Lattice Boltzmann simulations of droplet dynamics in time-dependent flows

TL;DR

This paper uses 3D lattice Boltzmann simulations to study droplet deformation and dynamics in time-dependent flows, assessing the limitations of analytical models and exploring phenomena like transparency transition under oscillating shear flows.

Contribution

It provides a mesoscale simulation framework to evaluate and extend existing analytical models of droplet behavior in dynamic flows, including effects of flow frequency and turbulence.

Findings

Droplet deformation depends on flow frequency and shear conditions.

Simulations reveal limitations of ellipsoidal shape assumptions in analytical models.

Potential for developing a DNS approach for small droplets in turbulent 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.