Film drainage between two surfactant-coated drops colliding at constant approach velocity

The drainage of the intervening continuous phase film between two drops approaching each other at constant velocity under the influence of insoluble surfactant is investigated. The mathematical model to be solved is a coupled pair of fourth-order nonlinear partial differential equations which arise from the relationships governing the evolution of the film thickness and the surfactant interfacial concentration in the lubrication approximation. We adopt a simplified approach which uses lubrication theory to describe the flow within the drop, marking a departure from the conventional framework in which Stokes flow is assumed. When the model is solved numerically together with the relevant initial and boundary conditions, the results obtained are compared with those found in the literature using the "boundary integral" method to solve for the flow in the drop phase. The close agreement between the results inspires confidence in the predictions of the simplified approach adopted. The analysis on the effect of insoluble surfactant indicates that its presence retards the drainage of the film: The fully immobile interface limit is recovered even in the presence of a small amount of surfactant above a critical concentration; film rupture is either prolonged or prevented. The retardation of the film was attributed to gradients of interfacial tension which gave rise to the Marangoni effect. A study of the influence of various system parameters on the drainage dynamics was conducted and three regimes of drainage and possible rupture were identified depending on the relative magnitudes of the drop approach velocity and the van der Waals interaction force: Nose rupture, rim rupture, and film immobilization and flattening. Finally, the possibility of forming secondary droplets by encapsulating the continuous phase film into the coalesced drop at rupture was examined and quantified in light of these regimes.     

A three-dimensional boundary-integral algorithm for thermocapillary motion of deformable drops

A three-dimensional boundary-integral algorithm has been developed to handle the tangential Marangoni stresses in thermocapillary motion of drops. Depending on whether the integration and observation points are on the same or different drops, singularity or near-singularity subtraction is used in the inhomogeneous term of the boundary-integral formulation. Integration is then performed analytically over flat triangles in the subtracted region. Relative trajectories for two deformable drops are calculated for different values of the drop size ratio, drop-to-medium thermal conductivity ratio, and viscosity ratio and compared to those for spherical and slightly deformable drops. Results indicate that deformation increases the minimum separation and inhibits coalescence but is not important enough for appropriate physical parameters to induce the capture or breakup behaviors observed in buoyancy. Interaction times calculated by artificially continuing spherical drop trajectories yield results accurate to within about 10%.     

Impact of compound drops: a perspective

Drop interaction with solid surfaces upon impact has been attracting a growing community of researchers who are focusing more and more on ‘complex’ surfaces and ‘complex’ drops. Recently, we are observing an emerging research trend related to the investigation of compound drop impact. Compound drops consist of two or more distinct continuous phases sharing common interfaces, surrounded by a third phase. Examples are core–shell and Janus drops. In this review, we address the fundamental aspects of compound drop impact and discuss the current challenges related to experimental testing and numerical simulation of multiphase fluid systems. Furthermore, we provide a perspective on the technological relevance of understanding and controlling compound drop impact, ranging from 3D printing to liquid separation for water cleaning and oil remediation.     

Film drainage between two captive drops: PEO-water in silicon oil

An experimental study of the deformation and drainage of a Newtonian liquid film trapped between two drops is performed for the cases of a constant and slightly rising interaction force. Series of polyethylene oxide (PEO) water solutions are used for the dispersed and polydimethylsiloxane (PDMS) for the continuous phase. The film evolution is observed by an interferometric technique. Experimental data for the film thinning rate and for the film profile allow quantitative comparison with the available drainage models.     

Photoinduced pH drops in water

A 2-hydroxyazobenzene platform has been evaluated to photorelease protons in aqueous solutions. Three different systems relying on molecular, supramolecular and polymeric strategies have been investigated in order to tune the water solubility and the thermodynamic and kinetic properties. This paper first reports on the syntheses and the physico chemical analyses for each system. Subsequently, we show that the three strategies are appropriate to reversibly photo-generate tunable pH drops in water up to one pH unit amplitude and at the 10-100 s timescale, upon transient illumination at 365 nm.     

Surfactant effects on thermocapillary interactions of deformable drops

A three-dimensional boundary-integral algorithm is used to study thermocapillary interactions of two deformable drops in the presence of bulk-insoluble, non-ionic surfactant. The primary effect of deformation is to slow down the rate of film drainage between drops in close approach and prevent coalescence in the absence of van der Waals forces. Both linear and non-linear models are used to describe the relationship between interfacial tension and surfactant surface concentration. In the linear model, non-monotonic behavior of the minimum separation between the drops as a function of the surface Peclet number Pe(s) is observed for equal drop and external medium viscosities and thermal conductivities. For bubbles with zero drop-to-medium viscosity and thermal conductivity ratios, however, the minimum separation increases with Pe(s). There is a nearly linear relationship between the minimum drop separation and elasticity E. In the simplest non-linear equation of state, the product of the temperature and the surfactant concentration is retained by allowing non-zero values of the dimensionless gas constant Lambda. For Lambda=O(0.05), it is possible for the smaller drop to move faster than the larger drop. In the Langmuir adsorption framework, the tendency of the smaller drop to catch up to the larger one decreases as the ratio of the equilibrium to maximum surfactant surface concentration increases. Finally, in the Frumkin model, a minimum in the drop separation occurs as a function of the interaction parameter lambda(F) for trajectories with all other parameters held constant.     

Theory of non-equilibrium force measurements involving deformable drops and bubbles

Over the past decade, direct force measurements using the Atomic Force Microscope (AFM) have been extended to study non-equilibrium interactions. Perhaps the more scientifically interesting and technically challenging of such studies involved deformable drops and bubbles in relative motion. The scientific interest stems from the rich complexity that arises from the combination of separation dependent surface forces such as Van der Waals, electrical double layer and steric interactions with velocity dependent forces from hydrodynamic interactions. Moreover the effects of these forces also depend on the deformations of the surfaces of the drops and bubbles that alter local conditions on the nanometer scale, with deformations that can extend over micrometers. Because of incompressibility, effects of such deformations are strongly influenced by small changes of the sizes of the drops and bubbles that may be in the millimeter range. Our focus is on interactions between emulsion drops and bubbles at around 100 μm size range. At the typical velocities in dynamic force measurements with the AFM which span the range of Brownian velocities of such emulsions, the ratio of hydrodynamic force to surface tension force, as characterized by the capillary number, is ~ 10^{− 6} or smaller, which poses challenges to modeling using direct numerical simulations. However, the qualitative and quantitative features of the dynamic forces between interacting drops and bubbles are sensitive to the detailed space and time-dependent deformations. It is this dynamic coupling between forces and deformations that requires a detailed quantitative theoretical framework to help interpret experimental measurements. Theories that do not treat forces and deformations in a consistent way simply will not have much predictive power. The technical challenges of undertaking force measurements are substantial. These range from generating drop and bubble of the appropriate size range to controlling the physicochemical environment to finding the optimal and quantifiable way to place and secure the drops and bubbles in the AFM to make reproducible measurements. It is perhaps no surprise that it is only recently that direct measurements of non-equilibrium forces between two drops or two bubbles colliding in a controlled manner have been possible. This review covers the development of a consistent theory to describe non-equilibrium force measurements involving deformable drops and bubbles. Predictions of this model are also tested on dynamic film drainage experiments involving deformable drops and bubbles that use very different techniques to the AFM to demonstrate that it is capable of providing accurate quantitative predictions of both dynamic forces and dynamic deformations. In the low capillary number regime of interest, we observe that the dynamic behavior of all experimental results reviewed here are consistent with the tangentially immobile hydrodynamic boundary condition at liquid–liquid or liquid–gas interfaces. The most likely explanation for this observation is the presence of trace amounts of surface-active species that are responsible for arresting interfacial flow.     

Two touching spherical drops in uniaxial extensional flow: analytic solution to the creeping flow problem

We solve the problem of the creeping motion of a uniaxial extensional flow past two touching spherical drops when the line of centers is parallel to the axis of symmetry of the flow, using tangent sphere coordinates. We apply this solution to the case of two equal size drops. It provides an exact result for the equal and opposite force acting on each drop along the line of centers. We also use it to determine the magnitude of the internal recirculating flow in the vicinity of the rear stagnation point, which can be used to evaluate the importance of this flow on the film drainage process for two (nearly) touching drops in a coalescence process for the limiting case, Ca < 1.     

Acoustofluidics 16: acoustics streaming near liquid-gas interfaces: drops and bubbles

In this sixteenth part of the series on "Acoustofluidics-exploiting ultrasonic standing waves forces and acoustic streaming in microfluidic systems for cell and particle manipulation," we continue our discussion on the analytical aspects of the streaming phenomenon. In particular, the use of the singular perturbation technique for this class of problems is delineated with a set of examples where fluid-fluid interaction takes place. In this category, we focus on drops and bubbles, and deal specifically with the effect of interfacial mobility on the streaming flow.     

Effect of mass transfer on the film drainage between colliding drops

The influence of mass transfer on the drainage behaviour of the thin liquid film between two drops immersed in another liquid colliding at constant approach velocity has been studied experimentally. The liquid-liquid system used is glycerol in silicone oil. The transferred solute is acetone and the volume concentration difference across the interface ranges from 1 to 5%. The film thickness evolution has been measured using a laser interferometry technique. The direction of mass transfer (from the drops towards the film phase and inversely) has been investigated and the results compared to the case with no mass transfer. When the solute transfers from the drops towards the continuous phase, the drainage rate is significantly higher than in the case with no mass transfer. This result is interpreted as a consequence of the mass transfer induced surface mobility in the film region (the so-called Marangoni effect) due to localized surface tension differences. This effect has been demonstrated by the visualization of the flow patterns in the drops and in the film phase (using a particle tracer technique). In this case, the slope of the film height as a function of time seems to be independent of the approach velocity condition imposed on the drop and appears to be controlled by the interfacial tension gradient. In the opposite case, when the solute transfers from the continuous phase towards the drops, the film drainage rate is lowered with respect to the case of no mass transfer, goes to zero or even changes its sign depending on the mass transfer intensity. The results also show that in the range of solute concentration studied, the effect of mass transfer on the film drainage process takes place at large distances compared to the scales at which lubrication theory is valid.     

Spreading of liquid drops over dry porous layers: complete wetting case

Spreading of small liquid drops over thin dry porous layers is investigated from both theoretical and experimental points of view. Drop motion over a porous layer is caused by an interplay of two processes: (a) the spreading of the drop over already saturated parts of the porous layer, which results in an expanding of the drop base; (b) the imbibition of the liquid from the drop into the porous substrate, which results in a shrinkage of the drop base and an expanding of the wetted region inside the porous layer. As a result of these two competing processes, the radius of the drop goes through a maximum value over time. A system of two differential equations is derived to describe the evolution with time of radii of both the drop base and the wetted region inside the porous layer. This system includes two parameters: one accounts for the effective lubrication coefficient of the liquid over the wetted porous substrate and the other is a combination of permeability and effective capillary pressure inside the porous layer. Two additional experiments are used for an independent determination of these two parameters. The system of differential equations does not include any fitting parameter after these two parameters are determined. Experiments were carried out on the spreading of silicone oil drops over various dry microfiltration membranes (permeable in both normal and tangential directions). The time evolution of the radii of both the drop base and the wetted region inside the porous layer are monitored. All experimental data fell on two universal curves if appropriate scales are used with a plot of the dimensionless radii of the drop base and of the wetted region inside the porous layer on dimensionless time. The predicted theoretical relationships are two universal curves accounting quite satisfactorily for the experimental data. According to our theory prediction, (i) the dynamic contact angle dependence on the same dimensionless time as before should be a universal function and (ii) the dynamic contact angle should change rapidly over an initial short stage of spreading and should remain a constant value over the duration of the rest of the spreading process. The constancy of the contact angle on this stage has nothing to do with hysteresis of the contact angle: there is no hysteresis in our system. These conclusions again are in good agreement with our experimental observations.     

Studies on the mechanism for the sudden mechanical property drops of graphene/polymer nanocomposites

Graphene/polymer nanocomposites (GPNCs) have gained intense research interest in recent years. Graphene can improve the properties of the nanocomposites at low loadings, but usually causes sudden drops in the mechanical properties of the nanocomposites at similarly low loadings, risking the performance, reproducibility, and batch stability of the nanocomposites. This problem has been troubling the GPNCs field for years, but it is difficult to solve mainly because the mechanism of the sudden mechanical property drops has not been well documented yet. Here, we present a systematic study on this problem. At first, a statistical study was made to provide an overview of the sudden mechanical property drops. It was found that the sudden mechanical property drops were almost independent of the surface modification of graphene, and the in situ polymerization method sometimes leads to lower critical concentration than the solvent blending and melt blending methods. Then, we demonstrated a cutting‐off mechanism which unveiled that the formation of a continuous or semicontinuous network of graphene throughout the polymeric matrix was the main cause of the sudden mechanical property drops, and the low critical concentration of the sudden mechanical property drops was mainly due to the large aspect ratio of graphene. Finally, future research prospects were proposed. Overall, our work has provided new understandings and insights to the mechanical properties of GPNCs.     

Static aspects of the fission and fusion of3He drops

Using an effective³He-³He interaction, we have investigated the fission and fusion of³He drops from a static point of view. Our calculations show that a fission barrier develops for these neutral systems, and that their saddle configurations are rather elongate. The transition from oblate to prolate shapes as a function of the angular momentumL, as well as critical values for fission and fusion are discussed for some selected cases. We show that a kind of proximity potential can be extracted from the drop-drop interaction potentials.     

Liquid ring formation from contacting, nonmiscible sessile drops

When two pure and nonmiscible liquid drops at rest on a rigid substrate come into close contact with a quasi-zero spreading velocity, one of them may be sucked around the second into a liquid ring, leading in some cases to the complete engulfment of the latter. We here show that the conditions for this amazing and unusual capillary effect to develop are defined by two sets of criteria: the "reciprocal" spreading of one drop with respect to the other and a "geometrical-wetting" criterion related to the opening of the groovelike channels along the base of the attracting drop. Despite the exceeding simplicity and roughness of liquid drops as compared to living cells, the phenomenon strangely recalls, at least in its mechanistic aspect, the fundamental biological process of phagocytosis. Besides these fundamental aspects, this effect may also have interesting implications for microstructuring techniques.     

Shape and buckling transitions in solid-stabilized drops

We study shape and buckling transitions of particle-laden sessile and pendant droplets that are forced to shrink in size. Monodisperse polystyrene particles were placed at the interface between water and decane at conditions that are known to produce hexagonal, crystalline arrangements on flat interfaces. As the volumes of the drops are reduced, the surface areas are likewise diminished. This effectively compresses the particle monolayer coating and induces a transition from a fluid film to a solid film. Since the particles are firmly attached to the interface by capillary forces, the shape transitions are reversible and shape/volume curves are the same for drainage and inflation. Measurements of the internal pressure of the drops reveal a strong transition in this variable as the buckling transition is approached.     

Polymeric stabilized emulsions: steric effects and deformation in soft systems

Polymeric stabilizers are used in a broad range of processes and products, from pharmaceuticals and engine lubricants to formulated foods and shampoos. In rigid particulate systems, the stabilization mechanism is attributed to the repulsive force that arises from the compression of the polymer coating or "steric brush" on the interacting particles. This mechanism has dictated polymer design and selection for more than thirty years. Here we show, through direct measurement of the repulsive interactions between immobilized drops with adsorbed polymers layers in aqueous electrolyte solutions, that the interaction is a result of both steric stabilization and drop deformation. Drops driven together at slow collision speeds, where hydrodynamic drainage effects are negligible, show a strong dependence on drop deformation instead of brush compression. When drops are driven together at higher collision speeds where hydrodynamic drainage affects the interaction force, simple continuum modeling suggests that the film drainage is sensitive to flow through the polymer brush. These data suggest, for drop sizes where drop deformation is appreciable, that the stability of emulsion drops is less sensitive to the molecular weight or size of the adsorbed polymer layer than for rigid particulate systems.     

Computer simulations of nematic drops: coupling between drop shape and nematic order

We perform Monte Carlo computer simulations of nematic drops in equilibrium with their vapor using a Gay-Berne interaction between the rod-like molecules. To generate the drops, we initially perform NPT simulations close to the nematic-vapor coexistence region, allow the system to equilibrate and subsequently induce a sudden volume expansion, followed with NVT simulations. The resultant drops coexist with their vapor and are generally not spherical but elongated, have the rod-like particles tangentially aligned at the surface and an overall nematic orientation along the main axis of the drop. We find that the drop eccentricity increases with increasing molecular elongation, κ. For small κ the nematic texture in the drop is bipolar with two surface defects, or boojums, maximizing their distance along this same axis. For sufficiently high κ, the shape of the drop becomes singular in the vicinity of the defects, and there is a crossover to an almost homogeneous texture; this reflects a transition from a spheroidal to a spindle-like drop.     

Film drainage and interfacial instabilities in polymeric systems with diffuse interfaces

We report an experimental investigation on the effect of mutual diffusion in polymeric systems on film drainage between two captive drops. The main objective is to study the influence of diffuse interfaces on film drainage. This is done by using material combinations with different interfacial properties and interferometric visualization of the film between two interacting drops. For highly diffusive systems film drainage is observed to be, in contrast to immiscible systems, non-axisymmetric and unstable immediately after the film formation (at a few micrometers film thickness). Depending on whether the total thickness of the diffusion layers in the film is smaller or larger than the thickness of the film, Marangoni convection is found to enhance or delay film drainage. Enhanced film drainage is determined to be in order of 100 times faster than predicted by the current models, while delayed film drainage is observed after a drainage period where experimental and predicted results (assuming, a partially mobile interface) are in close agreement.     

Migration study of zinc dibutyldithiocarbamate in eye drops solutions

The potential deleterious effects of extractables/leachables in pharmaceutical products and the need to preserve product safety throughout its shelf life have led the three major pharmacopoeias (USP, EP, JP) to require extractable and toxicity testing of container/closure systems. To that, a HPLC/UV method was developed and validated for the detection of zinc dibutyl dithiocarbamate (ZDBC) as potential extractable from pharmaceutical container closure system of eye drops solutions. The method consists of direct extraction of the analyte with chloroform; the lower layer was evaporated to dryness and further reconstituted with acetonitrile. The chromatographic separation was performed on a Nova-Pak C18 column using as mobile phase a mixture of acetonitrile:water. Calibration curves were linear and relative standard deviation was sufficient. Detection limit of ZDBC was found to be 0.015 μg/mL. The HPLC method was further applied in seven currently marketed eye drops solutions, confirming its applicability for monitoring dithiocarbamates migration from container closure systems into the eye drops solutions.