ILASS-Europe ‘99 SINGLE DROP SPLASH ON THIN FILM: MEASUREMENTS OF CROWN CHARACTERISTICS

Abstract

The impact of a single drop on a liquid film was studied by photographic techniques. A drop generator capable to produce single liquid (water) drops of millimetric size (with a good repeatability) was positioned at different distances from the horizontal wall onto which drops impacted by gravity. The wall was covered by a liquid layer whose thickness could be varied. The fluid motion was studied by means of a CCD camera (1μs exposure time) from different positions. In particular, the use of a transparent (glass) wall allowed to study the impact phenomenon from below by a proper optical set-up. Quantitative analysis of the crown evolution was then possible, crown diameter (internal and external), crown elevation and thickness were measured, with different degree of accuracy, as a function of impact Weber number and nondimensional film thickness. Number of jets protruding from the upper rim was also recorded as well as their average size and growth rate. The gathered quantitative data allowed a thorough analysis of the process, and some interesting features of crown evolution are reported together with comparison with existing models. INTRODUCTION When a drop impact vertically on a liquid film a axial-symmetric liquid sheet (crown) grows up and, depending on impinging drop size and velocity and liquid characteristics (like viscosity, density, surface tension), liquid jets may protrude from the crown and subsequently break-up to form secondary droplets. Theoretical models of crown evolutions have been proposed (Engel (1967), Maclin & Metaxas (1976), Yarin and Weiss (1995)) and recently many numerical simulation of the phenomenon have been performed (see for example: Rieber and Frohn (1998), Gueyffier and Zaleski (1998)). However fewer experimental results are available on the crown characteristics during evolution (see for example Mundo et al. (1995), Cossali et al. (1997)), despite of the need of data for models evaluation. The paper presents experimental results on crown characteristics (crown diameter, height thickness, number of jets), for a limited range of drop impact Weber number and film thickness, for single water drop impingement. Whenever possible, comparisons with available theoretical models were reported. EXPERIMENTAL SET-UP The experimental set-up comprised a needle suspended at a distance from the impact liquid film ranging between 0.3 and 0.9 m and connected to a small water tank; a small pressure pulse produced by the opening of a solenoid valve detached single drops from the needle. The repeatability of the drop diameter (measured from enlarged pictures of the falling drops) was better than 6%; terminal velocities ranged between 2.3m/s and 4.2 m/s. A thin cylindrical rubber or aluminium ring (diameter >50 mm) was stuck on a transparent glass window (thickness <3mm) and the inner region was filled with water to produce a thin liquid film onto which drops impinged. To maintain relatively constant the film thickness after the impact of several drops, a drain was inserted into the wall. The film thickness was measured by photographic enlargement and comparison. By using different rings, film thickness ranging between 1.1 and 4.3 mm were obtained. Pictures of the phenomenon were obtained by a CCD camera (PCO Flashcam 752x286): illumination was given by a lamp (flash duration 10 μs) controlled through a delay circuit triggered by the obscuration of a laser beam (imaged onto a photodiode and parallel to the film surface) caused by the passage of the falling drop. By varying the delay between the trigger signal and the flash, the entire process could be recorded. The choice of a transparent support for the liquid film allowed the observation of the splashing phenomenon from below, and through, the liquid film: a mirror was positioned underneath the glass support and the CCD camera was focused on the film surface through the mirror, this configuration allowed to measure the inner and outer crown radius and to count the number of jets protruding from the crown rim. The crown evolution was observed also from the side to measure the crown height and the jets growth. RESULTS AND DISCUSSION The experiments were performed maintaining constant the impacting drop diameter (Do=3.82mm); the drop generator was positioned to four different values obtaining four different Weber number (We=ρDoVo /σ) values; for each impacting velocity three different nondimensional film thickness (δ=h/Do) were set: δ=0.29, 0.67, and 1.13. Pictures of the event were taken at different times after drop impact (setting t=0 the time at which the drop touches the film), the uncertainty on timing was evaluated to be about 0.02ms. Pictures were taken, at equal times after impact, using the two set-up above described (from the side and from the below the target), in this way the splash event was observed at the same time from two different point of view, allowing to measure different crown characteristics. Crown diameter The crown evolution was analysed by measuring the radial extent of the crown. Some uncertainty is hidden into the definition of the “crown diameter”, in fact, as it can be observed in fig 3), the crown is not usually cylindrical, and the diameter of the external surface varies with the distance from the upper surface of the film. Two diameters where then defined when analysing the pictures taken from the side: the upper external diameter (Deu) and the lower external diameter (Del), the first measured at the base of the rim, the second at the crown base. The difficulties in defining exactly the position where to measure those diameters introduces an uncertainty connected to the operator that manually “measures” (by means of a proper image analysis software) the parameters. The error introduced by the operator was estimated by evaluating the discrepancies between parameters measured by two different operators on the same set of pictures and it was found to be of about 7%. The upper external diameter was found to be consistently smaller than the lower external diameter and the differences ranges between 14% and 24% of the average diameter (Dem=(Deu+Del)/2), depending slightly on drop velocity (the larger the velocity, the larger the difference). The radial evolution of the crown was also investigated by examining the pictures obtained from below the target, (see fig 1b)) and again uncertainties rise in defining the “crown diameter”. As figure 1 b) shows, it is always possible to observe a ring having larger luminosity which is evidently connected to the liquid crown. A simple simulation was performed to explain the particular intensity distribution: a crown profile like that reported in figure X6b) was used to evaluate, by a ray tracing method (taking into account Snell and Fresnel laws), the intensity distribution of the light falling on the crown from the top and crossing it. the result, shown in figure 1a) (and fig. 2b), bears a certain resemblance to the measured light intensity (fig 1 b)), the thickness of the inner ring appears to be related to the crown thickness, and it can be considered, apart of a scaling parameter of the order of unity, a measure of the crown thickness. Then, from the picture taken from below, it is possible to define two more “crown diameters” (see fig 1b)): the inner diameter (Din) and the outer diameter (Dou), and figure 4) reports as an example the relations among them and Deu , Del. To compare the results coming from different experimental conditions, the nondimensional time τ=Vo t / Do (Vo= impact velocity, Do=impinging drop diameter) and the nondimensional “crown diameters” ∆x = Dx/Do will be used. Following Yarin and Weiss (1995) the evolution of the crown size is supposed to follow the relation: ( ) o x C τ τ − = ∆ (1) with n=0.5. However, such a relation is not supposed to hold for all the crown evolution, and the attempts to fit the whole experimental data with equ.1) were not successful. In order to find the constants (n, C, τo) in 1) the following procedure was used. Let ( ) τ f x = ∆ be the relation describing the evolution of the nondimensional crown diameter, then it is always possible to calculate: ( ) ( ) ∫ = τ

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Cite this paper

@inproceedings{CogheILASSEuropeS, title={ILASS-Europe ‘99 SINGLE DROP SPLASH ON THIN FILM: MEASUREMENTS OF CROWN CHARACTERISTICS}, author={Aldo Coghe and Cossali and Massimo Marengo} }