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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.

Water purification technologies such as microfiltration/ultrafiltration and reverse osmosis utilize porous membranes to remove suspended particles and solutes. These membranes, however, cause many drawbacks such as a high pumping cost and a need for periodic replacement due to fouling. Here we show an alternative membraneless method for separating suspended particles by exposing the colloidal suspension to CO2. Dissolution of CO2 into the suspension creates solute gradients that drive phoretic motion of particles. Due to the large diffusion potential generated by the dissociation of carbonic acid, colloidal particles move either away from or towards the gas–liquid interface depending on their surface charge. Using the directed motion of particles induced by exposure to CO2, we demonstrate a scalable, continuous flow, membraneless particle filtration process that exhibits low energy consumption, three orders of magnitude lower than conventional microfiltration/ultrafiltration processes, and is essentially free from fouling.