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 $\unicode[STIX]{x1D719}$ , we demonstrate that droplet breakup extracts kinetic energy from the larger scales while injecting energy into the smaller scales, increasingly with higher $\unicode[STIX]{x1D719}$ , 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 $We\approx 1$ . 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 (Garrettet 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 $E_{k}$ , enstrophy $\unicode[STIX]{x1D714}^{2}$ 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 $E_{k}$ are manifested in the evolution of $\unicode[STIX]{x1D714}^{2}$ and $N_{d}$ with a delay of ${\sim}0.3{\mathcal{T}}$ and ${\sim}0.9{\mathcal{T}}$ respectively (with ${\mathcal{T}}$ 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.

The aim of Magnetic Drug Targeting (MDT) is to concentrate drugs, attached to magnetic particles, in a specific part of the human body by applying a magnetic field. Computational simulations are performed of blood flow and magnetic particle motion in a left coronary artery and a carotid artery, using the properties of presently available magnetic carriers and strong superconducting magnets (up to B ≈ 2 T). For simple tube geometries it is deduced theoretically that the particle capture efficiency scales as \(\eta \sim \sqrt{{Mn}_{\rm p}}\), with Mn _p the characteristic ratio of the particle magnetization force and the drag force. This relation is found to hold quite well for the carotid artery. For the coronary artery, the presence of side branches and domain curvature causes deviations from this scaling rule, viz. η ∼ Mn ^β_p , with β > 1/2. The simulations demonstrate that approximately a quarter of the inserted 4 μm particles can be captured from the bloodstream of the left coronary artery, when the magnet is placed at a distance of 4.25 cm. When the same magnet is placed at a distance of 1 cm from a carotid artery, almost all of the inserted 4 μm particles are captured. The performed simulations, therefore, reveal significant potential for the application of MDT to the treatment of atherosclerosis.