### Abstract

Simulating droplet coalescence is challenging because small-scale (tens of nanometers) phenomena determine the behavior of much larger (micrometer- to millimeter-scale) droplets. In general, Liquid droplets colliding in a liquid medium coalesce when the capillary number is less than a critical value. We present simulations of droplet collisions and coalescence in simple shear flow using the free-energy binary-liquid lattice Boltzmann method. In previous simulations of low-speed collisions, droplets coalesced at unrealistically high capillary numbers. Simulations of noncoalescing droplets have not been reported, and therefore, the critical capillary number for simulated collisions was unknown. By simulating droplets with radii up to 100 lattice nodes, we determine the critical capillary number for coalescence and quantify the effects of several numerical and geometric parameters. The simulations were performed with a well-resolved interface, a Reynolds number of one, and capillary numbers from 0.01 to 0.2. The ratio of the droplet radius and interface thickness has the greatest effect on the critical capillary number. As in experiments, the critical capillary number decreases with increasing droplet size. A second numerical parameter, the interface diffusivity (Peclet number) also influences the conditions for coalescence: coalescence occurs at higher capillary numbers with lower Peclet numbers (higher diffusivity). The effects of the vertical offset between the droplets and the confinement of the droplets were also studied. Physically reasonable results were obtained and provide insight into the conditions for coalescence. Simulations that match the conditions of experiments reported in the literature remain computationally impractical. However, the scale of the simulations is now sufficiently large that a comparison with experiments involving smaller droplets (approximate to 10 mu m) and lower viscosities (approximate to 10(-6) m(2)/s, the viscosity of water) may be possible. Experiments at these conditions are therefore needed to determine the interface thickness and Pedet number that should be used for predictive slmulations of coalescence phenomena.

Original language | English |
---|---|

Pages (from-to) | 6201-6212 |

Number of pages | 12 |

Journal | Langmuir |

Volume | 29 |

Issue number | 21 |

Early online date | 3 May 2013 |

DOIs | |

Publication status | Published - 28 May 2013 |

### Keywords

- LATTICE-BOLTZMANN METHOD
- INCOMPRESSIBLE 2-PHASE FLOWS
- 2-DIMENSIONAL LINEAR FLOW
- EQUAL-SIZED DROPS
- NUMERICAL SIMULATIONS
- IMMISCIBLE FLUIDS
- DEFORMABLE DROPS
- COMPLEX FLOWS
- MODEL
- COLLISION

### Cite this

*Langmuir*,

*29*(21), 6201-6212. https://doi.org/10.1021/la304919p

**Simulations of Droplet Coalescence in Simple Shear Flow.** / Shardt, Orest; Derksen, J. J.; Mita, Sushanta K.

Research output: Contribution to journal › Article

*Langmuir*, vol. 29, no. 21, pp. 6201-6212. https://doi.org/10.1021/la304919p

}

TY - JOUR

T1 - Simulations of Droplet Coalescence in Simple Shear Flow

AU - Shardt, Orest

AU - Derksen, J. J.

AU - Mita, Sushanta K.

N1 - ACKNOWLEDGMENTS This research was enabled by the use of computing resources provided by WestGrid and Compute/Calcul Canada. O.S. is supported by an Alexander Graham Bell Canada Graduate Scholarship from NSERC.

PY - 2013/5/28

Y1 - 2013/5/28

N2 - Simulating droplet coalescence is challenging because small-scale (tens of nanometers) phenomena determine the behavior of much larger (micrometer- to millimeter-scale) droplets. In general, Liquid droplets colliding in a liquid medium coalesce when the capillary number is less than a critical value. We present simulations of droplet collisions and coalescence in simple shear flow using the free-energy binary-liquid lattice Boltzmann method. In previous simulations of low-speed collisions, droplets coalesced at unrealistically high capillary numbers. Simulations of noncoalescing droplets have not been reported, and therefore, the critical capillary number for simulated collisions was unknown. By simulating droplets with radii up to 100 lattice nodes, we determine the critical capillary number for coalescence and quantify the effects of several numerical and geometric parameters. The simulations were performed with a well-resolved interface, a Reynolds number of one, and capillary numbers from 0.01 to 0.2. The ratio of the droplet radius and interface thickness has the greatest effect on the critical capillary number. As in experiments, the critical capillary number decreases with increasing droplet size. A second numerical parameter, the interface diffusivity (Peclet number) also influences the conditions for coalescence: coalescence occurs at higher capillary numbers with lower Peclet numbers (higher diffusivity). The effects of the vertical offset between the droplets and the confinement of the droplets were also studied. Physically reasonable results were obtained and provide insight into the conditions for coalescence. Simulations that match the conditions of experiments reported in the literature remain computationally impractical. However, the scale of the simulations is now sufficiently large that a comparison with experiments involving smaller droplets (approximate to 10 mu m) and lower viscosities (approximate to 10(-6) m(2)/s, the viscosity of water) may be possible. Experiments at these conditions are therefore needed to determine the interface thickness and Pedet number that should be used for predictive slmulations of coalescence phenomena.

AB - Simulating droplet coalescence is challenging because small-scale (tens of nanometers) phenomena determine the behavior of much larger (micrometer- to millimeter-scale) droplets. In general, Liquid droplets colliding in a liquid medium coalesce when the capillary number is less than a critical value. We present simulations of droplet collisions and coalescence in simple shear flow using the free-energy binary-liquid lattice Boltzmann method. In previous simulations of low-speed collisions, droplets coalesced at unrealistically high capillary numbers. Simulations of noncoalescing droplets have not been reported, and therefore, the critical capillary number for simulated collisions was unknown. By simulating droplets with radii up to 100 lattice nodes, we determine the critical capillary number for coalescence and quantify the effects of several numerical and geometric parameters. The simulations were performed with a well-resolved interface, a Reynolds number of one, and capillary numbers from 0.01 to 0.2. The ratio of the droplet radius and interface thickness has the greatest effect on the critical capillary number. As in experiments, the critical capillary number decreases with increasing droplet size. A second numerical parameter, the interface diffusivity (Peclet number) also influences the conditions for coalescence: coalescence occurs at higher capillary numbers with lower Peclet numbers (higher diffusivity). The effects of the vertical offset between the droplets and the confinement of the droplets were also studied. Physically reasonable results were obtained and provide insight into the conditions for coalescence. Simulations that match the conditions of experiments reported in the literature remain computationally impractical. However, the scale of the simulations is now sufficiently large that a comparison with experiments involving smaller droplets (approximate to 10 mu m) and lower viscosities (approximate to 10(-6) m(2)/s, the viscosity of water) may be possible. Experiments at these conditions are therefore needed to determine the interface thickness and Pedet number that should be used for predictive slmulations of coalescence phenomena.

KW - LATTICE-BOLTZMANN METHOD

KW - INCOMPRESSIBLE 2-PHASE FLOWS

KW - 2-DIMENSIONAL LINEAR FLOW

KW - EQUAL-SIZED DROPS

KW - NUMERICAL SIMULATIONS

KW - IMMISCIBLE FLUIDS

KW - DEFORMABLE DROPS

KW - COMPLEX FLOWS

KW - MODEL

KW - COLLISION

U2 - 10.1021/la304919p

DO - 10.1021/la304919p

M3 - Article

VL - 29

SP - 6201

EP - 6212

JO - Langmuir

JF - Langmuir

SN - 0743-7463

IS - 21

ER -