Session Z12: Drops: Instability and Break-up II

Instability mediated self-templating of drop crystals

The breakup of liquid threads into droplets is prevalent in engineering and natural settings. While drop formation in these systems has a long-standing history, existing studies typically consider axisymmetric systems. Conversely, the physics at play when multiple threads are involved and the interaction of a thread with a symmetry breaking boundary remain unexplored. Here, we show that the breakup of closely spaced liquid threads sequentially printed in an immiscible bath locks into crystal-like lattices of droplets. We rationalize the hydrodynamics at the origin of this previously unknown phenomenon. We leverage this knowledge to tune the lattice pattern via the control of injection flow rate and nozzle translation speed, thereby overcoming the limitations in structural versatility typically seen in existing fluid manipulations paradigms. We further demonstrate that these drop crystals have the ability to self-correct and propose a simple mechanism to describe the convergence toward a uniform pattern of drops.   

The end-pinching mechanism for surfactant-laden multiphase flows

The presence of surfactants in any multiphase flow system often reduces the local value of surface tension but it also generates tangential stress at the interface due to the surfactant interfacial gradient known as Marangoni stress. Depending on the prevailing flow fields, these stresses can act to rigidify the interface and inhibit droplet end-pinching particularly if they dominate inertia. We will present through this talk different examples of end-pinching mechanisms that have recently been studied such as in retracting ligaments, bursting bubbles, and drop coalescence. The results that will be discussed were generated via three-dimensional simulations using a hybrid interface-tracking/level-set approach that accounts for variations in surfactant interfacial concentrations coupled to the flow dynamics; this methodology is capable of capturing accurately changes in interfacial topology.   

Absence of scaling transitions in breakup of liquid jets caused by surface viscosity

Breakup of surfactant-covered jets is central to diverse applications, e.g. inkjet printing. During thinning, convection and diffusion compete to determine surfactant distribution along the interface. As fluid evacuates the thinning neck, surfactant is convected away from it. However, the resulting concentration gradient gives rise to diffusion which tries to replenish it with surfactant. When surface rheological effects are negligible, regardless of $Pe$ (measure of importance of convection to diffusion), the dynamics is self-similar and there is always a transition from a diffusion-dominated to a convection-dominated regime as breakup nears. Theory and simulations are used to show that a highly viscous thread breaking up when surface viscous stresses are present gives rise to unexpected dynamics. In contrast to previous studies where there is always a transition between different scaling regimes as breakup nears, presence of surface viscous stresses cuts off this universal response. It is shown that when $PePe_c$, the dynamics is self-similar and exhibits power-law dependence on time until breakup. That a transition between the two regimes is not possible is also demonstrated.

    

Author not Attending

When an immiscible oil is deposited over soapy water, a liquid lens is formed. Subsequently, when a smaller droplet of ethanol-water mixture is deposited on the oil lens, rupture occurs within a few minutes. This rupture time is found to depend on the shape and size of the liquid lens and the concentration of the ethanol-water mixture. The rupture can be attributed to the moment when the ethanol-water mixture comes in contact with the miscible soapy water solution. Spontaneous emulsification and the density-difference (Rayleigh-Taylor instability) phenomenon influence the ethanol-water descent. Rupture is characterized by a large radial but thin circular film rapidly expanding (<2 ms) to a radius often larger than the original oil lens. The  phenomenon continues as the radius then retracts towards the center and the now non-uniform ethanol-water mixture forms a fingering instability (< 4 ms),  finally retracting to near-zero radii. Data from high-speed imaging predicts a power law correlation for this thin film spreading behavior.   

Dynamics and instability of liquid sheets and 2D drops

In a number of spray or atomization nozzles, liquid is ejected as a sheet---a film with two free surfaces---and then disintegrates into drops. The instability of liquid sheets is therefore of both practical and theoretical importance. Near the nozzle, the cross-section of a liquid sheet resembles a slender rectangle, possibly corrugated, with rounded ends. Surface tension causes the two nearly-circular ends to move toward each other or the slender two-dimensional (2D) drop to retract or contract. A number of authors have analyzed sheet retraction (e.g. Brenner and Gueyffier, PoF, 1999) and the possible breakup of the 2D drop during contraction (e.g. Burton and Taborek, PoF, 2007). In this talk, we present new insights into this problem by carrying out fully 2D free-surface flow calculations as well as solving a set of one-dimensional (1D) slender-sheet equations.   

Atomisation of a thin liquid sheet by an impulsive air flow: the cough machine revisited.

We study experimentally and numerically the perturbation growth and the subsequent atomization of a thin liquid sheet by an impulsive airflow. The flow mimics the aerosolization of the muco-salivary fluid in the respiratory tract and revisits the "cough machine". We test both Newtonian and non-Newtonian fluids. Velocity ranges from ten to thirty m/s. In the Newtonian case, waves form that amplify into sheets. One sees bags inflating the sheerts. Holes then perforate these bags and leave behind a spray of droplets and ligaments. The depth, width, and thickness of the bags are correlated. Deeper, wider, and thinner bags are observed just before hole formation as viscosity is increased. The droplet size distribution is close to a log-normal PDF, and the geometric mean is decreasing with increasing fluid viscosity. In the non-Newtonian case, sheets are much more resilient and hole formation is difficult to observe. Simulations of the Newtonian case are performed using a VOF method with adaptive octree grid refinement, and a continuous surface force method with height function computation of curvature, all implemented in Basilisk (http://basilisk.fr). The simulations show qualitatively identical phenomena of sheet formation and hole formation and expansion.   

Fragmentation of liquids into droplets via secondary flows of Newtonian and viscoelastic fluids.

Fragmentation of liquids into a population of smaller droplets is of great importance in many natural and industrial processes. In this talk we explore a new method of fragmentation that is based on secondary flows around a spinning top. We first use dye injection and visualize the flow around the spinning top as it rotates in a transparent tank filled with either Newtonian or viscoelastic liquids. In the Newtonian case, inertially-driven secondary flows generate toroidal vortices that roll around the geometry in an ever-spinning spiral. For viscoelastic liquids, presence of long macromolecules leads to normal stresses that defy inertial effects. Thus, the flow separates into viscoelastic and inertial zones, giving rise to a unique butterfly pattern that revolves around the spinning top. We use the kinematics of these secondary flows for atomization of viscous immiscible oils. As we introduce a volume of the immiscible oil into the tank, the oil blob follows the secondary flows and stretches into a continuous manifold that resembles the geometry of a toroidal sheet. The gentle nature of the secondary flow stretches the thinning oil layer continuously until it eventually breaks into a set of small droplets. We study the size distribution of these droplets under different operational conditions and provide a theoretical framework that explains our measurements.   

Superradiant droplet emission from parametrically excited cavities

Superradiance occurs when a collection of atoms exhibits cooperative, spontaneous emission of

photons at a rate that exceeds that of its component parts. Here, we reveal a similar phenomenon

in a hydrodynamic system consisting of a pair of vibrationally-excited cavities, coupled through

their common wavefield, that spontaneously emit droplets via interfacial fracture. We show that

the droplet emission rate of two coupled cavities is higher than the emission rate of two isolated

cavities. We further show that the amplified emission rate varies sinusoidally with distance between

the cavities, thus demonstrating a hydrodynamic phenomenon that captures the essential features

of superradiance in optical systems.   

Is the maximum water droplet diameter fixed by the capillary length?

Water droplet break-up has been studied extensively but typically focuses on droplets with radii near the capillary length (< 3 mm). Droplets larger than this typically break-up when their velocity approaches terminal velocity, with larger droplets breaking up well before they reach terminal speeds. In general, studies involving large droplet break-up are scarce and part of the reason is the difficulty performing such experiments. We propose a method to suspend droplets of radii up to 60 mm using a series of release mechanisms and release speeds to illustrate the complexity and parameter space for practical solutions to these problems. The research details the effects of release acceleration, surface geometry and surface features on the initial droplet perturbations. Droplet perturbations are recorded with high speed imaging and are used to determine what oscillation frequencies and modes are present in the falling droplet. Analysis of the droplet frequencies and amplitudes reveals five major mode types. Droplet volume predicts the frequencies in accordance with Rayleigh theory. The best shape and acceleration of release are presented.   

All-aqueous printing of viscoelastic droplets in yield-stress fluids

All-aqueous printing of viscoelastic droplets (aaPVD) in yield-stress fluids is the core of an emerging voxelated bioprinting technology that enables the digital assembly of spherical bio-ink particles (DASP) to create functional tissue mimics. However, the mechanism of aaPVD is largely unknown. Here, by quantifying the dynamics of the whole printing process in real-time, we identify two parameters critical to aaPVD: (1) acceleration of print nozzle, and (2) droplet/nozzle diameter ratio. Moreover, we distinguish three stages associated with aaPVD: droplet generation, detachment, and relaxation. To generate a droplet of good roundness, the ink should be a highly viscous shear-thinning fluid. Using particle image velocimetry and scaling theory, we establish a universal description for the droplet displacements at various printing conditions. Along the direction of nozzle movement, the droplet displacement is determined by the ratio between the dragging force from the nozzle and the confinement force from the supporting matrix. Perpendicular to the direction of nozzle movement, the droplet displacement is determined by Oldroyd number. For a relaxed droplet, the droplet tail length is independent of droplet/nozzle diameter ratio but determined by the nozzle acceleration. We conclude that printing droplets of good fidelity requires a relatively large droplet/nozzle diameter ratio and intermediate nozzle accelerations. These ensure that the droplet is more solid-like to not flow with the nozzle to form a tadpole-like morphology and that the confinement force from the yield-stress fluid is large enough to prevent large droplet displacement. Our results provide the knowledge and tools for in situ generating and depositing highly viscoelastic droplets of good roundness at prescribed locations in 3D space, which help establish the foundational science for voxelated bioprinting.