Nonspherical Drops Research Articles

Coalescence of non-spherical drops with a liquid surface

We employ three-dimensional numerical simulations to explore the impact dynamics of non-spherical drops in a deep liquid pool by varying the aspect ratios (Ar) and Weber numbers (We). We observe that when a non-spherical drop is gently placed on a liquid pool, it exhibits a partial coalescence phenomenon and the emergence of a daughter droplet for Ar>0.67. In contrast to the prolate (Ar<1) and spherical drops (Ar=1), an oblate (Ar>1) drop with a high aspect ratio encapsulates air in a ring-like bubble within the pool and emerges a liquid column that undergoes Rayleigh–Plateau capillary instability, leading to the formation of two daughter droplets with complex shapes. When the parent drop is impacted with finite velocity, our observations indicate that increasing the Weber number leads to elevated crater heights on the free surface for all aspect ratios. A prolate drop produces a less pronounced wave swell and exhibits a prolonged impact duration owing to its negligible impact area. Conversely, an oblate drop generates a much wider wave swell than spherical and prolate drops. We analyze the relationship between rim formation dynamics and the kinetic and surface energies of the system. Finally, we establish an analogy by comparing the dynamics of a freely falling non-spherical drop, undergoing topological oscillations during its descent from a height, with the impact dynamics of parent drops of various shapes striking the liquid surface with an equivalent velocity. Our investigation involving non-spherical drops contrasts the extensive studies conducted by various researchers on the impact of a parent spherical drop just above the free surface of a liquid pool.

Machine learning enabled orthogonal camera goniometry for accurate and robust contact angle measurements

Characterization of surface wettability plays an integral role in physical, chemical, and biological processes. However, the conventional fitting algorithms are not suitable for accurate estimation of wetting properties, especially on hydrophilic surfaces, due to optical distortions triggered by changes in the focal length of the moving drops. Therefore, here we present an original setup coupled with Convolutional Neural Networks (CNN) for estimation of Contact Angle (CA). The developed algorithm is trained on 3375 ground truth images (at different front-lit illuminations), less sensitive to the edges of the drops, and retains its stability for images that are synthetically blurred with higher Gaussian Blurring (GB) values (GB: 0–22) if compared to existing goniometers (GB: 0–12). Besides, the proposed technique can precisely analyze drops of various colors and chemistries on different surfaces. Finally, our automated orthogonal camera goniometer has a significantly lower average standard deviation (6.7° vs. 14.6°) and coefficient of variation (14.9 vs. 29.2%) than the existing techniques and enables wettability assessment of non-spherical drops on heterogeneous surfaces.

A Conservative Level Set Approach to Non-Spherical Drop Impact in Three Dimensions.

A recently developed conservative level set model, coupled with the Navier-Stokes equations, was invoked to simulate non-spherical droplet impact in three dimensions. The advection term in the conservative level set model was tackled using the traditional central difference scheme on a half-staggered grid. The pressure velocity coupling was decoupled using the projection method. The inhouse code was written in Fortran and was run with the aid of the shared memory parallelism, OpenMP. Before conducting extensive simulations, the model was tested on meshes of varied resolutions and validated against experimental works, with satisfyingly qualitative and quantitative agreement obtained. The model was then employed to predict the impact and splashing dynamics of non-spherical droplets, with the focus on the effect of the aspect ratio. An empirical correlation of the maximum spread factor was proposed. Besides, the number of satellite droplets when splashing occurs was in reasonable agreement with a theoretical model.

Dependence of raindrop size and shape parameters on rain attenuation prediction over a tropical location

Rain attenuation is a phenomenon that weakens signal propagation, particularly in high frequency bands and in areas with significant rainfall rates, one of which is the tropical area. Falling raindrops undergo changes in shapes as they grow in sizes. The goal of this research is to use a theoretical method to examine the impact of drop shapes and sizes on rain attenuation prediction. The extinction cross section of spherical and non-spherical raindrops was calculated using the Mie theory and T-matrix respectively. The specific rain attenuation for spherical and non-spherical raindrops was computed at various frequencies in the microwave band and compared with the ITU-R838 model. It was observed that the non-spherical drops model has higher values for rain attenuation, and thus is best suitable for predicting rain attenuation.

Drop Impact Dynamics: Impact Force and Stress Distributions

Dynamic variables of drop impact such as force, drag, pressure, and stress distributions are key to understanding a wide range of natural and industrial processes. While the study of drop impact kinematics has been in constant progress for decades thanks to high-speed photography and computational fluid dynamics, research on drop impact dynamics has only peaked in the last 10 years. Here, we review how recent coordinated efforts of experiments, simulations, and theories have led to new insights on drop impact dynamics. Particularly, we consider the temporal evolution of the impact force in the early- and late-impact regimes, as well as spatiotemporal features of the pressure and shear-stress distributions on solid surfaces. We also discuss other factors, including the presence of water layers, air cushioning, and nonspherical drop geometry, and briefly review granular impact cratering by liquid drops as an example demonstrating the distinct consequences of the stress distributions of drop impact.

Phase Inversion of Ellipsoid-Stabilized Emulsions.

The efficacy of anisotropic particles in Pickering emulsion stabilization, attributed to shape-induced capillary interactions, is well-documented in the literature. In this contribution, we show that the surface of hematite ellipsoids can be modified in situ by the addition of oleic acid to effect transitional phase inversion of Pickering emulsions. Interestingly, incorporation of oleic acid results in the formation of nonspherical emulsion drops. The phase inversion of oil-in-water to water-in-oil and the transition in shape of emulsion drops from spherical to nonspherical is observed in two different particle systems, namely, nanoellipsoids and microellipsoids. The surface of spherical emulsion drops stabilized by particles or particles along with high concentration of oleic acid is found to consist of ellipsoids arranged in a close-packed configuration with their major axis parallel to the interface. In contrast, at intermediate oleic acid concentration, the surface of nonspherical emulsion drops is observed to be covered with loosely packed particle monolayer, with the ellipsoids at the oil/water interface taking up many different orientations. Using contact angle goniometry, the change in the wettability of hematite particles due to adsorption of oleic acid is established to be the mechanism responsible for the phase inversion of Pickering emulsions.

The Effect of Drop Shape, Sensing Volume and Raindrop Size Statistics to the Scattered Field on 300 GHz

Scattering and attenuation properties of rain using various drop models are calculated using Mie theory, the T-matrix method and numerical technique respectively. Ellipsoidal and oblate drops use the axis ratio of raindrops reported in literature. Scattering are presented both for small volumes containing a single drop and for large volumes with multiple drops in which the statistics of drop size distribution need to be taken into account. The angular dependence of scattering, absorption and scattering cross sections and polarization ratios are investigated. For single scattering the angular dependence and cross sections of nonspherical drops differed from those of a spherical drop. Differences between ellipsoid and oblate drops were minimal. Drop shape affected the polarization mostly at 40-140 degree detection angles. The averaged linear attenuation and rain induced cross channel signal were studied. Attenuation was close to the ITU-R.838 model and in the same order of magnitude as the attenuation due to atmospheric moisture. The cross channel signal was calculated as a function of rain rate and transmitter/receiver angle. Vertical polarization was observed to produce a higher cross channel signal than horizontal polarization. It was concluded that drop shape is not an important factor at 300 GHz due to small drops dominating the scattering signal. Overall, the results showed that in single scattering, the ellipsoid is a good approximation for raindrops and that for large volumes, a spherical drop approximation and a Mie solution may be sufficient at frequencies of 300 GHz and higher.

Role of interfacial elasticity for the rheological properties of saponin-stabilized emulsions

HypothesisSaponins are natural surfactants which can provide highly viscoelastic interfaces. This property can be used to quantify precisely the effect of interfacial dilatational elasticity on the various rheological properties of bulk emulsions. ExperimentsWe measured the interfacial dilatational elasticity of adsorption layers from four saponins (Quillaja, Escin, Berry, Tea) adsorbed on hexadecane-water and sunflower oil-water interfaces. In parallel, the rheological properties under steady and oscillatory shear deformations were measured for bulk emulsions, stabilized by the same saponins (oil volume fraction between 75 and 85%). FindingsQuillaja saponin and Berry saponin formed solid adsorption layers (shells) on the SFO-water interface. As a consequence, the respective emulsions contained non-spherical drops. For the other systems, the interfacial elasticities varied between 2 mN/m and 500 mN/m. We found that this interfacial elasticity has very significant impact on the emulsion shear elasticity, moderate effect on the dynamic yield stress, and no effect on the viscous stress of the respective steadily sheared emulsions. The last conclusion is not trivial, because the dilatational surface viscoelasticity is known to have strong impact on the viscous stress of steadily sheared foams. Mechanistic explanations of all observed effects are described.

Spheroidal approximation for finite-amplitude highly viscous axisymmetric drop/bubble free shape relaxation.

A common simplification used in different physical contexts by both experimentalists and theoreticians when dealing with essentially non-spherical drops is treating them as ellipsoids or, in the axisymmetric case, spheroids. In the present theoretical study, we are concerned with such a spheroidal approximation for free viscous shape relaxation of strongly deformed axisymmetric drops towards a sphere. A general case of a drop in an immiscible fluid medium is considered, which includes the particular cases of high and low inside-to-outside viscosity ratios (e.g., liquid drops in air and bubbles in liquid, respectively). The analysis involves solving for the accompanying Stokes (creeping) flow inside and outside a spheroid of an evolving aspect ratio. Here this is accomplished by an analytical solution in the form of infinite series whose coefficients are evaluated numerically. The study aims at the aspect ratios up to about 3 at most in both the oblate and prolate domains. The inconsistency of the spheroidal approximation and the associated non-spheroidal tendencies are quantified from within the approach. The spheroidal approach turns out to work remarkably well for the relaxation of drops of relatively very low viscosity (e.g., bubbles). It is somewhat less accurate for drops in air. A semi-heuristic result encountered in the literature, according to which the difference of the squares of the two axes keeps following the near-spherical linear evolution law even for appreciable deformations, is put into context and verified against the present results.

An analytical model of heat and mass transfer from liquid drops with temperature dependence of gas thermo-physical properties

An analytical model for heating and evaporation of a single component liquid drop is developed. The model accounts for the temperature dependence of density, diffusivity, thermal conductivity and specific heat of the gas species. The effect of variable properties on heat and evaporation rates is analysed and a comparison with the prediction of the classical constant property model is reported for six different species and different operating conditions. The model allows to evaluate the effect of the choice of the gas mixture averaging parameter (the relative weight of free stream and drop surface conditions) on the prediction of the constant property model, and a way to optimise the choice is proposed. The results can be extended to non-spherical drop and examples are reported.

Dynamics of formation and oscillation of non-spherical drops

Present study focuses on the shape of a drop during pinch-off and how the shape of a drop is affected by the flow parameters and different physical properties of the fluids. Both experimental and numerical investigations are performed to unveil the mechanism of non-spherical drop formation and the oscillatory motion of a drop after pinch-off. Numerical simulations are performed over a wide range of density ratios (0.001–0.9) and viscosity ratios (0.01–10) ranging from a gas-liquid system to a liquid-liquid system. The deformation of a drop at the incipience of pinch-off depends on the internal stress distribution within the drop. A larger velocity gradient inside the drop culminates in a stronger shear force within the drop leading to a non-spherical drop during pinch-off. We reveal that the shape of a drop remains either in prolate or in spherical form during pinch-off. A drop undergoes prolate-oblate-prolate oscillation while falling through the surrounding medium. The oscillatory motion is generated due to the local capillary pressure that develops across the drop surface because of the deformed shape of the drop after pinch-off. Present investigation reveals that the deformation of the drop because of the downward pull generated near the pinching region makes the drop shape non-spherical after pinch-off and initiates the oscillatory motion of the drop. The oscillation of a drop reduces substantially at higher relative strength of the viscous force.

An analytical approach to model heating and evaporation of multicomponent ellipsoidal drops

An analytical model for heating and evaporation of non-spherical multicomponent drops is reported, based on the solution of energy and species conservation equations in orthogonal curvilinear coordinates, accounting also for the effect of convective conditions according to the film theory approach. The instantaneous heat and evaporation rates of multicomponent drops is calculated as function of increased surface area due to drop deformation. The model is applied to predict evaporation characteristics of spheroidal drops under quasi-steady and transient conditions, analysing the effect of drop size, composition and velocity on the temperature evolution, for a range of drop and gas temperature conditions

Residence time distribution in packed bed microreactor – Lattice Boltzmann model validation

An analytical model for heating and evaporation of a single component liquid drop is developed. The model accounts for the temperature dependence of density, diffusivity, thermal conductivity and specific heat of the gas species. The effect of variable properties on heat and evaporation rates is analysed and a comparison with the prediction of the classical constant property model is reported for six different species and different operating conditions. The model allows to evaluate the effect of the choice of the gas mixture averaging parameter (the relative weight of free stream and drop surface conditions) on the prediction of the constant property model, and a way to optimise the choice is proposed. The results can be extended to non-spherical drop and examples are reported.

Sedimentation of a surfactant-laden drop under the influence of an electric field

The sedimentation of a surfactant-laden deformable viscous drop acted upon by an electric field is considered theoretically. The convection of surfactants in conjunction with the combined effect of electrohydrodynamic flow and sedimentation leads to a locally varying surface tension, which subsequently alters the drop dynamics via the interplay of Marangoni, Maxwell and hydrodynamic stresses. Assuming small capillary number and small electric Reynolds number, we employ a regular perturbation technique to solve the coupled system of governing equations. It is shown that when a leaky dielectric drop is sedimenting in another leaky dielectric fluid, the Marangoni stress can oppose the electrohydrodynamic motion severely, thereby causing corresponding changes in the internal flow pattern. Such effects further result in retardation of the drop settling velocity, which would have otherwise increased due to the influence of charge convection. For non-spherical drop shapes, the effect of Marangoni stress is overcome by the ‘tip-stretching’ effect on the flow field. As a result, the drop deformation gets intensified with an increase in sensitivity of the surface tension to the local surfactant concentration. Consequently, for an oblate type of deformation the elevated drag force causes a further reduction in velocity. For similar reasons, prolate drops experience less drag and settle faster than the surfactant-free case. In addition to this, with increased sensitivity of the interfacial tension to the surfactant concentration, the asymmetric deformation about the equator gets suppressed. These findings may turn out to be of fundamental significance towards designing electrohydrodynamically actuated droplet-based microfluidic systems that are intrinsically tunable by varying the surfactant concentration.

Simultaneous measurement of surface tension and viscosity using freely decaying oscillations of acoustically levitated droplets

Oscillations of small liquid drops around a spherical shape have been of great interest to scientists measuring physical properties such as interfacial tension and viscosity, over the last few decades. A powerful tool for contactless positioning is acoustic levitation, which has been used to simultaneously determine the surface tension and viscosity of liquids at ambient pressure. In order to extend this acoustic levitation measurement method to high pressure systems, the method is first evaluated under ambient pressure. To measure surface tension and viscosity using acoustically levitated oscillating drops, an image analysis method has to be developed and factors which may affect measurement, such as sound field or oscillation amplitude, have to be analyzed. In this paper, we describe the simultaneous measurement of surface tension and viscosity using freely decaying shape oscillations of acoustically levitated droplets of different liquids (silicone oils AK 5 and AK 10, squalane, 1-propanol, 1-butanol, 1-pentanol, 1-hexanol, 1-heptanol, and 1-octanol) in air. These liquids vary in viscosity from 2 to about 30 mPa s. An acoustic levitation system, including an optimized standing wave acoustic levitator and a high-speed camera, was used for this study. An image analysis was performed with a self-written Matlab® code. The frequency of oscillation and the damping constant, required for the determination of surface tension and viscosity, respectively, were calculated from the evolution of the equatorial and polar radii. The results and observations are compared to data from the literature in order to analyze the accuracy of surface tension and viscosity determination, as well as the effect of non-spherical drop shape or amplitude of oscillation on measurement.

Light scattering from sessile water drops and raindrop-shaped glass beads as a validation tool for rainbow simulations.

The shape deviation of falling raindrops from exact spheres is known to affect the appearance of natural rainbows, e.g., by enhancing the visibility of supernumerary arcs around the top or by creating branching effects known as "twinned rainbows." To check the accuracy of numerical optical models for rainbow scattering from such nonspherical drops, two simple and low-cost experiments are presented in this paper: (1) sessile, i.e., sitting, drops on ultrahydrophobic surfaces, and (2) glass beads in the shape of falling raindrops. The experimental results are compared to polarization-resolved Monte Carlo ray-tracing simulations, with special emphasis on circular polarization, which results from total internal reflections in these nonspherical scatterers.

Linear (in oscillation dimensionless amplitude) interaction between the modes of a nonspherical charged drop in an external electrostatic field

The stability of a heavily charged drop in a weak uniform electrostatic field (in which the equilibrium shape of the drop can be represented by a prolate spheroid) is calculated in the fourth order of smallness in the eccentricity of the spheroidal drop and in the first order of smallness in the drop oscillation dimensionless amplitude. It is found that as the order of approximation in eccentricity grows, so does the number of modes interacting with the initially excited mode. In the given order of smallness, the preferred (initially excited) mode is shown to interact with the nearest eight modes. The drop becomes unstable if such is the second mode.

Production of Particle‐Stabilized Nonspherical Emulsion Drops in Simple Shear Flow

AbstractNonspherical drops are of interest in the formation of microcapsules in life sciences like food, pharmacy, and cosmetics, agro and fine chemicals as well as material sciences. Out of many systems, particle‐stabilized emulsion drops, so‐called Pickering emulsions, exhibit an interesting formulation. Systems with Pickering particles applied in an excess amount were investigated. During deformation, the particles fully covered the enlarged drop interfaces and prevented its relaxation to a spherical drop shape. Nonspherical drops could be produced in simple shear flow using an adequate process routine. The production in a simple device is a promising high‐throughput alternative to microfluidic devices.

On scattering cross-section calculation accuracy of nonspherical particles of rain precipitation using the dipole scattering approximation

Comparative relationships of the numerical simulation results of the scattering cross-section (SCS) of raindrops have been presented using the approximate method of dipole scattering and the rigorous method of moments. The scope of applicability of the dipole scattering were also determined with due regard for the calculation accuracy of nonspherical drop SCS.

Formation of Particle Coated Fusiform Droplets via Lowering Interface Tension with Polyaluminum Sulfate

It was found that the interface tension between water and alkenyl succinic anhydride (ASA) was significantly reduced by polyaluminum sulfate (PAS), increased considerably though by TiO2 nanoparticle. PAS with basicity of 0.75 (PAS-0.75) reduced the interface tension to a larger extent than PAS with basicity of 0.3 (PAS-0.3). By reducing interface tension with PAS-0.75, ASA-in-water emulsion bearing fusiform geometries was constructed. The emulsion stabilized by PAS-0.3 and TiO2 nanoparticle bore spherical shapes with the exception when mass fraction of TiO2 nanoparticle was low, in which case fused nonspherical drops were formed. Forming nonspherical emulsion crucially depends on ASA-water interface tension, where a critical interface tension was identified to be 0.6–0.7 mN/m. The fusiform geometries were transformed into spherical shapes when interface tension was higher than 0.7 mN/m. Both the lowering mechanism of the interface tension and the formation mechanism of the fusiform emulsion were proposed.