## Simulations of Droplet Coalescence in Simple Shear Flow

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posted on 28.05.2013, 00:00 by Orest Shardt, J. J. Derksen, Sushanta
K. MitraSimulating
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 (Péclet number) also influences the conditions
for coalescence: coalescence occurs at higher capillary numbers with
lower Péclet 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 (≈10 μm) and lower viscosities (≈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 Péclet number that should be used for predictive simulations of coalescence phenomena.