Constant Weber Number Research Articles

Departure Velocity of Rolling Droplet Jumping.

Droplet jumping phenomenon widely exists in the fields of self-cleaning, antifrosting, and heat transfer enhancement. Numerous studies have been reported on the static droplet jumping while the rolling droplet jumping still remains unnoticed even though it is very common in practice. Here, we used the volume of fluid (VOF) method to simulate the droplet jumping induced by coalescence of a rolling droplet and a stationary one with corresponding experiments conducted to validate the correctness of the simulation model. The departure velocity of the jumping droplet was the main concerned here. The results show that when the center velocity of the rolling droplet (V0 = ωR, where ω is the angular velocity of the rolling droplet and R is the droplet radius) is fixed, the vertical departure velocity satisfies a power law which can be expressed as Vz,depar = aRb. When the droplet radius is fixed, the vertical departure velocity first decreases and then increases if the center velocity exceeds a critical value. Interestingly, the critical center velocity is demonstrated to be approximately 0.76 times the capillary-inertial velocity, corresponding to a constant Weber number of 0.58. Different from the vertical departure velocity, the horizontal departure velocity is basically proportional to the center velocity of the rolling droplet. These results deepen the understanding of the droplet jumping physics, which shall further promote related applications in engineering fields.

Drop deformation and breakup in flows with shear

A Volume of Fluid (VOF) method is applied to study the deformation and breakup of a single liquid drop in shear flows superimposed on uniform flow. The effect of shearing on the breakup mechanism is investigated as a function of the shear rate. Sequential images are compared for the parameter range studied; density ratios of liquid to gas of 20, 40, and 80, viscosity ratios in the range 0.5–50, Reynolds numbers between 20, a constant Weber number of 20, and the non-dimensional shear rate of the flow G=0–2.1875. It is found that while shear breakup remains similar for all values of shear rate considered, other breakup modes observed for uniform flows are remarkably modified with increasing shear rate. The time required for breakup is significantly decreased in strong shear flows. A simple model predicting the breakup time as a function of the shear rate and the breakup time observed in uniform flows is suggested.

Drop deformation and breakup

A Volume of Fluid (VOF) method is applied to investigate the deformation and breakup of an initially spherical drop in the bag- and shear breakup regimes, induced by steady disturbances. The onset of breakup is sought by studying steady-shape deformations while increasing the Weber number until breakup occurs. A parameter study is carried out applying different material properties and a wide range of drop Reynolds numbers in the steady wake regime. Density ratios of liquid to gas of 20, 40, and 80, viscosity ratios in the range 0.5–50, and Reynolds numbers between 20 and 200 are investigated for a constant Weber number of 20. The critical Weber number is found to be 12, in agreement with observations of earlier studies. For Weber number of 20 varying density, viscosity ratios and Reynolds numbers, interesting mixed breakup modes are discovered. Moreover, a new regime map including all modes observed is presented. A criterion for the transition between bag- and shear breakup is defined relating the competing inertial and shear forces appearing in the flow. Furthermore, results on breakup times and the time history of the drag coefficient are presented; the latter is concluded to be a potential parameter to indicate the occurrence of breakup.

Dynamic Impact Behavior of Water Droplet on a Superhydrophobic Surface in the Presence of Stagnation Flow

The following study investigates splashing of impinging water droplets on superhydrophobic surfaces with and without the presence of a stagnation flow. Droplets were accelerated by either gravity or gravity and co-flow. By changing the height and the air flow velocity different combinations of stagnation flow and droplet velocity were created. The spreading diameter, spreading velocity and contact time were studied for different air and droplet speeds. It was clearly observed that for a fixed impact velocity (i.e. constant Weber number), the presence of the stagnation flow promotes splashing and formation of satellite droplets. Consequently, for the co-flow droplet impact experiments, the mass of the recoiled droplet is significantly smaller than that of the impinging droplet in still air.

Numerical simulation of membrane emulsification: Effect of flow properties in the transition from dripping to jetting

In this work, the roles of the Weber number ( We) and Capillary number ( Ca) in characterizing different stages, i.e. dripping, jetting and transition states, of droplet formation in a membrane emulsification process have been investigated. A numerical investigation of the emulsification process has been investigated for a range of We (0.009 ≤ We ≤ 1.82) and for Ca (0.004 ≤ Ca ≤ 0.04). The full transient simulation of the process was made using volume of fluid (VOF)/finite volume method and was performed starting from the injection of the dispersed phase to the breakup into droplets, for different operating conditions. Based on the study, a critical Weber number ( We c ) has been derived at which the process shows transition from dripping to jetting. Some interesting phenomena such as sudden decrease of droplet diameter and high rate of droplet formation have been observed during the transition from dripping to jetting. The qualitative differences of dispersed phase topology in case of less confined case (membrane emulsification) have been discussed compared to more confined situations (T-junction emulsification) available in the literature. It has been observed that, although the dripping and jetting regions in the present work have shown some topological differences compared to those in T-junction emulsification, the transition phenomenon between the two regions are remarkably similar in both cases. Two ways of dripping to jetting transition have been observed: one at constant Capillary number while varying the Weber number and another at the constant Weber number while varying the Capillary number. Qualitative differences between the dispersed phase flow controlled ( We dependence) and surface tension controlled ( Ca dependence) transition were observed. In dispersed phase flow controlled case, diameter of the droplet increases initially then decreases rapidly while in surface tension controlled case the diameter decreases continuously. Finally, at large values of the Capillary number a transition from dripping to jetting was observed in the membrane emulsification system, similar to the case of drop formation from a nozzle in an unbounded fluid under gravity.

Drop Impact on Porous Superhydrophobic Polymer Surfaces

Water drop impacts are performed on porous-like superhydrophobic surfaces. We investigate the influence of the drop size and of the impact velocity on the event. The Cassie-Baxter/Wenzel transition is observed to be a function of the drop size, as well as the outcomes of the impact or deposition process, which can be deposition, rebound, sticking, or fragmentation. A quantitative analysis on the experimental conditions required to observe rebound is provided. Our analysis shows that the wettability hysteresis controls the limit between deposition and rebound events. This limit corresponds to a constant Weber number. A survey of literature results on impact over patterned superhydrophobic surfaces is provided as a comparison.

Mili-Scale Visualization of Bubble Growth-Translation and Droplet Impact Dynamics

The dynamic behavior of an air bubble, emanating from a 0.32 mm i.d., 0.64 mm o.d., vertical capillary-tube orifice with a bubble interval of 0.22–0.28 s at constant pressure and adiabatic (T=25°C) conditions, as well as droplet impact and spreading on a hydrophobic surface are characterized. Images of the mili-scale spatial-temporal evolution of bubbles (embryonic appearance at orifice tip → growth and detachment → translation) as well as droplets were acquired using a high-speed (5000 frames/s) digital video camera fitted with a 8× optical zoom lens. It was triggered through a computer interface to record continuous high-speed video from which any desired frame can be captured by digital-video-processing software; the equivalent departure diameter was estimated by area-averaging using image processing software. The impact, spreading, and recoil behaviors of ethanol and water droplets on a horizontal stainless steel surface are depicted in Fig. 1. For constant Weber number (We∼10), the spreading and recoil dynamics in the two cases are significantly different. Higher wettability of ethanol promotes greater spreading and dampens recoil in comparison with that seen in water. Figure 2 depicts the growth of an air bubble in pools of ethanol and water. While displaying similar ebullience, a bubble of smaller size and surface age is produced in low-surface-tension ethanol. Dynamic shape variations of the air bubble as it translates upwards in the pool are seen in Fig. 3. From a nearly spherical, tear-drop bubble, the shape changes to an oblate ellipsoid during translation, and surface tension effects are manifest only in the size of respective bubbles.

Collisions between Small Precipitation Drops. Part I: Laboratory Measurements of Bounce, Coalescence, and Temporary Coalescence

Self-collection efficiencies were measured for isolated drop pairs failing at terminal velocity using orthogonal cameras to obtain the horizontal offset of the drops before collision and the collision outcome. Data were obtained on four different drop-size pairs over a range of impact Weber number (1–10) and size ratio (0.45–0.73). Collision offsets and outcomes were recorded during 45 experiment runs as a function of drop charge. The collision results from all 4200 events were tabulated by offset and charge, and the coalescence efficiency was determined for each run as a function of charge. Collision results revealed a coalescence region for small offset and a bounce region at intermediate-to-large offset and low-to-intermediate charge. The critical offset that separated the regions of coalescence and bounce was independent of charge. At higher values of charge, increasing charge was found to induce permanent and/or temporary coalescence from smaller and larger offsets until bounce was completely eliminated. In the offset range for temporary coalescence, the filament connecting the separating drops often collapsed into one and, occasionally, two satellite drops. Mean satellite sizes of 58–81-µm radius were generally consistent with previous measurements using colliding drop streams. The production of satellite drops by colliding precipitation drops should provide precipitation embryos that would accelerate the accretion of cloud water in warm-base convective clouds. Coalescence efficiencies of 15%–55% at minimal charge were significantly lower than previously reported for smaller drops; therefore, the results indicate a further reduction in the growth rate of precipitation drops. The efficiencies did not vary in a simple way with either Weber number or size ratio. For a constant size ratio (p ≈ 0.7) the coalescence efficiency decreased with increasing Weber number, whereas for a constant Weber number (We ≈ 4.2) the coalescence efficiency decreased with increasing size ratio. An excellent fit to the laboratory coalescence efficiencies, using the theoretical scaling for inelastic collisions, is presented in a companion paper. The resulting formulas for precipitation drops will allow application of these findings to self collection, a process that controls the spreading of raindrops to larger sizes and the growth of radar reflectivity.