.  Lattice Boltzmann model of immiscible fluids. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[19]  R. Boom,et al.  Lattice Boltzmann simulations of droplet formation in a T-shaped microchannel. , 2006, Langmuir : the ACS journal of surfaces and colloids.

[20]  S. Zaleski,et al.  Volume-of-Fluid Interface Tracking with Smoothed Surface Stress Methods for Three-Dimensional Flows , 1999 .

[21]  Daniel H. Rothman,et al.  Immiscible cellular-automaton fluids , 1988 .

[22]  J. Buick,et al.  Gravity in a lattice Boltzmann model , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[23]  John R. Lister,et al.  Coalescence of liquid drops , 1999, Journal of Fluid Mechanics.

[24]  Patrick K. Notz,et al.  Satellite drops: Unexpected dynamics and change of scaling during pinch-off , 2001 .

[25]  Mitsuhiro Ohta,et al.  Numerical analysis of a single drop formation process under pressure pulse condition , 1995 .

[26]  David J. Benson,et al.  Volume of fluid interface reconstruction methods for multi - material problems , 2002 .

[27]  Konrad Steiner,et al.  Lattice Boltzmann model for free-surface flow and its application to filling process in casting , 2003 .

[28]  Banavar,et al.  Two-color nonlinear Boltzmann cellular automata: Surface tension and wetting. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[29]  G. Whitesides,et al.  Rapid Prototyping of Microfluidic Systems in Poly(dimethylsiloxane). , 1998, Analytical chemistry.

[30]  L. Yeo,et al.  Film drainage between two surfactant-coated drops colliding at constant approach velocity. , 2003, Journal of colloid and interface science.