Shape relaxation of an elongated viscous drop

Singular jets during droplet impact on superhydrophobic surfaces

HYPOTHESIS

The impact of droplets is prevalent in numerous applications, and jetting during droplet impact is a critical process controlling the dispersal and transport of liquid. New jetting dynamics are expected in different conditions of droplet impact on super-hydrophobic surfaces, such as new jetting phenomena, mechanisms, and regimes.

EXPERIMENTS

In this experimental study of droplet impact on super-hydrophobic surfaces, the Weber number and the Ohnesorge number are varied in a wide range, and the impact process is analyzed theoretically.

FINDINGS

We identify a new type of singular jets, i.e., singular jets induced by horizontal inertia (HI singular jets), besides the previously studied singular jets induced by capillary deformation (CD singular jets). For CD singular jets, the formation of the cavity is due to the propagation of capillary waves on the droplet surface; while for HI singular jets, the cavity formation is due to the large horizontal inertia of the toroidal edge during the retraction of the droplet after the maximum spreading. Key steps of the impact process are analyzed quantitatively, including the spreading of the droplet, the formation and the collapse of the spire, the formation and retraction of the cavity, and finally the formation of singular jets. A regime map for the formation of singular jets is obtained, and scaling relationships for the transition conditions between different regimes are analyzed.

Surface stress and shape relaxation of gelling droplets

Solidification is a heterogeneous transformation from liquid to solid, which usually combines transport, phase transition and mechanical strain. Predicting the shapes resulting from such a complex process is fascinating and has a wide range of implications from morphogenesis in biological tissues to industrial processes. For soft solids initially at equilibrium, elastic stresses, whether tensile or compressive, can be induced by heterogeneous volumetric deformations of the material. These stresses trigger surface instabilities leading to variations of curvature and shape of the solids. In this article, we study the shape evolution of elongated droplets of polymer and particle suspensions undergoing a solidification process caused by the inward diffusion of a gelling agent from the surface. We show experimentally and numerically that there appears a layer of gelled material growing at the surface. Due to volume contraction, this layer induces tensile stresses and drives a flow in the ungelled liquid core, resulting in the relaxation of the droplets toward spherical shapes. Over time, the thickness of this elastic membrane grows, hence the bending stiffness required to change its shape eventually balances the surface stresses, which arrests the relaxation process. These results provide general rules to understand the shape of solidifying materials combining both tension and bending driven deformations.

Role of Surfactants Based on Fatty Acids in the Wetting Behavior of Solid-Oil-Aqueous Solution Systems

Surfactants based on fatty acids have attracted extensive attention thanks to their eco-friendly and pH-responsive features. Here, we studied two fatty acid-based surfactants that were paired with the same organic counterion but distinguished by their aliphatic chain lengths (monoethanolamine-oleic acid (MEA-OA) and monoethanolamine-lauric acid (MEA-LA)). Both surfactants exhibited the ability to lower the oil-water interfacial tension but lost their interfacial activity in a low-pH environment. We experimentally investigated their influence on the receding and spreading of oil droplets on solid surfaces. It was found that the interfacial tension reduction could decrease the static contact angle of the aqueous phase and hindered displacement dynamics during the oil droplet receding. Meanwhile, the interfacial activity was more likely to suppress the initiation of the oil droplet spreading due to the more stable thin-film forming prior to the spreading process. Nevertheless, the experimental results also exhibited that MEA-OA was more effective than MEA-LA in suppressing the receding dynamics and the spreading initiation even when they were characterized by similar interfacial tension values. Such an interesting observation could be attributed to the more considerable Marangoni flow in the solution of MEA-OA whose molecules have longer aliphatic chains. The insight from this study is expected to improve the knowledge on the molecular design for more efficient applications of fatty acid-based surfactants.

Spreading and receding of oil droplets on silanized glass surfaces in water: Role of three-phase contact line flow direction in spontaneous displacement

HYPOTHESIS

The spontaneous displacement of both spreading and receding droplets on surfaces are extensively involved in numerous technical applications. We hypothesize that the spreading and receding displacement behaviors could be interpreted differently due to opposite flow directions at the three-phase contact line.

EXPERIMENTS

We performed two groups of displacement experiments using different initial setups of oil droplets on silanized glass surfaces in aqueous surroundings.

FINDINGS

The different initial configurations mostly resulted in oil displacement in opposite directions: either spreading or receding of the oil droplet. Different static states were observed at the end of the spreading and receding processes on surfaces with the same wettability due to the contact angle hysteresis. The dynamic displacement was analyzed using the hydrodynamic and molecular kinetic models, which showed distinct applicabilities for the data description of the spreading and receding possesses. The model analysis further indicated the different nature of these possesses, in particular, the resistance to displacement dynamics, which was illustrated by the interpretation of the microscopic slip length and contact line friction in the respective models. This study can shed light on the fundamental role of the displacement direction in the spontaneous liquid-liquid displacement.

Role of surfactants in spontaneous displacement of high viscosity oil droplets from solid surfaces in aqueous solutions

HYPOTHESIS

Displacement of oil droplets receding from solid surfaces in aqueous solutions plays a critical role in many household activities and industrial operations. Surfactants are often involved in these activities to control the displacement process. We hypothesize that the influence of surfactants on the displacement process of oil is highly dependent on the type and dosage of surfactants, with the mechanisms being elucidated by the analysis using appropriate dynamic wetting models.

EXPERIMENTS

We systematically investigated the spontaneous displacement of a high viscosity oil on curved hydrophilic glass surfaces in aqueous solutions of anionic sodium dodecylbenzene sulfonate, cationic hexadecyl trimethyl ammonium bromide, and nonionic Triton^TM X-100 over a wide range of concentrations.

FINDINGS

The rather different oil displacement behaviors were observed with different surfactant additions. The displacement dynamics of the receding oil droplet was found to be inhibited by surfactant additions and followed two distinct models quantitatively: the power-law model describing the temporal evolution of early-stage displacement, and the molecular kinetic model describing the dependence of the three-phase contact line displacement velocity on the dynamic contact angle at the late stage of oil displacement. The model-based data analysis provided insights on the role of surfactants in controlling the oil displacement dynamics.

Behavior of poly(d,l-lactic-co-glycolic acid) (PLGA)-based droplets falling into a complex extraction medium simulating the prilling process

HYPOTHESIS

Prilling process is one of advanced techniques for manufacturing microspheres of controlled and uniform size. In this process, homogenous polymer droplets fall into an extraction medium. The aim of this study was to identify the key parameters influencing the behavior of PLGA polymer-based droplets falling into a complex extraction medium, to select appropriate conditions for prilling.

EXPERIMENTS

Polymer solutions and extraction media were characterized by determining their viscosity, density and surface tension. A simple model simulating the prilling process was developed to study droplet behavior. Particle shape and velocity at the air-liquid interface and during sedimentation in the container were analyzed step by step. The correlations between the variables studied were visualized by principal component analysis (PCA).

FINDINGS

Droplet deformation at the interface greatly affected the recovery and final particle shape. It depended on the viscosity ratio of polymer solution/extraction medium. The particle shape recovery depended on the viscosity and density of extraction media and polymer solutions. The solidification speed is also an important parameter. In media which the solvent diffused slowly, particles were able to relax and recover their shape, however, they can also deform during sedimentation and collision with the bottom of the cuvette.

Spheroidal approximation for finite-amplitude highly viscous axisymmetric drop/bubble free shape relaxation

A common simplification used in different physical contexts by both experimentalists and theoreticians when dealing with essentially non-spherical drops is treating them as ellipsoids or, in the axisymmetric case, spheroids. In the present theoretical study, we are concerned with such a spheroidal approximation for free viscous shape relaxation of strongly deformed axisymmetric drops towards a sphere. A general case of a drop in an immiscible fluid medium is considered, which includes the particular cases of high and low inside-to-outside viscosity ratios (e.g., liquid drops in air and bubbles in liquid, respectively). The analysis involves solving for the accompanying Stokes (creeping) flow inside and outside a spheroid of an evolving aspect ratio. Here this is accomplished by an analytical solution in the form of infinite series whose coefficients are evaluated numerically. The study aims at the aspect ratios up to about 3 at most in both the oblate and prolate domains. The inconsistency of the spheroidal approximation and the associated non-spheroidal tendencies are quantified from within the approach. The spheroidal approach turns out to work remarkably well for the relaxation of drops of relatively very low viscosity (e.g., bubbles). It is somewhat less accurate for drops in air. A semi-heuristic result encountered in the literature, according to which the difference of the squares of the two axes keeps following the near-spherical linear evolution law even for appreciable deformations, is put into context and verified against the present results.

Spontaneous Displacement of High Viscosity Micrometer Size Oil Droplets from a Curved Solid in Aqueous Solutions

Spontaneous displacement of high viscosity (∼10³ Pa·s) micrometer size oil droplets from a curved solid in aqueous solutions was investigated. For high viscosity oils, the dynamic droplet shape was found to deviate significantly from a spherical cap shape due to the considerable viscous force in the oil phase. The displacement dynamics of high viscosity droplets were analyzed using molecular kinetic and hydrodynamic models. The molecular kinetic model was found to describe the dynamic displacement well for the droplets of small departure from the spherical cap shape, while the hydrodynamic model is more applicable to the droplets of higher three-phase contact line displacement velocities and hence larger deviation of the droplets from the spherical cap shape.

Nonspherical liquid droplet falling in air

The dynamics of an initially nonspherical liquid droplet falling in air under the action of gravity is investigated via three-dimensional numerical simulations of the Navier-Stokes and continuity equations in the inertial regime. The surface tension is considered to be high enough so that a droplet does not undergo breakup. Vertically symmetric oscillations which decay with time are observed for low inertia. The amplitude of these oscillations increases for high Gallilei numbers and the shape asymmetry in the vertical direction becomes prominent. The reason for this asymmetry has been attributed to the higher aerodynamic inertia. Moreover, even for large inertia, no path deviations or oscillations are observed.

Interfacial sciences in unconventional petroleum production: from fundamentals to applications

With the ever increasing demand for energy to meet the needs of growth in population and improvement in the living standards, in particular in developing countries, the abundant unconventional oil reserves (about 70% of total world oil), such as heavy oil, oil/tar sands and shale oil, are playing an increasingly important role in securing global energy supply.

Universal retraction process of a droplet shape after a large strain jump

We evidenced a universal relaxation behavior of a droplet embedded in an immiscible fluid of the same density. After a large strain jump, the relaxation can be characterized by two related relaxation times tau(1)=4.4tau(2) independently of the viscosity ratio and of the applied strain. The change in the kinetic process is driven by the drop geometry and happens invariably when the shape of the drop is an oblate ellipsoid of revolution where the relation between the major (L) and the minor (B) axis is given by ln(LB) approximately 0.5. This universal behavior can be explained by considering the normal stress difference across the droplet interface, i.e., the curvature of the drop.

Roles of interfacial properties on the stability of emulsified bitumen droplets

Because of the deformable nature of emulsion droplets, it is imperative to consider the inter-droplet pressure in assessing the stability of a liquid-liquid dispersion. In a novel methodology, the pressure generated between droplets in axial compression is estimated through considerations of equilibrium shape mechanics. The applied compressive pressure is compared to the disjoining pressure, induced by the surface charges, resisting droplet-droplet interaction. The stability of bitumen droplets, emulsified in aqueous media, is assessed from surface mechanical and electrostatic perspectives. In support of the analysis, the tensions at, and zeta potentials near, the bitumen droplet surfaces are measured. The predicted trends of stability against coalescence are confirmed by novel droplet interaction experiments: Individual emulsified bitumen droplets, manipulated by suction micropipettes, are compressed against one another along a mutual axis at up to 100 nN force. The force is measured via the deflection of a sensitive microcantilever. Because of the statistical nature of the experimental observations, a probability of coalescence is quantified. The water chemistry dramatically influences bitumen droplet coalescence, which is enhanced in acidic environments and at high ionic strength.