Turbulence and its organization, long conceptualized in terms of "coherent structures,"has resisted clear description. A significant limitation has been the lack of tools to identify instantaneous, spatially finite structures, while unraveling their superposition. We present a framework of generalized correlations, which can be used to readily define a variety of correlation measures, aimed at identifying field patterns. Coupled with Helmholtz-decomposition, this provides a paradigm to identify and disentangle structures. We demonstrate the correlations using vortex-based canonical flows and then apply them to incompressible, homogeneous, isotropic turbulence. We find that high turbulence kinetic energy (Ek) regions form compact velocity-jets that are spatially exclusive from high enstrophy (ω 2) regions that form vorticity-jets surrounded by swirling velocity. The correlation fields reveal that the energetic structures in turbulence, being invariably jets, are distinct from those in vortex-based canonical flows, where they can be jet-like as well as swirling. A full Biot-Savart decomposition of the velocity field shows that the velocity-jets are neither self-induced, nor induced by the interaction of swirling, strong vorticity regions, and are almost entirely induced, non-locally, by the permeating intermediate range (rms level) vorticity. Velocity-swirls, instead, are a superposition of self-induced and background-induced velocity. Interestingly, it is the mild intermediate vorticity that dominantly induces the velocity-field everywhere. This suggests that turbulence organization could result from non-local and non-linear field interactions, leading to an emergent description unlike the notion of a strict structural hierarchy. Our correlation-decomposition framework lends itself readily to the study of generic vector and scalar fields associated with diverse phenomena.

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 inertial range scaling and where coalescence becomes dominant. This is done using the Weber number spectrum , constructed from the multiphase kinetic energy spectrum , which indicates the critical droplet scale at which . This scale roughly separates coalescence and breakup dynamics as it closely corresponds to the transition of the droplet size distribution into a 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 , enstrophy and the droplet number density , we find that their dynamics resemble limit cycles with a time delay. Extreme values in the evolution of are manifested in the evolution of and with a delay of and respectively (with 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.

We present a pseudopotential lattice Boltzmann method to simulate liquid–liquid emulsions with a slightly soluble surfactant. The model is investigated in 2-D, over a wide parameter space for a single, stationary, immiscible droplet, and surface tension reduction by up to 15% is described in terms of a surfactant strength Λ (which roughly follows a Langmuir isotherm). The basic surfactant model is shown to be insufficient for arresting phase segregation—which is then achieved by changing the liquid–liquid interaction strength locally as a function of the surfactant density. 3-D spinodal decomposition (phase separation) is simulated, where the surfactant is seen to adapt rapidly to the evolving interfaces. Finally, for pendent droplet formation in an immiscible liquid, the addition of surfactant is shown to alter the droplet-size distribution and dynamics of newly formed droplets.

While various multiphase flow simulation techniques have found acceptance as predictive tools for processes involving immiscible fluids, none of them can be considered universally applicable. Focusing on accurate simulation of liquid-liquid emulsions at the scale of droplets, we present a comparative assessment of the single-component multiphase pseudopotential lattice Boltzmann method (PP-LB, classical and modified) and the Volume of Fluid method (VOF, classical and modified), highlighting particular strengths and weaknesses of these techniques. We show that a modified LB model produces spurious velocities 1–3 orders of magnitude lower than all VOF models tested, and find that LB is roughly 10 times faster in computation time, while VOF is more versatile. Simulating falling liquid droplets, a realistic problem, we find that despite identical setups, results can vary with the technique in certain flow regimes. At lower Reynolds numbers, all methods agree reasonably well with experimental values. At higher Reynolds numbers, all methods underpredict the droplet Reynolds number, while being in good agreement with each other. Particular issues regarding LB simulations at low density ratio are emphasized. Finally, we conclude with the applicability of VOF vis-à-vis PP-LB for a general range of multiphase flow problems relevant to myriad applications.