Influence of the Surface Viscosity on the Breakup of a Surfactant-Laden Drop

Stability and thinning of liquid jets in the presence of soluble surfactants

The dynamics of many multiphase fluid systems involve the thinning and eventual break up of a slender fluid filament or a liquid jet. The interfacial instability that controls the rate of jet thinning depends on the relative magnitudes of capillary, viscous, and inertial stresses. Surfactants add an additional layer of physicochemical dynamics by reducing the surface tension of the interface and introducing reverse Marangoni flows in response to surface concentration gradients. Surfactants may also introduce an intrinsic surface rheology that affects jet thinning. Quantifying these effects has been a significant problem in chemical physics and a topic of key research interest. Recent studies have shown that insoluble surfactants delay thread thinning and suppress instabilities in Newtonian jets. However, the role of surfactant solubility in liquid jet stability is still unknown. In this work, we use linear stability analysis to quantitatively show the stabilizing effects of Marangoni stresses, surfactant adsorption and desorption time, and intermolecular forces upon adsorption. We highlight the seemingly indistinguishable way in which various surfactant properties result in the same outcome. We also identify a surface dissipative contribution that arises from the interplay of Marangoni flows with finite adsorption and desorption, which acts as an "apparent" surface viscosity. We verify predictions of our linear stability results against numerical simulations and conclude by noting that tuning surface activity and kinetics of adsorbed surfactants or particles can potentially suppress droplet formation, which is of significant impact in the printing industry and in the control of the spread of aerosols.

Dynamics of Droplet Pinch-Off at Emulsified Oil-Water Interfaces: Interplay between Interfacial Viscoelasticity and Capillary Forces

The presence of submicrometer structures at liquid-fluid interfaces modifies the properties of many science and technological systems by lowering the interfacial tension, creating tangential Marangoni stresses, and/or inducing surface viscoelasticity. Here we experimentally study the break-up of a liquid filament of a silica nanoparticle dispersion in a background oil phase that contains surfactant assemblies. Although self-similar power-law pinch-off is well documented for threads of Newtonian fluids, we report that when a viscoelastic layer is formed in situ at the interface, the pinch-off dynamics follows an exponential decay. Recently, such exponential neck thinning was found theoretically when surface viscous effects were taken into account. We introduce a simple approach to calculate the effective relaxation time of viscoelastic interfaces and estimate the thickness of the interfacial layer and the viscoelastic properties of liquid-fluid interfaces, where the direct measurement of interfacial rheology is not possible.

Receding Phase and Rebound Behavior for Drop Impact onto an Ultrathin Film

Experimentally, the recoil phase leading to rebound behavior for drop impact onto ultrathin oil-covered solid surfaces was studied. It was found that the oil film can rupture during the impact process when the contact angle between the drop liquid and substrate is smaller than 90°. Due to such rupture, the substrate wettability of the substrate can affect the behavior of the drop impact. The rupture of the oil film can be promoted by an increase in impact Weber number (We) and a decrease in the film viscosity and thickness. The effect of We, oil viscosity, and film thickness on the rebound behavior of the drop was also investigated. For low-viscous oil films (5 cSt), it was shown that the smooth and circular edge of the liquid lamella is the key parameter affecting the level of rebound. The smooth rim of the lamella can cause an elongated rebound, while a lamella with a jagged rim will result in a stout rebound. For the impact cases onto oil films with medium and high viscosity, the effects of the film viscosity become more important; the rebound type can be suppressed due to the viscous dispassion. We have also shown that silicone oil can cloak the daughter drops generated in the rebound process for the first time. Due to the existence of the oil, the daughter drops do not merge even when they make contact in the air.

Influence of the surface viscous stress on the pinch-off of free surfaces loaded with nearly-inviscid surfactants

We analyze the breakup of a pendant water droplet loaded with SDS. The free surface minimum radius measured in the experiments is compared with that obtained from a numerical solution of the Navier–Stokes equations for different values of the shear and dilatational surface viscosities. This comparison shows the small but measurable effect of the surface viscous stresses for sufficiently small spatiotemporal distances from the breakup point, and allows to establish upper bounds for the values of the shear and dilatational viscosities. We study numerically the distribution of Marangoni and viscous stresses over the free surface as a function of the time to the pinching, and describe how surface viscous stresses grow in the pinching region as the free surface approaches its breakup. When Marangoni and surface viscous stresses are taken into account, the surfactant is not swept away from the thread neck in the time interval analyzed. Surface viscous stresses eventually balance the driving capillary pressure in in the pinching region for small enough values of the time to pinching. Based on this result, we propose a scaling law to account for the effect of the surface viscosities on the last stage of temporal evolution of the neck radius.

Universal Thinning of Liquid Filaments under Dominant Surface Forces

Theory and numerical simulations of the thinning of liquid threads at high superficial concentration of surfactants suggest the existence of an asymptotic regime where surface tension balances surface viscous stresses, leading to an exponential thinning with an e-fold time F(Θ)(3μ_{s}+κ_{s})/σ, where μ_{s} and κ_{s} are the surface shear and dilatational viscosity coefficients, σ is the interfacial tension, Θ=κ_{s}/μ_{s}, and F(Θ) is a universal function. The potential use of this phenomenon to measure the surface viscosity coefficients is discussed.

Dripping, jetting and tip streaming

Dripping, jetting and tip streaming have been studied up to a certain point separately by both fluid mechanics and microfluidics communities, the former focusing on fundamental aspects while the latter on applications. Here, we intend to review this field from a global perspective by considering and linking the two sides of the problem. First, we present the theoretical model used to study interfacial flows arising in droplet-based microfluidics, paying attention to three elements commonly present in applications: viscoelasticity, electric fields and surfactants. We review both classical and current results of the stability of jets affected by these elements. Mechanisms leading to the breakup of jets to produce drops are reviewed as well, including some recent advances in this field. We also consider the relatively scarce theoretical studies on the emergence and stability of tip streaming in open systems. Second, we focus on axisymmetric microfluidic configurations which can operate on the dripping and jetting modes either in a direct (standard) way or via tip streaming. We present the dimensionless parameters characterizing these configurations, the scaling laws which allow predicting the size of the resulting droplets and bubbles, as well as those delimiting the parameter windows where tip streaming can be found. Special attention is paid to electrospray and flow focusing, two of the techniques more frequently used in continuous drop production microfluidics. We aim to connect experimental observations described in this section of topics with fundamental and general aspects described in the first part of the review. This work closes with some prospects at both fundamental and practical levels.

Effects of Surface Viscosity on Breakup of Viscous Threads

In addition to surface tension lowering and Marangoni stresses, surfactants also induce surface rheological effects when they deform against themselves at fluid interfaces. Because surface viscosities are functions of surfactant concentration, surface rheological stresses can compete with capillary, Marangoni, and bulk stresses in surfactant-laden free surface flows with breakup. To elucidate the effects of surface rheology, we examine the breakup of a Stokes thread covered with a monolayer of insoluble surfactant when either surfactants are convected away from the space-time singularity or diffusion is dominant. Surprisingly, in both limits, surface rheological effects always enter the dominant balance of forces and alter the thread's thinning rate. Moreover, if surfactants are convected away from the singularity, we provide an analytical expression for thinning rate that explicitly depends on surface rheological parameters, providing a simple route for measuring surface viscosity.

Determination of Interfacial Concentration of a Contaminated Droplet from Shape Oscillation Damping

We present a method to measure the very small interfacial concentration of a contaminant that is irreversibly adsorbed on the interface of a bubble or droplet. It is an application of the linear theory of shape oscillation which relates the Gibbs elasticity to the damping, extended by numerical simulations to deal with moving droplets. It explains previous unexpected observations on the effect of contamination at various oscillation wavelengths. The experimental procedure is easy to implement and can thereby deeply enhance the analysis of most systems involving uncontrolled contamination.

Viscous Effects on Inertial Drop Formation

The breakup of low-viscosity droplets like water is a ubiquitous and rich phenomenon. Theory predicts that in the inviscid limit one observes a finite-time singularity, giving rise to a universal power law, with a prefactor that is universal for a given density and surface tension. This universality has been proposed as a powerful tool to determine the dynamic surface tension at short time scales. We combine high-resolution experiments and simulations to show that this universality is unobservable in practice: in contrast to previous studies, we show that fluid and system parameters do play a role; notably a small amount of viscosity is sufficient to alter the breakup dynamics significantly.

Amphiphilic nanoparticles suppress droplet break-up in a concentrated emulsion flowing through a narrow constriction

This paper describes the break-up behavior of a concentrated emulsion comprising drops stabilized by amphiphilic silica nanoparticles flowing in a tapered microchannel. Such geometry is often used in serial droplet interrogation and sorting processes in droplet microfluidics applications. When exposed to high viscous stresses, drops can undergo break-up and compromise their physical integrity. As these drops are used as micro-reactors, such compromise leads to a loss in the accuracy of droplet-based assays. Here, we show droplet break-up is suppressed by replacing the fluoro-surfactant similar to the one commonly used in current droplet microfluidics applications with amphiphilic nanoparticles as droplet stabilizer. We identify parameters that influence the break-up of these drops and demonstrate that break-up probability increases with increasing capillary number and confinement, decreasing nanoparticle size, and is insensitive to viscosity ratio within the range tested. Practically, our results reveal two key advantages of nanoparticles with direct applications to droplet microfluidics. First, replacing surfactants with nanoparticles suppresses break-up and increases the throughput of the serial interrogation process to 3 times higher than that in surfactant system under similar flow conditions. Second, the insensitivity of break-up to droplet viscosity makes it possible to process samples having different composition and viscosities without having to change the channel and droplet geometry in order to maintain the same degree of break-up and corresponding assay accuracy.