Repeated formation of fluid threads in breakup of a surfactant-covered jet

Secondary Bubble Entrainment via Primary Bubble Bursting at a Viscoelastic Surface

Bubble bursting at liquid surfaces is ubiquitous and plays a key role for the mass transfer across interfaces, impacting global climate and human health. Here, we document an unexpected phenomenon that when a bubble bursts at a viscoelastic surface of a bovine serum albumin solution, a secondary (daughter) bubble is entrapped with no subsequent jet drop ejection, contrary to the counterpart experimentally observed at a Newtonian surface. We show that the strong surface dilatational elastic stress from the viscoelastic surface retards the cavity collapse and efficiently damps out the precursor waves, thus facilitating the dominant wave focusing above the cavity nadir. The onset of daughter bubble entrainment is well predicted by an interfacial elastocapillary number comparing the effects of surface dilatational elasticity and surface tension. Our Letter highlights the important role of surface rheology on free surface flows and may find important implications in bubble dynamics with a contaminated interface exhibiting complex surface rheology.

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.

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.

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.

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

We examine both theoretically and experimentally the breakup of a pendant drop loaded with an insoluble surfactant. The experiments show that a significant amount of surfactant is trapped in the resulting satellite droplet. This result contradicts previous theoretical predictions, where the effects of surface tension variation were limited to solutocapillarity and Marangoni stresses. We solve numerically the hydrodynamic equations, including not only those effects but also those of surface shear and dilatational viscosities. We show that surface viscosities play a critical role to explain the accumulation of surfactant in the satellite droplet.

Capillary breakup of discontinuously rate thickening suspensions

Using discontinuously rate thickening suspensions (DRTS) as a model system, we show that beads-on-a-string morphologies can arise as a result of external viscous drag acting during capillary-driven breakup of a non-Newtonian fluid. To minimize the perturbative effect of gravity, we developed a new experimental test platform in which the filament is supported in a horizontal position at the surface of an immiscible oil bath. We show that the evolution of thin DRTS filaments during the capillary thinning process is well described by a set of one-dimensional slender filament equations. The strongly rate-dependent rheology of the test fluid and the aspect ratio of the filament couple to control the thinning dynamics and lead to a simple criterion describing the localized arrest of the capillary thinning process and the subsequent formation of complex, high aspect ratio beads-on-a-string structures.

Rheology of human blood plasma: viscoelastic versus Newtonian behavior

We investigate the rheological characteristics of human blood plasma in shear and elongational flows. While we can confirm a Newtonian behavior in shear flow within experimental resolution, we find a viscoelastic behavior of blood plasma in the pure extensional flow of a capillary breakup rheometer. The influence of the viscoelasticity of blood plasma on capillary blood flow is tested in a microfluidic device with a contraction-expansion geometry. Differential pressure measurements revealed that the plasma has a pronounced flow resistance compared to that of pure water. Supplementary measurements indicate that the viscoelasticity of the plasma might even lead to viscoelastic instabilities under certain conditions. Our findings show that the viscoelastic properties of plasma should not be ignored in future studies on blood flow.

Effect of surface tension variations on the pinch-off behavior of small fluid drops in the presence of surfactants

It is shown experimentally that surfactants can change the thinning rate of fluid necks undergoing rupture. In the case of two-fluid pinch-off, two or three linear regimes are observed for the variation of the neck radius versus time. The surface tension in the neck region changes with time, as a result of surfactant depletion. Similar results are obtained for the case of a single fluid pinching in air. The depletion of surfactant can be either partial or complete depending on the rate of transport of the surfactant from the bulk to the surface.

Role of dimensionality and axisymmetry in fluid pinch-off and coalescence

We present data on the pinch-off and coalescence of thin liquid alkane lenses floating on water. Pinch-off in quasi-2D lenses is distinctly different from pinch-off in axisymmetric 3D drops and involves a cascade of satellite droplets which extends to micron length scales. In contrast, coalescence of lenses is qualitatively similar to coalescence of 3D drops. Coalescence is predicted to involve entrainment of the exterior fluid as the droplets merge. This reentrant folding is obscured in 3D droplets but is clearly visible in coalescence of thin lenses.

Fluid pinch-off in superfluid and normal 4He

We present frames from high-speed videos of the pinch-off of liquid 4He droplets. The temperature of the fluid droplets ranged from 1.33 K to 4.8 K, and the size of the drops was proportional to the temperature-dependent capillary length. We observed no qualitative difference between pinch-off in the normal and superfluid states. In both cases, the shape of the fluid in the final stages of pinch-off resembles a cone piercing a sphere, which is typical of other low-viscosity fluids. The evolution of the minimum neck radius rmin can be characterized by power laws rmin proportional, taun, where tau is the time remaining until pinch-off occurs. In the regime near pinch-off, the data from image analysis are consistent with n=2/3. The data at the beginning of the pinch process when the neck is of the order of the capillary length are also described by n=2/3, but with a different proportionality factor. There is an intermediate crossover regime characterized by n=2/5.

Can surfactant be present at pinch-off of a liquid filament?

Surfactants lower surface tension and are used to facilitate breakup and spreading. How much surfactant remains where a filament of initial radius R breaks is set by the ratio of convection, which sweeps surfactant away, to diffusion, which replenishes it, or Peclet number Pe proportional, variantR. Thus, as is well known, surfactant concentration Gamma-->0 when a macroscale filament breaks. Here theory and simulation are used to investigate pinch-off of microscopic filaments. At breakup, Gamma is shown to be nonzero but uniform on a filament of negligible Pe. Since R must be finite, the zero-Pe limit is transitory and yields to a final regime. Two such regimes with distinct dynamics characterized by different scaling exponents are reported.