Lattice Boltzmann simulations of droplet dynamics in time-dependent flows

Abstract

We study the deformation and dynamics of droplets in time-dependent flows using 3D numerical simulations of two immiscible fluids based on the lattice Boltzmann model (LBM). Analytical models are available in the literature, which assume the droplet shape to be an ellipsoid at all times (P.L. Maffettone, M. Minale, J. Non-Newton. Fluid Mech 78, 227 (1998); M. Minale, Rheol. Acta 47, 667 (2008)). Beyond the practical importance of using a mesoscale simulation to assess "ab-initio" the robustness and limitations of such theoretical models, our simulations are also key to discuss -in controlled situations -some relevant phenomenology related to the interplay between the flow time scales and the droplet time scales regarding the "transparency" transition for high enough shear frequencies for an external oscillating flow. This work may be regarded as a step forward to discuss extensions towards a novel DNS approach, describing the mesoscale physics of small droplets subjected to a generic hydrodynamical strain field, possibly mimicking the effect of a realistic turbulent flow on dilute droplet suspensions.

Droplets in isotropic turbulence: deformation and breakup statistics

“…It would also be interesting to understand possible intermittency effects for such sub-Kolmogorov scale droplets (Biferale, Meneveau & Verzicco 2014) (and also studied for larger droplets (Perlekar et al 2012)) and if there are analogues of transparency effects, seen in oscillatory, laminar flows (Milan et al 2018) for droplets in fully developed turbulence.…”

Sub-Kolmogorov droplet dynamics in isotropic turbulence using a multiscale lattice Boltzmann scheme

“…Our numerical method can be seen as a novel hybrid approach to the sub-Kolmogorov droplet dynamics: The simulation domain can be of the same order as the droplet's size, see section 4, but should be ideally much larger than the droplet radius R, see section 5. The surrounding turbulent flow is used as an input via an open boundary condi-tion method [1], similar to the setups in [50,53]. This enables us to study the deformation and breakup behaviour of a sub-Kolmogorov droplet in fully developed isotropic turbulence, which we can compare to the results obtained via the widely used MM-model.…”

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The deformation and dynamics of a single droplet in isotropic turbulence is studied using a Lattice Boltzmann diffuse interface model involving exact boundary flow conditions [1] to allow for the creation of an external turbulent flow. We focus on a small, sub-Kolmogorov droplet, whose scale is much smaller than the Kolmogorov length scale of the turbulent flow.

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A lattice Boltzmann study of particle settling in a fluctuating multicomponent fluid under confinement

“…Among all mesoscale methods, we are interested in the lattice Boltzmann models (LBM). Over the last decades, LBM have been successfully used to model complex hydrodynamic phenomena at large scales, such as particle suspensions [ 4 , 13 , 14 ], non-ideal fluids with phase transition and/or phase segregation [ 15 – 20 ], polymer flows [ 21 – 23 ], active matter [ 24 ] just to cite some prominent examples. Especially in the last decade, there has been a boost to push the applicability of LBM simulations toward nano-scales via the inclusion of thermal fluctuations [ 25 – 29 , 31 ], designing the so-called fluctuating lattice Boltzmann methodology (FLBM).…”