posted on 2019-10-10, 09:13authored bySiddhartha Mukherjee, Arman Safdari, Orest Shardt, Sasa Kenjere, Harry E.A. Van den Akker
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. 289–295)
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. 2163–2171; 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.