CHARACTERISTICS OF DROP IMPACT ON ELASTIC AND COMPLIANT SURFACES

Abstract

Due to its importance and wide application, drop impact on solid and liquid surfaces have been well studied. However, with the progress and wider applications of more sophisticate materials, the relatively less studied physical properties and behavior of a drop impact on elastic or compliant surfaces gradually become more important. Three kinds of common liquid drops impact on both elastic and compliant surfaces were studied experimentally using high-speed digital camera with regular light source at three different impact speeds. The impact effects on compliant surface and the expansion-contraction processes of impacted drops were recorded and analyzed. Dimensionless diameter-time relationships of tested liquids were compared. Maximum spreading diameter of each impact condition was examined and compared to impact on solid surface case. The results also show that splashing criteria developed from solid surface impact results may not be applicable to impacts on elastic and compliant surfaces. INTRODUCTION The phenomenon of liquid drop impact on surfaces is very common in nature and also important in many industrial applications, such as spray painting, spray cooling, combustion, ink-jet printers, criminal forensics, fire suppression by sprinkler or water spray, drug spray in biotechnology, and even transportation vehicles in rain. It has been studied since the late 19 century. Most of the studies to date have focused on two aspects: liquid drop impact on rigid surfaces and on a liquid surface. Many experimental observations, theories, and even simulations have been reported as seen in [4][5][6][7][8] and references cited therein. In the contrast to these well-studied cases, very little is known about the behavior of a liquid drop impacting on a compliant surface [2] or an elastic surface. These kinds of non-rigid solid surfaces are actually as common as rigid surfaces in the nature, and also become more and more important in industry and rising biotechnology applications. For example, leaking oil drops falling on high temperature solid surfaces in a machine room will splash, increase oil mist density, and thus raise the risk of fire. A possible solution is to cover hot pipes and machines with materials having compliant surface. More understanding on drop falling on such kind of surfaces could help us verify and develop this fire-prevention method. On medicine application aspect, drug spray on skins (a kind of compliant surface) is a similar problem. More understanding of drop impact behavior will improve drug spray methods. The drop impact dynamics is largely controlled by the initial energy state of the fluid that is a function of the mass and velocity (V) of the drop, the drop’s original size (diameter, D), and energy storage and dissipation mechanisms during the impact deformation process, that is density (ρ), surface tension (σ) and kinematic viscosity (ν). Therefore, these characteristics can be expressed in several dimensionless numbers by dimensional analysis. Reynolds number (VD/ν, Weber number (ρVD/σ), and Ohnesorge number (μ/(ρDσ)=(We/Re) ) are usually used. Other parameters such as the interface contact angle and surface roughness also play important roles in impact dynamics, mainly through the determination of the final diameter and possibility of controlling wetting and fingering instabilities along the contact line. The material behavior of elastic surface may be approached by material mechanics using parameters like surface elasticity and Poisson ratio. On the contrary, the behavior of compliant surfaces was less studied [1][2] and more complex than liquid, rigid or elastic surfaces, mainly due to more structure parameters like damping coefficient, surface thickness, Young’s modulus and tension per width of the surface [1]. Thus, there is no theoretical approach of drop impingement on these kinds of surfaces to date [3]. The present study’s object is to provide qualitative and some quantitative experimental observations for further study in the future. EXPERIMENTAL METHOD The experiment was designed to generate liquid drops impacting on different kinds of surfaces, including rigid surface, compliant surface, and elastic surface. The drop was generated by carefully and slowly pressing a dropper to let the drop drip off when its weight is larger than surface tension. The drop sizes were examined and appeared to be quite consistent since the size is determined by the liquid surface tension, density and the diameter of dropper’s tube. The dropper was set at three different heights to generate different drop impact speeds, and thus different Reynolds numbers. The impact surface was set on the top of a can and was exchangeable, too. The compliant surface was constructed using a plastic film (BOPP, Bi-axially-Oriented Poly Propylene, 35μm thick, density = 0.91g/cm, produced by Nan-Ya Plastics Co.) with water underneath. Water underneath serves as a kind of damper and may change the property of the impact surface. The elastic surface was constructed in the same way, but with air underneath. Another kind of plastic film (PVC) was also tried for elastic surface for preliminary test of the effect of material on the splashing behavior on elastic surface. The plastic film were fixed on the wall of the can by elastic band. Therefore, the surface tension of the compliant surface and elastic surface were fixed for the present experiments. Photo-studio-type continuous light was used for photographic record. A paper diffuser was used in front of the light source to diffuse light. A high speed digital CCD camera (Dalsa CA-D6 with 260 x 260 pixel resolution at 955 frame/sec recording rate) was used to record the impact process. The camera was set on the opposite side of light source and took pictures from about 15 degree elevation angle. The images recorded by the camera were sent to a personal computer immediately for further image processing. The apparatus and instrument configuration was shown in Figure 1. The liquids used in the experiments include water, ethyl alcohol, and lubrication oil 20W/50 (China Petroleum Co.). Their properties and drop properties as well as test conditions are listed in Table 1. Low impact velocities were determined from the last two successive images before the drop hit the surface by dividing the distance of the same drop on these two frames by their time interval. For middle and high impact velocities, the velocities were obtained by dividing the streak distance of the drop by camera’s exposure time (0.974ms) right before impact. The measurement uncertainty caused by these methods was less than 10%. RESULTS AND DISCUSSION (1) Typical Impact Process: A drop’s typical impact process on a compliant surface or elastic surface is similar to that on a rigid surface. It includes spreading, fingering, and contracting steps. However, there are some differences. Figure 2 shows a typical water drop impact process on a compliant surface from 320mm height. It can be seen that the compliant surface formed a waving motion caused by the drop’s impact immediately after the impact. A bright circle on the compliant surface was spreading out. For low impact velocity case, the wave motion was less visible. The fingering process can also be seen in the picture taken 5.24ms after impact. Then, the drop started to contract and capillary waves can be seen inside the outer ring in pictures taken at 13.61, 15.71, and 20.94ms after impact. Finally, the drop contracted to a half sphere shape. It is also clear that no splashing at all was observed. The waving motion of elastic surface after drop impact was less obvious than that of compliant surface, mainly due to its much faster speed. (2) Maximum spreading diameter: Early findings of various aspects of liquid drop impact on rigid and liquid surfaces were reviewed by Rein [6]. One of the traditional attentions of the impact process is the maximum spreading diameter, dmax. Usually, it is correlated with Reynolds number and Weber number. But, Scheller and Bousfield recently proposed a more accurate empirical formula to correlate non-dimensional maximum spreading diameter, dmax/D, with Reynolds number and Ohnesorge number for rigid impact surface [7]: dmax/D=0.61(ReOh) (1) The present experiment results of non-dimensional maximum spreading diameter was shown in Figure 3 with Equation (5). Although the present data are for elastic or compliant impact surfaces, the correlation seems to work as well. This may be explained by the fact that the elastic and compliant surfaces used in the experiments were actually closer to rigid surface than to other kinds of interfaces. (3) Splashing: Whether a drop impact event will lead to liquid splashing due to the breakup mechanism of fingering phenomenon during the drop spreading process is very important to many applications. For example, in the spray painting or ink-jet printer cases, engineers wish the splashing phenomenon can be reduced or even vanished in order to save material or maintain work quality. Thus, splashing has been another focus in the study of drop impact. Various kinds of methods to reduce or prevent splashing are under investigating, including changing fluid properties and changing impact surface properties. Most past studies concentrated on drop impact on rigid surfaces. Mundo proposed a criterion of splashing condition for rigid impact surface based on a series of experiments [5]. This criterion is a function of Reynolds number and Ohnesorge number only: