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Droplet-turbulence interactions and quasi-equilibrium dynamics in turbulent emulsions
Date
2019
Abstract
We perform direct numerical simulations (DNS) 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 , we demonstrate that droplet breakup extracts kinetic energy from the larger scales while injecting energy into the smaller scales, increasingly with higher , with approximately the Hinze scale (Hinze, AIChE J., vol. 1 (3), 1955, pp. 289â 295) separating the two effects. A generalization of the Hinze scale is proposed, which applies both to dense and dilute suspensions, including cases where there is a deviation from the k-5/3 inertial range scaling and where coalescence becomes dominant. This is done using the Weber number spectrum We.k/, constructed from the multiphase kinetic energy spectrum E.k/, which indicates the critical droplet scale at which We 1. This scale roughly separates coalescence and breakup dynamics as it closely corresponds to the transition of the droplet size (d) distribution into a d-10/3 scaling (Garrett et al., J. Phys. Oceanogr., vol. 30 (9), 2000, pp. 2163â 2171; Deane & Stokes, Nature, vol. 418 (6900), 2002, p. 839). 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 Ek, enstrophy !2 and the droplet number density Nd, we find that their dynamics resemble limit cycles with a time delay. Extreme values in the evolution of Ek are manifested in the evolution of !2 and Nd 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 from single-phase turbulence than previously thought. In particular, vortex compression and axial straining mechanisms increase in the droplet phase.
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Description
peer-reviewed
Publisher
Cambridge University Press
Citation
Journal of Fluid Mechechanics;878, pp. 221-276
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Safdari_2019_Droplet.pdf
Adobe PDF, 1.88 MB
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Funding Information
Sustainable Process Technology