Rebound of self-lubricating compound drops

Drop impact on solid surfaces is encountered in numerous natural and technological processes. Although the impact of single-phase drops has been widely explored, the impact of compound drops has received little attention. Here, we demonstrate a self-lubrication mechanism for water-in-oil compound drops impacting on a solid surface. Unexpectedly, the core water drop rebounds from the surface below a threshold impact velocity, irrespective of the substrate wettability. This is interpreted as the result of lubrication from the oil shell that prevents contact between the water core and the solid surface. We combine side and bottom view high-speed imaging to demonstrate the correlation between the water core rebound and the oil layer stability. A theoretical model is developed to explain the observed effect of compound drop geometry. This work sets the ground for precise complex drop deposition, with a strong impact on two- and three-dimensional printing technologies and liquid separation.

A Preliminary Model for the Migration of Sulfide Droplets in a Magmatic Conduit and the Significance of Volatiles

A close relationship between Ni–Cu–(PGE) sulfide deposits and magmatic conduit systems has been widely accepted, but our present understanding still rests on empirical inductions that sulfide liquids are entrained during magma ascent and aggregated at hydrodynamic traps such as the opening of a conduit into a larger magma body. In this contribution, a preliminary quantitative model for the dynamics of mm-scale sulfide droplets in a vertical magmatic conduit is developed, examining such limiting parameters as the size, transport velocity and the magmas’ maximum carrying capacity for sulfide droplets. Addition of numerous dense sulfide droplets significantly reduces magma buoyancy and rapidly increases the bulk viscosity, and the resulting pressure gradient in the propagating conduit dyke restricts the maximum volume fraction of droplets that can be carried by ascending magma. For sulfide droplets alone, the maximum carrying capacity is low, but it will be improved dramatically by the addition of volatiles which reduces the density and viscosity of silicate melt. Potential volatile degassing during decompression further facilitates sulfide entrainment by reducing bulk magma density, and the formation of buoyant compound vapour-sulfide liquid bubble drops also greatly enhances the carrying capacity. The breakdown of compound drops by detachment of parts of the vapour bubble or sulfide droplet may occur at low pressure, which liberates sulfide liquids from rising compound drops, potentially to collect in traps in the conduit system. When sulfide-laden magma flows through a widening conduit, many droplets can be captured by the re-circulation flow just downstream of the expanding section, followed by sulfide liquid accumulation and enhanced chemical interaction via diffusive exchange with the recirculating magma, potentially resulting in an economic, high-tonnage ore body. We apply our models to the emplacement of sulfide-rich magmatic suspensions at Noril’sk and show that the disseminated mineralization in intrusions could have formed when magmas carrying re-suspended sulfide liquid entrained from pre-existing sulfide accumulations in the conduit system reached their limiting sulfide carrying capacity as dictated by buoyancy and were deflected into blind sills flanking the principal conduit for flood basalt volcanism.

Formation and Breakup of an Immiscible Compound Jet with Density or Viscosity Stratification

Formation of compound drops by breakup of an axisymmetric compound jet injected from a coaxial nozzle into another immiscible coflowing fluid, at various density and viscosity ratios, is numerically investigated. The fluids are assumed to be Newtonian and incompressible and gravity is neglected for simplicity. A Finite Difference Method with Front Tracking is used to track the evolution and breakup of the compound jet. The outcomes of our numerical results show how density and viscosity ratios affect the compound jet’s transition from dripping to jetting mode. The density ratios of inner-to-outer and intermediate-to-outer fluids affect compound jet breakup length, drop diameter and drop formation time more than comparable viscosity ratios. At high density and viscosity ratios, due to high inertia and viscous force respectively, the drop formation is more chaotic and mostly multi-core drops are formed.

On the maximal spreading of impacting compound drops

We numerically study the impact of a compound drop on a hydrophobic substrate using a ternary-fluid diffuse-interface method, aiming to understand how the presence of the inner droplet affects the spreading dynamics and maximal spreading of the compound drop. First, it is interesting to see that the numerical results for an impacting pure drop agree well with the universal rescaling of maximal spreading ratio proposed by Lee et al. (J. Fluid Mech., vol. 786, 2016, R4). Second, two flow regimes have been identified for an impacting compound drop: namely jammed spreading and joint rim formation. The maximal spreading ratio of the compound drop is found to depend on the volume fraction of the inner droplet $\unicode[STIX]{x1D6FC}$, the surface tension ratio $\unicode[STIX]{x1D6FE}$, the Weber number and the flow regime. Moreover, we propose a universal rescaling of maximal spreading ratio for compound drops, by integrating the one for pure drops with a corrected Weber number that takes $\unicode[STIX]{x1D6FC}$, $\unicode[STIX]{x1D6FE}$ and the flow regime into account. The predictions of the universal rescaling are in good agreement with the numerical results for impacting compound drops.

Effect of surfactant on motion and deformation of compound droplets in arbitrary unbounded Stokes flows

This study deals with the motion and deformation of a compound drop system, subject to arbitrary but Stokesian far-field flow conditions, in the presence of bulk-insoluble surfactants. We derive solutions for fluid velocities and the resulting surfactant concentrations, assuming the capillary number and surface Péclet number to be small, as compared with unity. We first focus on a concentric drop configuration and apply Lamb’s general solution, assuming the far-field flow to be arbitrary in nature. As representative case studies, we consider two cases: (i) flow dynamics in linear flows and (ii) flow dynamics in a Poiseuille flow, although for the latter case, the concentric configuration does not remain valid in general. We further look into the effective viscosity of a dilute suspension of compound drops, subject to linear ambient flow, and compare our predictions with previously reported experiments. Subsequently, the eccentric drop configuration is addressed by using a bipolar coordinate system where the far-field flow is assumed to be axisymmetric but otherwise arbitrary in nature. As a specific example for eccentric drop dynamics, we focus on Poiseuille flow and study the drop migration velocities. Our analysis shows that the presence of surfactant generally opposes the imposed flows, thereby acting like an effective augmented viscosity. Our analysis reveals that maximizing the effects of surfactant makes the drops behave like solid particles suspended in a medium. However, in uniaxial extensional flow, the presence of surfactants on the inner drop, in conjunction with the drop radius ratio, leads to a host of interesting and non-monotonic behaviours for the interface deformation. For eccentric drops, the effect of eccentricity only becomes noticeable after it surpasses a certain critical value, and becomes most prominent when the two interfaces approach each other. We further depict that surfactant and eccentricity generally tend to suppress each other’s effects on the droplet migration velocities.