Droplet size distribution in homogeneous isotropic turbulence

Perlekar, Prasad; Biferale, Luca; Sbragaglia, Mauro; Srivastava, S Sudhir; Toschi, Federico

doi:10.1063/1.4719144

Cited by 80 publications

(108 citation statements)

References 19 publications

(23 reference statements)

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“…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.…”

Section: Our Studysupporting

confidence: 61%

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

Mukherjee

Safdari²,

Shardt³

et al. 2019

J. Fluid Mech.

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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.

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Section: Our Studysupporting

confidence: 61%

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

Mukherjee

Safdari²,

Shardt³

et al. 2019

J. Fluid Mech.

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“…This behavior has been attributed by other authors to limited grid resolution that cannot necessarily accommodate the full size range of the smaller daughter-droplets that result from breakup. 14 Somewhat larger breakup products are generated in the simulations, and this leads to an overestimation of the DSD for the smaller droplets sizes below the average diameter. We discuss the consequences of this effect in Sec.…”

Section: Variations With Input Energymentioning

confidence: 99%

“…A stochastic force was added to the (lattice) Boltzmann equation using an established method, [11][12][13] and it was implemented such that the turbulence remained isotropic and with constant energy over time. 12,13 Derksen and Van Den Akker 11 and Perlekar et al 14 used the same approach in two fluid LBM (Lattice Boltzmann Method) simulations of emulsions without surfactant, to study the droplet size distribution. The same forcing scheme was adopted in our lattice Boltzmann method that also incorporates soluble surfactant.…”

Section: Introductionmentioning

confidence: 99%

Droplet size distributions in turbulent emulsions: Breakup criteria and surfactant effects from direct numerical simulations

Skartlien

Sollum

Schümann

2013

The Journal of Chemical Physics

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Lattice Boltzmann simulations of water-in-oil (W/O) type emulsions of moderate viscosity ratio (≃1/3) and with oil soluble amphiphilic surfactant were used to study the droplet size distribution in forced, steady, homogeneous turbulence, at a water volume fraction of 20%. The viscous stresses internal to the droplets were comparable to the interfacial stress (interfacial tension), and the droplet size distribution (DSD) equilibrated near the Kolmogorov scale with droplet populations in both the viscous and inertial subranges. These results were consistent with known breakup criteria for W/O and oil-in-water emulsions, showing that the maximum stable droplet diameter is proportional to the Kolmogorov scale when viscous stresses are important (in contrast to the inviscid Hinze-limit where energy loss by viscous deformation in the droplet is negligible). The droplet size distribution in the inertial subrange scaled with the known power law ~d(-10/3), as a consequence of breakup by turbulent stress fluctuations external to the droplets. When the turbulent kinetic energy was sufficiently large (with interfacial Péclet numbers above unity), we found that turbulence driven redistribution of surfactant on the interface inhibited the Marangoni effect that is otherwise induced by film draining during coalescence in more quiescent flow. The coalescence rates were therefore not sensitive to varying surfactant activity in the range we considered, and for the given turbulent kinetic energies. Furthermore, internal viscous stresses strongly influenced the breakup rates. These two effects resulted in a DSD that was insensitive to varying surfactant activity.

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“…external forcing is applied, and the emergent characteristic length scale of blob size is consistent with the Hinze scale: L H ∼ ( ρ σ ) −3/5 ϵ −2/5 where ρ is density, σ is surface tension, and ϵ is the energy dissipation rate per unit mass [23,24]. In the inverse energy cascade regime of the 2D CHNS system, the characteristic length scale is also consistent with the Hinze scale [25].…”

Section: -2mentioning

confidence: 66%

Cascades and spectra of a turbulent spinodal decomposition in two-dimensional symmetric binary liquid mixtures

et al. 2016

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We study the fundamental physics of cascades and spectra in two-dimensional (2D) Cahn-Hilliard-Navier-Stokes (CHNS) turbulence, and compare and contrast this system with 2D magnetohydrodynamic (MHD) turbulence. The important similarities include basic equations, ideal quadratic invariants, cascades, and the role of linear elastic waves. Surface tension induces elasticity, and the balance between surface tension energy and turbulent kinetic energy determines a length scale (Hinze scale) of the system. The Hinze scale may be thought of as the scale of emergent critical balance between fluid straining and elastic restoring forces. The scales between the Hinze scale and dissipation scale constitute the elastic range of the 2D CHNS system. By direct numerical simulation, we find that in the elastic range, the mean square concentration spectrum H ψ k of the 2D CHNS system exhibits the same power law (−7/3) as the mean square magnetic potential spectrum H A k in the inverse cascade regime of 2D MHD. This power law is consistent with an inverse cascade of H ψ , which is observed. The kinetic energy spectrum of the 2D CHNS system is E K k ∼ k −3 if forced at large scale, suggestive of the direct enstrophy cascade power law of 2D Navier-Stokes turbulence. The difference from the energy spectra of 2D MHD turbulence implies that the back reaction of the concentration field to fluid motion is limited. We suggest this is because the surface tension back reaction is significant only in the interfacial regions. The interfacial regions fill only a small portion of the 2D CHNS system, and their interface packing fraction is much smaller than that for 2D MHD.

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Droplet size distribution in homogeneous isotropic turbulence

Cited by 80 publications

References 19 publications

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

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

Droplet size distributions in turbulent emulsions: Breakup criteria and surfactant effects from direct numerical simulations

Cascades and spectra of a turbulent spinodal decomposition in two-dimensional symmetric binary liquid mixtures

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