Deformation of drops by outer eddies in turbulence

Drop deformation in fluid flows is investigated as an exchange between the kinetic energy of the fluid and the surface energy of the drop. We show analytically that this energetic exchange is controlled only by the stretching (or compression) of the drop surface by the rate-of-strain tensor. This mechanism is analogous to the stretching of the vorticity field in turbulence. By leveraging the non-local nature of turbulence dynamics, we introduce a new decomposition that isolates the energetic exchange arising from local drop-induced surface effects from the non-local action of turbulent fluctuations. We perform direct numerical simulations of single inertial drops in isotropic turbulence and show that an important contribution to the increments of the surface energy arises from the non-local stretching of the fluid–fluid interface by eddies far from the drop surface (outer eddies). We report that this mechanism is dominant and independent of surface dynamics in a range of Weber numbers in which drop breakup occurs. These findings shed new light on drop deformation and breakup in turbulent flows, and opens the possibility for the improvement and simplification of breakup models.

Toward a theory of the evolution of drop morphology and splintering by freezing

The drop freezing process is described by a phase-field model. Two cases are considered: when the freezing is triggered by central nucleation and when nucleation occurs on the drop surface. Depending on the environmental temperature and drop size, different morphological structures develop. Detailed dendritic growth was simulated at the first stage of drop freezing. Independent of the nucleation location, a decrease in temperature within the range from ~ −5 to −25°C led to an increase in the number of dendrites and a decrease in their width and the interdendritic space. At temperatures lower than about −25°C, a planar front developed following surface nucleation, while dendrites formed a granular-like structure with small interdendritic distances following bulk nucleation. An ice shell grew in at the same time (but slower) as dendrites following surface nucleation, while it started forming once the dendrites have reached the drop surface in the case of central nucleation. The formed ice morphology at the first freezing stage predefined the splintering probability. We assume that stresses needed to break the ice shell arose from freezing of the water in the interdendritic spaces. Under this assumption, the number of possible splinters/fragments was proportional to the number of dendrites, and the maximum rate of splintering/fragmentation occurred within a temperature range of about −10 °C to −20°C, in agreement with available laboratory and in situ measurements. At temperatures < −25°C, freezing did not lead to the formation of significant stresses, making splintering unlikely. The number of dendrites increased with drop size, causing a corresponding increase in the number of splinters. Examples of morphology that favors drop cracking are presented, and the duration of the freezing stages is evaluated. Sensitivity of the freezing process to the surface fluxes is discussed.

Fluid separation and network deformation in wetting of soft and swollen surfaces

When a water drop is placed onto a soft polymer network, a wetting ridge develops at the drop periphery. The height of this wetting ridge is typically governed by the drop surface tension balanced by elastic restoring forces of the polymer network. However, the situation is more complex when the network is swollen with fluid, because the fluid may separate from the network at the contact line. Here we study the fluid separation and network deformation at the contact line of a soft polydimethylsiloxane (PDMS) network, swollen with silicone oil. By controlling both the degrees of crosslinking and swelling, we find that more fluid separates from the network with increasing swelling. Above a certain swelling, network deformation decreases while fluid separation increases, demonstrating synergy between network deformation and fluid separation. When the PDMS network is swollen with a fluid having a negative spreading parameter, such as hexadecane, no fluid separation is observed. A simple balance of interfacial, elastic, and mixing energies can describe this fluid separation behavior. Our results reveal that a swelling fluid, commonly found in soft networks, plays a critical role in a wetting ridge.

The Delay in Cavity Formation in the Intrusive Mode of Coalescence of a Freely Falling Drop with a Target Liquid

The dynamics of a cavity formed in the intrusive mode of coalescence of a freely falling drop flowing smoothly into a liquid have been traced for the first time by the methods of photo and video registration. The cavity begins to form when the bottom part of the drop submerges, when the fluid coalescence line contracts to the center of the flow, and, simultaneously with the annihilation of the drop surface, the surface of the target liquid is restored. In this case, the orientation of ligaments (thin trickles), formed in the vicinity of the contact line changes. At the initial phase, they are directed outward and distribute the transmitted momentum and energy of the drop over the entire surface of the intrusion. Retraction of the coalescence line holds the transmitted energy and momentum of the drop in the contact patch. If the kinetic energy of the falling drop noticeably exceeds the potential surface energy, the cavity begins to form at the initial contact of the fluids and deepens in the course of the entire coalescence process, capturing the drop matter.

Direct Numerical Simulation of Water Droplets in Turbulent Flow

Details on the fall speeds of raindrops are essential in both applications and natural events, such as rain-rate retrieval and soil erosion. Here, we examine the influence of turbulence on the terminal velocity of two water drops of different sizes. For the first time, computations of droplets in turbulent surroundings are conducted with a direct numerical simulation code based on a volume of fluid method. Both the drop surface deformation and internal circulation are captured. The turbulence intensity at the inflow area, as well as the turbulence length scale are varied. In turbulent flow, we find a decline in the terminal velocities for both drops. Based on the study of the wake flow characteristics and drop surface deformation, the decrease in the terminal velocity is found to be directly linked to a shortening of the wake recirculation region resulting from an earlier and more drastic increase in the turbulence kinetic energy in the shear layer. The turbulent surroundings trigger substantial rises in the drop axis ratio amplitude and a slight increase in the drop oscillation frequency, but barely influence the time-averaged drop axis length.

Electrorheology of a dilute emulsion of surfactant-covered drops

We investigate the effects of surfactant coating on a deformable viscous drop under the combined action of shear flow and a uniform electric field. Employing a comprehensive three-dimensional approach, we analyse the non-Newtonian shearing response of the bulk emulsion in the dilute suspension regime. Our results reveal that the location of the peak surfactant accumulation on the drop surface may get shifted from the plane of shear to a plane orthogonal to it, depending on the tilt angle of the applied electric field and strength of the electrical stresses relative to their hydrodynamic counterparts. The surfactant non-uniformity creates significant alterations in the flow perturbation around the drop, triggering modulations in the bulk shear viscosity. Overall, the shear-thinning or shear-thickening behaviour of the emulsion appears to be greatly influenced by the interplay of surface charge convection and Marangoni stresses. We show that the balance between electrical and hydrodynamic stresses renders a vanishing surface tension gradient on the drop surface for some specific shear rates, rendering negligible alterations in the bulk viscosity. This critical condition largely depends on the electrical permittivity and conductivity ratios of the two fluids and orientation of the applied electric field. Also, the physical mechanisms of charge convection and surface deformation play their roles in determining this critical shear rate. As a consequence, we obtain new discriminating factors, involving electrical property ratios and the electric field configuration, which govern the same. Consequently, the surfactant-induced enhancement or attenuation of the bulk emulsion viscosity depends on the electrical conductivity and permittivity ratios. The concerned description of the drop-level flow physics and its connection to the bulk rheology of a dilute emulsion may provide a fundamental understanding of a more complex emulsion system encountered in industrial practice.

Influence of pressure-dependent surface viscosity on dynamics of surfactant-laden drops in shear flow

We study numerically the dynamics of an insoluble surfactant-laden droplet in a simple shear flow taking surface viscosity into account. The rheology of drop surface is modelled via a Boussinesq–Scriven constitutive law with both surface tension and surface viscosity depending strongly on the surface concentration of the surfactant. Our results show that the surface viscosity exhibits non-trivial effects on the surfactant transport on the deforming drop surface. Specifically, both dilatational and shear surface viscosity tend to eliminate the non-uniformity of surfactant concentration over the drop surface. However, their underlying mechanisms are entirely different; that is, the shear surface viscosity inhibits local convection due to its suppression on drop surface motion, while the dilatational surface viscosity inhibits local dilution due to its suppression on local surface dilatation. By comparing with previous studies of droplets with surface viscosity but with no surfactant transport, we find that the coupling between surface viscosity and surfactant transport induces non-negligible deviations in the dynamics of the whole droplet. More particularly, we demonstrate that the dependence of surface viscosity on local surfactant concentration has remarkable influences on the drop deformation. Besides, we analyse the full three-dimensional shape of surfactant-laden droplets in simple shear flow and observe that the drop shape can be approximated as an ellipsoid. More importantly, this ellipsoidal shape can be described by a standard ellipsoidal equation with only one unknown owing to the finding of an unexpected relationship among the drop’s three principal axes. Moreover, this relationship remains the same for both clean and surfactant-laden droplets with or without surface viscosity.