11 research outputs found
Scaling of the Splash Threshold for Low-Viscosity Fluids
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.Comment: 5 pages, 5 figure
Patterns in Illinois Educational School Data
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. In the last six years, their students' scores overtook those of
students in traditional Chicago high schools.Comment: 9 pages, 6 figure
Thin Film Formation During Splashing of Viscous Liquids
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, , 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.Comment: 8 pages, 11 figure
Creation of prompt and thin-sheet splashing by varying surface roughness or increasing air pressure
A liquid drop impacting a solid surface may splash 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 air
pressure and surface roughness influence both splash mechanisms. Roughness
increases prompt splashing at the advancing contact line but inhibits the
formation of the thin sheet. If the air pressure is lowered, droplet ejection
is suppressed not only during thin-sheet formation but for prompt splashing as
well. The threshold pressure depends on impact velocity, liquid viscosity and
surface roughness
Jamming Transition In Non-Spherical Particle Systems: Pentagons Versus Disks
We investigate the jamming transition in a quasi-2D granular material composed of regular pentagons or disks subjected to quasistatic uniaxial compression. We report six major findings based on experiments with monodisperse photoelastic particles with static friction coefficient μ≈1. (1) For both pentagons and disks, the onset of rigidity occurs when the average coordination number of non-rattlers, Znr, reaches 3, and the dependence of Znr on the packing fraction ϕ changes again when Znr reaches 4. (2) Though the packing fractions ϕc1 and ϕc2 at these transitions differ from run to run, for both shapes the data from all runs with different initial configurations collapses when plotted as a function of the non-rattler fraction. (3) The averaged values of ϕc1 and ϕc2 for pentagons are around 1% smaller than those for disks. (4) Both jammed pentagons and disks show Gamma distribution of the Voronoi cell area with same parameters. (5) The jammed pentagons have similar translational order for particle centers but slightly less orientational order for contacting pairs compared to jammed disks. (6) For jammed pentagons, the angle between edges at a face-to-vertex contact point shows a uniform distribution and the size of a cluster connected by face-to-face contacts shows a power-law distribution
Jamming Transition In Non-Spherical Particle Systems: Pentagons Versus Disks
We investigate the jamming transition in a quasi-2D granular material composed of regular pentagons or disks subjected to quasistatic uniaxial compression. We report six major findings based on experiments with monodisperse photoelastic particles with static friction coefficient μ≈1. (1) For both pentagons and disks, the onset of rigidity occurs when the average coordination number of non-rattlers, Znr, reaches 3, and the dependence of Znr on the packing fraction ϕ changes again when Znr reaches 4. (2) Though the packing fractions ϕc1 and ϕc2 at these transitions differ from run to run, for both shapes the data from all runs with different initial configurations collapses when plotted as a function of the non-rattler fraction. (3) The averaged values of ϕc1 and ϕc2 for pentagons are around 1% smaller than those for disks. (4) Both jammed pentagons and disks show Gamma distribution of the Voronoi cell area with same parameters. (5) The jammed pentagons have similar translational order for particle centers but slightly less orientational order for contacting pairs compared to jammed disks. (6) For jammed pentagons, the angle between edges at a face-to-vertex contact point shows a uniform distribution and the size of a cluster connected by face-to-face contacts shows a power-law distribution
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Patterns in Illinois educational school data
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
Collisional model of the drag force of granular impact
A dense, dry granular target can cause a free-falling intruding object to come to an abrupt stop as its momentum is lost to the grains. An empirical force law describes this process, characterizing the stopping force as the sum of depth-dependent friction and velocity-dependent inertial drag. However, a complete interpretation of the stopping force, incorporating grain-scale interactions during impact, remains unresolved. Here, the momentum transfer is proposed to occur through sporadic, normal collisions with clusters of high force-carrying grains at the intruder’s surface. To test this model in impact experiments, we determine the forces acting on an intruder decelerating through a dense granular medium using high-speed imaging of its trajectory. We vary the geometry of the impacting object to infer intruder-grain interactions. As a result, we connect the inertial drag to the effect of intruder shape based on the proposed collisional model. These impact studies serve as an approach to understand dynamic force transmission in granular media