A liquid drop impacting a solid surface may splash either by emitting a thin liquid sheet that subsequently breaks apart or by promptly ejecting droplets from the advancing liquid-solid contact line. Using high-speed imaging, we show that surface roughness and air pressure influence both mechanisms. Roughness inhibits thin-sheet formation even though it also increases prompt splashing at the advancing contact line. If the air pressure is lowered, droplet ejection is suppressed not only during thin-sheet formation but for prompt splashing as well.PACS numbers: 47.20.Cq, 47.20.Gv, 47.20.Ma,Will a drop hitting a dry surface splash? Different criteria [1][2][3][4][5] have been proposed to predict when such a drop will splash by comparing the roughness of the solid surface with hydrodynamic length scales, which depend on parameters such as the drop velocity, radius, viscosity and surface tension. Several years ago Xu et al. [6,7] found that these criteria ignore a crucial parameter: the ambient gas pressure, P . When a drop splashes on a smooth surface it spreads smoothly forming a lamella before ejecting a thin sheet that subsequently breaks up into secondary droplets. As P is reduced below a threshold pressure, the drop no longer splashes [6][7][8][9][10]. On the other hand, when splashing occurs on a rough surface, no thin sheet is formed and droplets are ejected directly from the advancing liquid-substrate contact line via a "prompt" splash [1][2][3][4]8].It has been suggested that thin-sheet splashes depend on air pressure while prompt splashes do not and depend only on surface roughness [8]. Here we show that the situation is more complex in that both types of splashing depend, albeit in opposite ways, on surface roughness. In particular, we observe four distinct regimes. In agreement with earlier results [4], we observe a thin-sheet splash on very smooth surfaces and a prompt splash on very rough ones. However, at intermediate roughness, we identify two new regimes: at low viscosities both prompt and thin-sheet splashes occur during a single impact, while at high viscosities neither splash is formed. In addition, as found for thin-sheet splashing [6], we find that a drop deposits smoothly on a rough surface if P is low enough. Clearly, the role of both air pressure and substrate roughness must be considered in all cases.The experiments were conducted with silicone oil (PDMS, Clearco Products) with kinematic viscosity ν ranging from 5 cSt to 14.4 cSt and surface tension σ between 19.7 dyn/cm and 20.8 dyn/cm. The basic results were replicated using water/glycerin mixtures with a similar viscosity range but higher surface tension: σ=67 dyn/cm. Low-viscosity impacts were studied with ethanol. Drops with reproducible diameter D=3.1 mm were produced using a syringe pump (Razel Scientific, Model R99-E) and released in a chamber from a height above a substrate. This height set the impact velocity u 0 which was varied between 2.7 m/s and 4.1 m/s. These parameters determine the Reynolds number Re=Du 0 /ν giving the rati...

After impact onto a smooth dry surface, a drop of viscous liquid initially spreads in the form of a thick lamella. If the drop splashes, it first emits a thin fluid sheet that can ultimately break up into droplets causing the splash. Ambient gas is crucial for creating this thin sheet. The time for sheet ejection, t{ejt}, depends on impact velocity, liquid viscosity, gas pressure, and molecular weight. A central air bubble is trapped below the drop at pressures even below that necessary for this sheet formation. In addition, air bubbles are entrained underneath the spreading lamella when the ejected sheet is present. Air entrainment ceases at a lamella velocity that is independent of drop impact velocity as well as ambient gas pressure.

We explore the evolution of a splash when a liquid drop impacts a smooth, dry surface. There are two splashing regimes that occur when the liquid viscosity is varied, as is evidenced by its dependence on ambient gas pressure. A high-viscosity drop splashes by emitting a thin sheet of liquid from a spreading liquid lamella long after the drop has first contacted the solid. Likewise, we find that there is also a delay in the ejection of a thin sheet when a low-viscosity drop splashes. We show how the ejection time of the thin sheet depends on liquid viscosity and ambient gas pressure.PACS numbers: 47.20.Gv,47.55.Ca,The discovery by Xu et al. [1], that the splash of a liquid drop hitting a smooth dry surface is suppressed by lowering the ambient air pressure, has galvanized research on gas-liquid interactions during impact. However, despite numerous experimental [2][3][4][5][6][7][8], theoretical [9,10], and numerical [3,11,12] efforts, the mechanism by which air causes a drop to splash remains unresolved.The situation is made more complicated, by the influence of liquid viscosity µ on the interplay of gas and liquid. At low viscosities, a beautiful crown-shaped corona emerges almost immediately after impact as shown in Fig. 1(a) [1,2]. However, a small increase in viscosity reveals a splash with a strikingly different appearance, that evolves much more slowly ( Fig. 1(b)). This higher-µ drop first contacts the surface and then spreads smoothly as a thick lamellar sheet. From this lamella, a thinner sheet of liquid is subsequently ejected almost parallel to the substrate. It is the thin sheet that eventually breaks apart to form the splash [4]. The existence of two distinct splashing regimes is made manifest in the non-monotonic dependence of the threshold pressure, P T , which is the ambient gas pressure above which splashing occurs, on the viscosity [2]. As shown in Fig. 2, P T decreases with increasing viscosity at low-µ, while the trend is reversed at higher µ.These differences have been taken to suggest that distinct mechanisms might underlie the two types of splash. Indeed, theories for low-µ splashes have been proposed that do not take into account any spreading of a liquid film on the substrate before the onset of the splash [9,10]. On the other hand, the fact that, regardless of viscosity, splashes are invariably suppressed when the ambient pressure is sufficiently low suggests that there may be a common mechanism for both the violent corona and the slowly evolving thin sheet. It is therefore imperative that one investigate whether the splash mechanisms in these two cases have common features even though the timescales for corona (or thin-sheet) ejection and the overall shape of the splashing drops differ dramatically. This paper studies the onset of thin-sheet and corona ejection in the two cases. As previously noted, at high-µ, thin-sheet ejection is delayed when the pressure is lowered [4]. The major conclusion from the present work is that this is also true in the low-viscosity regime. Corona ejection ...

The ambient gas pressure is determined for the onset of splashing of low-viscosity liquid drops on smooth dry surfaces as we change the control parameters: drop impact velocity, drop radius, viscosity, surface tension, density, and gas molecular weight. This threshold pressure indicates that there are two distinct regimes when drop impact velocity is varied. By rescaling data using functions of only three dimensionless numbers, the commonly used Reynolds and Weber numbers, as well as the ratio of drop radius to gas mean free path, all data is collapsed to a single curve that encompasses both regimes.

We examine Illinois educational data from standardized exams and analyze primary factors affecting the achievement of public school students. We focus on the simplest possible models: representation of data through visualizations and regressions on single variables. Exam scores are shown to depend on school type, location, and poverty concentration. For most schools in Illinois, student test scores decline linearly with poverty concentration. However, Chicago must be treated separately. Selective schools in Chicago, as well as some traditional and charter schools, deviate from this pattern based on poverty. For any poverty level, Chicago schools perform better than those in the rest of Illinois. Selective programs for gifted students show high performance at each grade level, most notably at the high school level, when compared to other Illinois school types. The case of Chicago charter schools is more complex. Up to 2008, Chicago charter and neighborhood schools had similar performance scores. In the last few years, charter students' scores overtook those of students in traditional schools as the number of charter school locations increased.