Nonspherical liquid droplet falling in air

Numerical implementation of three-dimensional vectorial complex ray model and application to rainbow scattering of spheroidal drops

The rainbow patterns of oblate spheroidal drops have been observed in experiments nearly forty years ago [Nature312, 529 (1984)10.1038/312529a0]. However, the prediction for those complex patterns has been a challenge for conventional light scattering models. The vectorial complex ray model (VCRM) allows to account for the direction, the polarization, the phase, the amplitude and the wavefront curvature of waves and provides a powerful tool for the study of the light/electromagnetic wave interaction with a homogeneous object of any shape with smooth surface. In [Opt. Lett.46, 4585 (2021)10.1364/OL.434149], the authors have reported an important breakthrough of VCRM for the three-dimensional scattering (VCRM3D) and the simulated rainbow patterns of oblate drops. The present paper is devoted to the detailed description of the numerical implementation allowing the simulation of the 3D scattering field by a nonspherical particle. Its ability to predict both the fine and coarse intensity structures of the rainbows and the near-backward scattering patterns of spheroids is demonstrated. This work opens perspectives for exploring the 3D scattering characteristics of large objects with any smooth shape and developing relevant optical techniques for particle characterization.

Influence of Light-Intensity-Dependent Droplet Directionality on Dimensions of Structures Constructed Using an In Situ Light-Guided 3D Printing Method

As an alternative to conventional 3D printing methods that require supports, a new 3D printing strategy that utilizes guided light in situ has been developed for fabricating freestanding overhanging structures without supports. Light intensity has been found to be a crucial factor in modifying the dimensions of structures printed using this method; however, the underlying mechanism has not been clearly identified. Therefore, the light-intensity-dependent changes in the structure dimensions were analyzed in this study to elucidate the associated mechanism. Essentially, the entire process of deposition was monitored by assessing the behavior of photocurable droplets prior to their collision with the structure using imaging analysis tools such as a high-speed camera and MATLAB®. With increasing light intensity, the instability of the ejected falling droplets increased, and the droplet directionality deteriorated. This increased the dispersion of the droplet midpoints, which caused the average midpoints of the deposited single layers to shift further away from the center of the structure. Consequently, the diameter of the structure formed by successive stacking of single layers increased, and the layer thickness per droplet decreased. These led to light-intensity-dependent differences in the diameter and height of structures that were created from the same number of droplets.

Dislocated spots and triple splittings of natural rainbows generated by large drop distortions, oscillations, and tilts

For an accurate modeling of natural rainbows, it is necessary to take into account the flattened shape of falling raindrops. Larger drops do also oscillate, and their axes exhibit tilt angles with respect to the vertical. In this paper, I will discuss two rare rainbow phenomena that are influenced by these effects: bright spots belonging to various rainbow orders, but appearing at remarkable angular distances from their traditional locations, as well as triple-split primary rainbows. While the former have not been observed in nature so far, the latter have been documented in a few photographs. This paper presents simulations based on natural drop size distributions using both a geometric optical model, as well as numerically calculated Möbius shifts applied to Debye series data.

Shape Dynamics of Bouncing Droplets

Oscillating shape motion of a freely falling and bouncing water droplet has long fascinated and inspired scientists. We propose dynamic non-linear equations for closed, two-dimensional surfaces in gravity and apply it to analyze shape dynamics of freely falling and bouncing drops. The analytic and numerical solutions qualitatively well explain why drops oscillate among prolate/oblate morphology and display a number of features consistent with experiments. In addition, numerical solutions for simplified equations indicate nonlinear effects of nonperiodic/asymmetric motion and the growing amplitude in the surface density oscillations and well agree to previous experimental data.

Shape oscillations of a nonspherical water droplet

The dynamics of a nonspherical droplet falling in air is investigated via three-dimensional numerical simulations of the Navier-Stokes and continuity equations. The main focus of this work is to study the effects of the relative influence of surface tension force over the inertial force and the orientation of the droplet. The values of the dimensionless parameters considered in this study are similar to those of a typical falling raindrop. Our results obtained from the numerical simulations for low values of Galilei number agree well with the theoretical predictions in the microgravity condition and in the limit of creeping flow. However, in the inertia-dominated region and for high initial aspect ratio, the droplet undergoes predominant nonlinear oscillations and subsequently breaks up. To the best of our knowledge, none of the previous studies have investigated dynamics of a tilted drop and observed the behavior reported in the present study.

Investigation of Puffing and Micro-Explosion of Water-in-Diesel Emulsion Spray Using Shadow Imaging

Water-in-diesel emulsions potentially favor the occurrence of micro-explosions when exposed to elevated temperatures, thereby improving the mixing of fuels with the ambient gas. The distributions and sizes of both spray and dispersed water droplets have a significant effect on puffing and micro-explosion behavior. Although the injection pressure is likely to alter the properties of emulsions, this effect on the spray flow puffing and micro-explosion has not been reported. To investigate this, we injected a fuel spray using a microsyringe needle into a high-temperature environment to investigate the droplets’ behavior. Injection pressures were varied at 10% v/v water content, the samples were imaged using a digital microscope, and the dispersed droplet size distributions were extracted using a purpose-built image processing algorithm. A high-speed camera coupled with a long-distance microscope objective was then used to capture the emulsion spray droplets. Our measurements indicated that the secondary atomization was significantly affected by the injection pressure which reduced the dispersed droplet size and hence caused a delay in puffing. At high injection pressure (500, 1000, and 1500 bar), the water was evaporated during the spray and although there was not enough droplet residence time, puffing and micro-explosion were clearly observed. This study suggests that high injection pressures have a detrimental effect on the secondary atomization of water-in-diesel emulsions.