Droplet Shape Oscillations Research Articles

Surface Tensions of Picoliter Droplets with Sub-Millisecond Surface Age.

Aerosols are key components of the atmosphere and play important roles in many industrial processes. Because aerosol particles have high surface-to-volume ratios, their surface properties are especially important. However, direct measurement of the surface properties of aerosol particles is challenging. In this work, we describe an approach to measure the surface tension of picoliter volume droplets with surface age <1 ms by resolving their dynamic oscillations in shape immediately after ejection from a microdroplet dispenser. Droplet shape oscillations are monitored by highly time-resolved (500 ns) stroboscopic imaging, and droplet surface tension is accurately retrieved across a wide range of droplet sizes (10-25 μm radius) and surface ages (down to ∼100 μs). The approach is validated for droplets containing sodium chloride, glutaric acid, and water, which all show no variation in surface tension with surface age. Experimental results from the microdroplet dispenser approach are compared to complementary surface tension measurements of 5-10 μm radius droplets with aged surfaces using a holographic optical tweezers approach and predictions of surface tension using a statistical thermodynamic model. These approaches combined will allow investigation of droplet surface tension across a wide range of droplet sizes, compositions, and surface ages.

Ultrafast imaging method to measure surface tension and viscosity of inkjet-printed droplets in flight

In modern drop-on-demand inkjet printing, the jetted droplets contain a mixture of solvents, pigments and surfactants. In order to accurately control the droplet formation process, its in-flight dynamics, and deposition characteristics upon impact at the underlying substrate, it is key to quantify the instantaneous liquid properties of the droplets during the entire inkjet-printing process. An analysis of shape oscillation dynamics is known to give direct information of the local liquid properties of millimeter-sized droplets and bubbles. Here, we apply this technique to measure the surface tension and viscosity of micrometer-sized inkjet droplets in flight by recording the droplet shape oscillations microseconds after pinch-off from the nozzle. From the damped oscillation amplitude and frequency we deduce the viscosity and surface tension, respectively. With this ultrafast imaging method, we study the role of surfactants in freshly made inkjet droplets in flight and compare to complementary techniques for dynamic surface tension measurements.

Effect of evaporation and agglomeration on droplet shape oscillations

The effects of evaporation and the presence of agglomerating nanoparticles on the oscillation characteristics of pendant droplets are studied experimentally using ethanol and aqueous nanoalumina suspension, respectively. Axisymmetric oscillations induced by a round air jet are considered. Wavelet transform of the time evolution of the 2nd modal coefficient revealed that while a continuous increase in the natural frequency of the droplet occurs with time due to the diameter regression induced by vaporization in the case of ethanol droplet, no such change in resonant frequency occurs in the case of the agglomerating droplet. However, a gradual reduction in the oscillation amplitude ensues as the agglomeration becomes dominant.

Ultrafast magnetic-resonance-imaging velocimetry of liquid-liquid systems: overcoming chemical-shift artifacts using compressed sensing.

We present simultaneous measurement of dispersed and continuous phase flow fields for liquid-liquid systems obtained using ultrafast magnetic resonance imaging. Chemical-shift artifacts, which are otherwise highly problematic for this type of measurement, are overcome using a compressed sensing based image reconstruction algorithm that accounts for off-resonant signal components. This scheme is combined with high-temporal-resolution spiral imaging (188 frames per second), which is noted for its robustness to flow. It is demonstrated that both quantitative signal intensity and phase preconditioning are preserved throughout the image reconstruction algorithm. Measurements are acquired of oil droplets of varying viscosity rising through stagnant water. From these data it is apparent that the internal droplet flow fields are heavily influenced by the droplet shape oscillations, and that the accurate modeling of droplet shape is of critical importance in the modeling of droplet-side hydrodynamics. The application of the technique to three-component systems is also demonstrated, as is the measurement of local concentration maps of a mutually soluble species (acetone in polydimethylsiloxane-water).

Precision control of drying using rhythmic dancing of sessile nanoparticle laden droplets

This work analyses the unique spatio-temporal alteration of the deposition pattern of evaporating nanoparticle laden droplets resting on a hydrophobic surface through targeted low frequency substrate vibrations. External excitation near the lowest resonant mode (n = 2) of the droplet initially de-pins and then subsequently re-pins the droplet edge creating pseudo-hydrophilicity (low contact angle). Vibration subsequently induces droplet shape oscillations (cyclic elongation and flattening) resulting in strong flow recirculation. This strong radially outward liquid flow augments nanoparticle transport, vaporization, and agglomeration near the pinned edge resulting in much reduced drying time under certain characteristic frequency of oscillations. The resultant deposit exhibits a much flatter structure with sharp, defined peripheral wedge topology as compared to natural drying. Such controlled manipulation of transport enables tailoring of structural and topological morphology of the deposits and offers possible routes towards controlling the formation and drying timescales which are crucial for applications ranging from pharmaceutics to surface patterning.

Spectral response of a droplet in pulsating external flow field

A droplet introduced in an external convective flow field exhibits significant multimodal shape oscillations depending upon the intensity of the aerodynamic forcing. In this paper, a theoretical model describing the temporal evolution of normal modes of the droplet shape is developed. The fluid is assumed to be weakly viscous and Newtonian. The convective flow velocity, which is assumed to be incompressible and inviscid, is incorporated in the model through the normal stress condition at the droplet surface and the equation of motion governing the dynamics of each mode is derived. The coupling between the external flow and the droplet is approximated to be a one-way process, i.e., the external flow perturbations effect the droplet shape oscillations and the droplet oscillation itself does not influence the external flow characteristics. The shape oscillations of the droplet with different fluid properties under different unsteady flow fields were simulated. For a pulsatile external flow, the frequency spectra of the normal modes of the droplet revealed a dominant response at the resonant frequency, in addition to the driving frequency and the corresponding harmonics. At driving frequencies sufficiently different from the resonant frequency of the prolate-oblate oscillation mode of the droplet, the oscillations are stable. But at resonance the oscillation amplitude grows in time leading to breakup depending upon the fluid viscosity. A line vortex advecting past the droplet, simulated as an isotropic jump in the far field velocity, leads to the resonant excitation of the droplet shape modes if and only if the time taken by the vortex to cross the droplet is less than the resonant period of the P2 mode of the droplet. A train of two vortices interacting with the droplet is also analysed. It shows clearly that the time instant of introduction of the second vortex with respect to the droplet shape oscillation cycle is crucial in determining the amplitude of oscillation.

Dual-Frequency Electrowetting: Application to Drop Evaporation Gauging within a Digital Microsystem

This paper addresses a method to estimate the size of a sessile drop and to measure its evaporation kinetics by making use of both Michelson interferometry and coplanar electrowetting. From a high-frequency electrowetting voltage, the contact angle of the sessile droplet is monitored to permanently obtain a half-liquid sphere, thus complying perfectly with the drop evaporation theory based on a constant contact angle (Bexon, R.; Picknett, R. J. Colloid Interface Sci. 1977, 61, 336-350). Low-frequency modulation of the electrowetting actuation is also applied to cause droplet shape oscillations and capillary resonance. Interferometry allows us to measure a time-dependent capillary spectrum and, in particular, the shift in natural frequencies induced by drop evaporation. Consequently, diffusive kinetics of drop evaporation can be properly estimated, as demonstrated. Because of coplanar electrode configuration, our methodology can be integrated in open and covered microsystems, such as digital lab-on-a-chip devices.

Numerical Simulation of Unsteady Flows and Shape Oscillations in Liquid Droplets Induced by Deployment Needle Retraction

Retractable opposed needles are often used in reduced-gravity droplet combustion experiments to deploy droplets prior to ignition. Needle retraction induces droplet shape oscillations and internal flows that can have important effects on subsequent droplet behaviors. In the present paper, the unsteady flows and droplet shape oscillations associated with deployment needle retraction are investigated using the commercial CFD software package Fluent. A volume-of-fluid method with a second-order upwind scheme and a dual time stepping solver is employed to solve the conservation equations in 2-d and 3-d simulations of droplets prior to ignition. A moving-mesh method is employed to model needle movements. Calculations indicate that rapid needle retraction causes ligament formation between a droplet and a needle, with ligament breakage sometimes resulting in the formation of satellite droplets. Needle retraction also induces droplet shape oscillations that rapidly decay, though significant internal flows are predicted to remain within droplets even after droplet shape oscillations have damped to low levels. The calculations indicate that the initial needle spacing can have important effects on droplet shape oscillations and internal flow characteristics. Comparison of model predictions and experimental data is favorable.

Experimental Investigation of the Rising Behavior of CO2Droplets in Seawater under Hydrate-Forming Conditions

In a laboratory-based test series, seven experiments along a simulated Pacific hydrotherm at 152 degrees W, 40 degrees N were carried out to measure the rise velocities of liquefied CO2 droplets under (clathrate) hydrate forming conditions. The impact of a hydrate skin on the rising behavior was investigated by comparing the results with those from outside the field of hydrate stability at matching buoyancy. A thermostatted high-pressure tank was used to establish conditions along the natural oceanic hydrotherm. Under P-/T-conditions allowing hydrate formation, the majority of the droplets quickly developed a skin of CO2 hydrate upon contact with seawater. Rise rates of these droplets support the parametrization by Chen et al. (Tellus 2003, 55B, 723-730), which is based on empirical equations developed to match momentum of hydrate covered, deformed droplets. Our data do not support other parametrizations recently suggested in the literature. In the experiments from 5.7 MPa, 4.8 oC to 11.9 MPa, 2.8 degrees C positive and negative deviations from predicted rise rates occurred, which we propose were caused by lacking hydrate formation and reflect intact droplet surface mobility and droplet shape oscillations, respectively. This interpretation is supported by rise rates measured at P-/T-conditions outside the hydrate stability field atthe same liquid CO2-seawater density difference (delta rho) matching the rise rates of the deviating data within the stability field. The results also show that droplets without a hydrate skin ascend up to 50% faster than equally buoyant droplets with a hydrate skin. This feature has a significant impact on the vertical pattern of dissolution of liquid CO2 released into the ocean. The experiments and data presented considerably reduce the uncertainty of the parametrization of CO2 droplet rise velocity, which in the past emerged partly from their scarcity and contradictions in constraints of earlier experiments.

DROPLET SHAPE OSCILLATIONS: EFFECTS ON SPRAY IMPACTION AND RETENTION AND FOURIER ANALYSIS OF THEIR NATURAL FREQUENCIES

In-flight shape oscillations for 111 to 383- m diameter spray droplets were observed under moderate dynamicconditions using high-speed videography. Fourier analysis of oscillations determined droplet natural frequencies of 1.5 to9 kHz, results which agreed with a capillary-oscillation model. In addition, an ellipsoid model was employed to estimateaccompanying changes in droplet surface areas during flight. Results suggest droplet oscillations can limit surfactantadsorption at liquid-air and liquid solid interfaces such that droplets will arrive at a plant surface without the desiredlowering of surface tension being achieved. Consequently, full benefits of a surfactant in reducing droplet reflection andpromoting retention will not be realized. However, droplet shape oscillations can strengthen fluid motions within droplets,with some increase in rates of surfactant transfer to the interface. Results also showed the high natural frequenciescharacteristic of droplet sizes below 200 m will impose limits on cinematography or videography when attempting toobserve droplet distortions or identify energy dissipation pathways at droplet impact.

DYNAMIC AND QUASI-STATIC FORCE AND ENERGY REQUIREMENT FOR DETACHMENT AND BREAKAGE OF CHICKPEA PEDICEL AND POD

In-flight shape oscillations for 111 to 383- µm diameter spray droplets were observed under moderate dynamic conditions using high-speed videography. Fourier analysis of oscillations determined droplet natural frequencies of 1.5 to 9 kHz, results which agreed with a capillary-oscillation model. In addition, an ellipsoid model was employed to estimate accompanying changes in droplet surface areas during flight. Results suggest droplet oscillations can limit surfactant adsorption at liquid-air and liquid solid interfaces such that droplets will arrive at a plant surface without the desired lowering of surface tension being achieved. Consequently, full benefits of a surfactant in reducing droplet reflection and promoting retention will not be realized. However, droplet shape oscillations can strengthen fluid motions within droplets, with some increase in rates of surfactant transfer to the interface. Results also showed the high natural frequencies characteristic of droplet sizes below 200 µm will impose limits on cinematography or videography when attempting to observe droplet distortions or identify energy dissipation pathways at droplet impact.

Investigation of Liquid Surface Rheology of Surfactant Solutions by Droplet Shape Oscillations: Experiments

The experimental results of droplet shape oscillations are reported and applied to the analysis of surface rheological properties of surfactant solutions. An acoustic levitation technique is used to suspend the test drop in air and excite it into quadrupole shape oscillations. The equilibrium surface tension, Gibbs elasticity, and surface dilatational viscosity are determined from the measurements of droplet static shape under different levitation sound pressure, oscillation frequency, and free damping constant. Aqueous solutions of sodium dodecyl sulfate, dodecyltrimethylammonium bromide, andn-octyl β-d-glucopyranoside are tested with this system. The concentrations of the solutions are below the critical micelle concentration. For these solutions it is found that the surface Gibbs elasticity approaches a maximum at a moderate concentration, and its value is less than that directly calculated from the state equation of a static liquid surface. The surface dilatational viscosity is found to be in a range around 0.1 cps.

Investigations of liquid surface rheology of surfactant solutions by droplet shape oscillations: Theory

A theoretical analysis is presented for the shape oscillations of drops suspended in air. For drops of surfactant solution, the oscillation frequency is basically determined by the surface tension; the free-damping constant depends on the surface viscoelasticities. Different types of surfactant mass transfer at the droplet surface produce different surface rheological behaviors. Analytical approximate solutions for free-oscillation frequency and damping constant are derived by a perturbation method as functions of surface compositional elasticity, surface dilatational viscosity, and surface shear viscosity. These solutions are verified with exact numerical solutions. The existence of a second oscillation mode due to surface elasticity is illustrated. The phase relationships between the external driving forces and the droplet shapes for forced oscillations are discussed. It is found that at the 90° phase shift, the driving frequency and the slope of the phase diagram are equivalent to the free-oscillation frequency and damping constant.

Study of liquid drop shape oscillations with an automatic image analysis system

Droplet shape oscillations induced by acoustic radiation force can be applied to investigate liquid surface rheology. During experiments performed on the United States Microgravity Laboratory missions, the droplet shape was recorded both by video and by film cameras. In order to determine the free oscillation frequency and damping constant of droplets, an automatic image analysis system was developed to evaluate the variations of droplet shape versus time. With this system the edges of drops are automatically located frame by frame, and then matched by a polynomial function. The geometric center point, the maximum and minimum diameters, and the droplet aspect ratio are calculated from the fitting results, which give the droplet free oscillation frequency and damping constant. From these two parameters and the droplet size, the surface elasticity and viscosity of surfactant solutions can be evaluated. [Work supported by NASA through JPL, contract 958722.]

Detection of acoustically excited droplet shape oscillations with rainbow photometry

Shape oscillation resonances of liquid drops levitated acoustically in water have been excited by modulating the deforming part of the acoustic radiation pressure [P. L. Marston and R. E. Apfel. J. Acoust. Soc. Am. 61, S93(A) (1977); Bull. Am. Phys. Soc. 22, 1283 (1977)]. Small deformation of drops was detected by observing the blurring of fringes produced with optical interferometry. An improved method for detecting resonance, to be described here makes use of the rapid change in the phase difference between the deformation and the pressure modulation upon sweeping the oscillation frequency through shape resonance. The deformation produces a shift in the angles of Airy's rainbow maxima associated with the scattering of monochromatic light from a single drop. The scattered optical intensity for a fixed angle was converted to a voltage and compared with a harmonic of the pressure modulation. [Work supported by ONR and Petroleum Research Fund of the American Chemical Society.]