Numerical study of turbulent liquid‐liquid dispersions

Abstract

A numerical approach is developed to gain fundamental insight in liquid‐liquid dispersion formation under well‐controlled turbulent conditions. The approach is based on a free energy lattice Boltzmann equation method, and relies on detailed resolution of the interaction of the dispersed and continuous phase at the microscopic level, including drop breakup and coalescence. The capability of the numerical technique to perform direct numerical simulations of turbulently agitated liquid‐liquid dispersions is assessed. Three‐dimensional simulations are carried out in fully periodic cubic domains with grids of size . The liquids are of equal density. Viscosity ratios (dispersed phase over continuous phase) are in the range 0.3–1.0. The dispersed phase volume fraction varies from 0.001 to 0.2. The process of dispersion formation is followed and visualized. The size of each drop in the dispersion is measured in‐line with no disturbance of the flow. However, the numerical method is plagued by numerical dissolution of drops that are smaller than 10 times the lattice spacing. It is shown that to mitigate this effect it is necessary to increase the resolution of the Kolmogorov scales, such as to have a minimum drop size in the range 20–30 lattice units [lu]. Four levels of Kolmogorov length scale resolution have been considered , 2.5, 5, and 10 [lu]. In addition, the numerical dissolution reduces if the concentration of the dispersed phase is increased. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2618–2633, 2015

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

“…the Cahn number, an important criterion (Shardt et al 2013). The diffuse interface also leads to dissolution of small droplets as has been noted before (Perlekar et al 2012;Komrakova et al 2015a). We show that droplet dissolution can be limited to a minor effect in certain parameter ranges, and that a mass correction scheme as used in Biferale et al (2011);Perlekar et al (2012) is not requisite for simulating droplets in turbulence.…”

“…Upon increasing the liquid-liquid repulsion parameter G αβ (hence also changing the fluid composition and dimensionless numbers that include interfacial tension, like the Weber or Ohnesorge number) in case T5, we see that for the same turbulence intensity as case T4, φ/φ 0 remains stable. This reaffirms that, with the original PP-LB method, certain regions of the turbulent emulsions parameter space can be simulated properly, while in other cases (case T4 and to some degree also case T3) simulations may require additional numerical remedies like the mass correction scheme of Biferale et al (2011);Perlekar et al (2012) or an enhanced Kolmogorov scale resolution (to achieve higher Cahn numbers) as done by Komrakova et al (2015a). Figure 10 shows the evolution of the number of droplets for cases T1-T5 for varying turbulence forcing amplitudes (excluding case T4 where all the droplets eventually dissolve due to a relatively weaker inter-component repulsion).…”

“…The process of dispersion formation is investigated for varying volume fractions of the dispersed phase and varying turbulence intensities for an emulsion with a density and viscosity ratio of 1. Using an appropriate set of parameters (such that the pseudopotential repulsive force between components dominates the local turbulence force), the effect of droplet dissolution is mitigated, an issue that was found limiting in previous work (Perlekar et al 2012;Komrakova et al 2015a). While further maintaining spurious currents to well below the physical velocity scales, the multiphase kinetic energy spectra were shown to exhibit signatures of breakup and coalescence at wavenumbers smaller and larger than the inverse Hinze scale respectively.…”

“…The first issue, emphasized by Komrakova et al (2015a), is the utility of over-resolving Figure 11: Concentration spectrum and characteristic length characterizing the dispersion morphology for increasing turbulence intensity simulations, corresponding to cases T1-T5 in table 1. The structure factor S(k, t) was time averaged over 10 realizations separated by ≈ 50τ k , and further normalized by k S(k, t) to compare the relative difference in concentration at each wavelength.…”

“…This ensures that the energy density remains the same in these simulations, while larger droplet deformations (d ext ) can be resolved accurately. Successively increasing the domain size in this way allows separating N x from L. Note that doing this does not decrease Ch for droplets, as that would entail scaling L proportionally with N x while weakening the forcing amplitude such that Re λ remains constant and η is over-resolved (the approach of Komrakova et al (2015a)). We do not additionally pursue this as droplet dissolution is not significant in most of the parameter range considered in this study.…”