A Lattice Boltzmann method for turbulent emulsions

The breakup of droplets in a turbulent flow is key to many natural and industrial applications. Here we present and validate a computationally efficient numerical method that allows to study turbulent emulsion for very long times. The numerical method is based on a multi-component Lattice Boltzmann method based on the Shan-Chen model and supplemented with a large scale force to stir turbulence. A special treatment to limit mobility between different fluid components is introduced and validated. We demonstrate the potential of our approach in sustaining a turbulent emulsion over extremely long integration times (necessary to collect firm turbulence statistics) and we present first results on the probability distribution function of droplets' accelerations.

[1]  Geoffrey Ingram Taylor,et al.  The Viscosity of a Fluid Containing Small Drops of Another Fluid , 1932 .

[2]  Geoffrey Ingram Taylor,et al.  The formation of emulsions in definable fields of flow , 1934 .

[3]  J. Hinze.  Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes , 1955 .

[4]  Sauro Succi,et al.  Two-dimensional turbulence with the lattice Boltzmann equation , 1990 .

[5]  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.

[6]  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.

[7]  Xiaowen Shan,et al.  Multicomponent lattice-Boltzmann model with interparticle interaction , 1995, comp-gas/9503001.

[8]  Eberhard Bodenschatz,et al.  Lagrangian acceleration measurements at large Reynolds numbers , 1998 .

[9]  Haowen XiComer Duncan,et al.  Lattice Boltzmann simulations of three-dimensional single droplet deformation and breakup under simple shear flow , 1998, comp-gas/9807001.

[10]  D. Wolf-Gladrow.  Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction , 2000 .

[11]  G. Voth,et al.  Measurement of particle accelerations in fully developed turbulence , 2001, Journal of Fluid Mechanics.

[12]  J. Boon.  The Lattice Boltzmann Equation for Fluid Dynamics and Beyond , 2003 .

[13]  Li-Shi Luo,et al.  Lattice Boltzmann simulations of decaying homogeneous isotropic turbulence. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  John B. McLaughlin,et al.  SIMULATION OF BUBBLE BREAKUP DYNAMICS IN HOMOGENEOUS TURBULENCE , 2006 .

[15]  S Succi,et al.  Generalized lattice Boltzmann method with multirange pseudopotential. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Jos Derksen,et al.  MULTI-SCALE SIMULATIONS OF STIRRED LIQUID -- LIQUID DISPERSIONS , 2007 .

[17]  R. Benzi,et al.  Mesoscopic lattice Boltzmann modeling of soft-glassy systems: Theory and simulations , 2009, 0906.3611.

[18]  F. Toschi,et al.  Acceleration statistics of finite-sized particles in turbulent flow: the role of Faxén forces , 2008, Journal of Fluid Mechanics.

[19]  F. Toschi,et al.  Lagrangian Properties of Particles in Turbulence , 2009 .

[20]  Seiichiro Izawa,et al.  Lattice Boltzmann simulations of homogeneous isotropic turbulence , 2009, Comput. Math. Appl..