Droplet–turbulence interactions and quasi-equilibrium dynamics in turbulent emulsions

Abstract

We perform direct numerical simulations (DNSs) of emulsions in homogeneous, isotropic turbulence using a pseudopotential lattice-Boltzmann (PP-LB) method. Improving on previous literature by minimizing droplet dissolution and spurious currents, we show that the PP-LB technique is capable of long, stable simulations in certain parameter regions. Varying the dispersed phase volume fraction φ, we demonstrate that droplet breakup extracts kinetic energy from the larger scales while injecting energy into the smaller scales, increasingly with higher φ, with the Hinze scale dividing the two effects. Droplet size (d) distribution was found to follow the d −10/3 scaling (Deane & Stokes 2002). We show the need to maintain a separation of the turbulence forcing scale and domain size to prevent the formation of large connected regions of the dispersed phase. For the first time, we show that turbulent emulsions evolve into a quasi-equilibrium cycle of alternating coalescence and breakup dominated processes. Studying the system in its state-space comprising kinetic energy E k , enstrophy ω 2 and the droplet number density N d , we find that their dynamics resemble limit-cycles with a time delay. Extreme values in the evolution of E k manifest in the evolution of ω 2 and N d with a delay of ∼ 0.3T and ∼ 0.9T respectively (with T the large eddy timescale). Lastly, we also show that flow topology of turbulence in an emulsion is significantly more different than singlephase turbulence than previously thought. In particular, vortex compression and axial straining mechanisms become dominant in the droplet phase, a consequence of the elastic behaviour of droplet interfaces.

Effects of power-law entrainment on bubble fragmentation cascades

“…Bulk bubble-size distributions reasonably described by a power-law slope around β ≈ −10/3 for a > a H are observed during entrainment in a variety of air-entraining bubbly flows (Deane & Stokes 2002;Blenkinsopp & Chaplin 2010;Deane, Stokes & Callaghan 2016;Deike, Melville & Popinet 2016;Wang, Yang & Stern 2016;Yu et al 2020;Chan et al 2021). Droplet equilibrium distributions following a −10/3 power law have also been observed due to fragmentation and coalescence (without injection) at high void fractions (Skartlien, Sollum & Schumann 2013;Mukherjee et al 2019); however, it is not clear how the effect of coalescence is related to the entrainment we study here.…”

Turbulent Flows With Drops and Bubbles: What Numerical Simulations Can Tell Us—Freeman Scholar Lecture

“…The numerical simulation has been performed using a pseudo-potential lattice Boltzmann method. Adapted from Mukherjee et al [153].…”

Sub-Hinze scale bubble production in turbulent bubble break-up

“…The results were compared to Risso & Fabre (1998) in terms of deformation and confirmed the identification of a critical Weber number. More recently, Mukherjee et al (2019) used the lattice Boltzmann method to study droplet-turbulence interactions and quasi-equilibrium dynamics in turbulent emulsions. Rising deformable bubbles in turbulence have been studied by Loisy & Naso (2017) with a modified level-set method.…”