Session D11: Drops and Jets of Complex Fluids

Encapsulation of Droplets Using Cusp Formation Behind a Drop Rising in a Non-Newtonian Fluid

The rising of an oil drop in a non-Newtonian viscous solution is studied experimentally. The oil that we used was an alimentary corn oil, and the surrounding fluid is a water/glycerol polyacrylamide solution. In this case, the shape of the ascending drop is strongly affected by the non-Newtonian properties of the surrounding liquid. We found that the so-called velocity discontinuity phenomena is observed for drops larger than a certain critical size. Beyond the critical velocity, the formation of a long tail is observed, from which small droplets are continuously emitted. We determined that the fragmentation of the tail results mainly from the effect of capillary effects. We explore the idea of using this configuration as a new encapsulation technique, where the size and frequency of droplets are directly linked to the volume of the main rising drop, for the particular pair of fluids used. Those experimental results could lead to other experiments, which could help to predict the droplets deposition dynamics by tuning the two fluids properties, and adjusting only the volume of the main drop.   

Gel surface tension measurement via forced drop oscillation in an ultrasonic standing wave field

Many applications, particularly those in biology and medicine, require knowledge of the physical properties of soft matter such as gels.  Surface tension is one of those properties and is particularly difficult to measure.  Herein a non-contact ultrasonic levitation method is presented where the frequency response of a gel drop was used to measure surface tension.  Gel drops were formed by injecting a drop of liquid agarose solution into an ultrasonic standing wave field.  The drop was allowed to cool and set into a gel.  The gel drop thus formed was subjected to forced shape mode oscillations achieved by amplitude modulating the ultrasonic standing wave.  A frequency sweep was performed and the drop response, defined as the extent of drop deformation, was determined via laser intensity measurements.  The fundamental frequency of the gel drop under forced oscillation was then determined.  Using a dispersion relationship for elastic gels the surface tension was then calculated, using as inputs the gel shear modulus, the drop diameter, and the measured drop resonant frequency.   

The elastic Rayleigh drop

More than a century ago, Lord Rayleigh showed a spherical drop of inviscid liquid held by surface tension will oscillate with characteristic frequency and mode shape. This dispersion relationship has seen widespread use in multiple industries and applications. Bioprinting technologies rely on the formation of soft gel drops for printing tissue scaffolds and the dynamics of these drops can affect the process. Here we develop a model to compute the natural frequencies of a spherical drop with finite shear modulus and solid surface tension. We solve the time-dependent Navier equations of linear elasticity incorporating the solid surface tension. The motions are decomposed into i) shape oscillations and ii) rotational modes. Rotational modes are uncoupled and not affected by capillarity, whereas the frequency of shape oscillations depend upon the elastocapillary number and compressibility. For a compressible gel, there exists an infinity of radial modes for a fixed polar wavenumber and we show how these are affected by surface tension. For an incompressible gel, our results recover the Rayleigh frequency when the shear modulus is zero. Our predictions compare favorably to experiments on levitated gel drops.    

Evaporation of an axisymmetric-polymer liquid bridge

Experiments were performed to understand which conditions lead to a stable polymer gel structure after complete solvent evaporation, a structure resembling a micro-pillar. An axisymmetric-unbounded aqueous polymer liquid bridge was formed between two horizontal substrates at various Bond numbers ($0.2 \leq Bo = \Delta \rho g a^2/\gamma \leq 0.8$). Images of the liquid bridge were captured as it evaporated using a CCD camera. Polymer concentration (pre-evaporation) were initially low $0.5 \% <c_0<0.75 \%$ with initial drop volumes $1 \mu$l $<V_0<$250 $\mu$l. Due to evaporation of the solvent phase (water), the polymer concentration increased, and the liquid bridge became a gel. We measured the liquid bridge profile to estimate transient quantities such as volume, top and bottom contact angles, and minimum bridge diameter. For a given $Bo$ and $c_0$, we found a critical initial volume above which we observe stable gel structures. We discuss on how substrate properties, gap spacing and initial polymer concentration contributed to these observations.
  

Influence of flexibility, extensibility and charge on pinch-off dynamics, extensional rheology and printability of polymer solutions

Liquid transfer and drop formation in jetting, printing, coating, spraying and atomization applications involve complex free-surface flows, including the formation of columnar necks that undergo spontaneous capillary-driven thinning and pinch-off. The progressive self-thinning of neck is often characterized by self-similar profiles and scaling laws that depend on the relative magnitude of capillary, inertial and viscous stresses for simple, Newtonian fluids. Stream-wise velocity gradients that arise within the thinning columnar neck create an extensional flow field that can orient and stretch macromolecules, contributing extra elastic stresses and extensional viscosity that change the pinch-off dynamics for polymeric complex fluids. Here, we employ the dripping-onto-substrate (DoS) rheometry protocols for visualizing and analyzing the pinch-off dynamics of a columnar neck formed between a nozzle and a sessile drop. We show that the magnitude and concentration-dependence displayed by extensional rheology response are quite distinct from the values obtained in response to shear flow, and examine the macroscopic response in terms of the influence of charge, flexibility and extensibility on stretched polymer hydrodynamics.   

Flow dynamics of surfactant-laden droplets with complex interface rheology

The dynamics of individual droplets in viscous flows has received considerable attention owing to its significance in understanding the rheology of emulsions. Notably, the use of surfactants is often involved in real applications, but the influence of surfactants on drop dynamics and the underlying mechanisms are not fully understood, especially considering that many complex interface rheology have been revealed. We have developed a numerical methodology for the simulation of an insoluble surfactant-laden droplet in flows, in which the rheology of the drop surface is modeled via a Boussinesq–Scriven constitutive law with both the surface tension and surface viscosity depending strongly on local surfactant concentration. Our results show that the surface viscosity exhibits non-trivial effects on the surfactant transport, i.e., both dilatational and shear surface viscosity tend to eliminate the non-uniformity of surfactant concentration over the drop surface. As a consequent, the coupling between the surface viscosity and surfactant transport induces non-negligible effects in the dynamics of the whole droplet.