Large Force Fluctuations in a Flowing Granular Medium

We report the characteristics of the temporal fluctuations in the local force delivered to the wall of a 2D hopper by a granular medium flowing through it. The forces are predominantly impulsive at all flow rates for which the flow does not permanently jam. The average impulse delivered to the wall is much larger than the momentum acquired by a single particle under gravity between collisions, reflecting the fact that momentum is transferred to the walls from the bulk of the flow by collisions. At values larger than the average impulse, the probability distribution of impulses is broad and decays exponentially on the scale of the average impulse, just as it does in static granular media. At small impulse values, the probability distribution evolves continuously with flow velocity but does not show a clear signature of the transition from purely collisional flow to intermittently jamming flows. However, the time interval between collisions tends to a power law distribution, $P(\tau)\sim \tau^{-3/2}$, thus showing a clear dynamical signature of the approach to jamming.Comment: 4 pages, 3 figure

Force-velocity correlations in a dense, collisional, granular flow

We report measurements in a 2-dimensional, gravity-driven, collisional, granular flow of the normal force delivered to the wall and of particle velocity at several points in the flow. The wall force and the flow velocity are negatively correlated. This correlation falls off only slowly with distance transverse to the flow, but dies away on the scale of a few particle diameters upstream or downstream. The data support a picture of short-lived chains of frequently colliding particles that extend transverse to the flow direction, making transient load-bearing bridges that cause bulk fluctuations in the flow velocity. The time-dependence of these spatial correlation functions indicate that while the force-bearing structures are local in space, their influence extends far upstream in the flow, albeit with a time-lag. This leads to correlated velocity fluctuations, whose spatial range increases as the jamming threshold is approached.Comment: to be submitted for publicatio

Simultaneous Measurement of Changes in Thickness and Refractive Index of Weakly Absorbing Self-Standing Solid Films Using Optical Interferometry

A nondestructive optical interferometric method, which enables a direct and simultaneous measurement of small changes in both thickness and refractive index of thin films, is described. Optical interferometric methods are sensitive to the changes in the optical path length (the product of the refractive index and the physical thickness) through the film. Thus, when the film is subjected to changing environmental conditions such as changing temperature or humidity, it is a challenge to determine the change in thickness and the change in refractive index separately, using interferometry. By simultaneously monitoring two different sets of interference fringes, i.e., transmission and reflection fringes, we have been able to successfully address this challenge. Our measurements on well-characterized pedigree glass samples are presented. The results agree well with the expected values for these samples, supporting the feasibility of this characterization technique to new materials. Self-standing, transparent (weakly absorbing) films ranging in thickness from tens to hundreds of microns can be characterized from direct measurements

Search for an Instability on a Quenched-Liquid Interface

We searched for signs of an instability on the interface between the two phases of a binary-liquid mixture, isobutyric acid and water, after the mixture was quenched further into the two-phase region. Such an instability would be the liquid-liquid analog of the Mullins-Sekerka instability seen in quenched alloys. Never is any dramatic growth observed, but under conditions of small dimensionless quench depth (theta\u3c1.5×10−3), the intensity of light scattered from the interface grows for small values of the momentum transfer k

Evidence for Coupling of Velocity and Composition Fluctuations in a Binary Liquid Mixture

A critical mixture of isobutyric acid and water was quenched from the one-phase region into the two-phase region and, after the spinodal ring was well developed, a reverse quench returned the system to the one-phase region. Light-scattering measurements for this process exhibit a clearly nondiffusive relaxation which, at least for early times after the quench reversal, is in good agreement with Ruiz\u27s scheme for the coupling of velocity and composition fluctuations

Active-Coupling Mixing Times for a Stirred Binary Liquid

Mixing times measured for a stirred critical binary liquid mixture are seen to vary dramatically with Reynolds number, Prandtl number, and the initial value of the order parameter. These variations are far too large to be explained by passive-mixing calculations; they also differ in significant respects from the active-mixing predictions of Ruiz and Nelson

The Effect of Continuous Stirring on Off-Critical and Critical Samples of a Phase Separating Binary Liquid Mixture

The effect of shear on phase separation in a continuously stirred mixture of isobutyric acid and water has been studied. The data for the onset of phase separation in the stirred samples that are as far away as 500 mK from the critical point compare favorably with the theory of Onuki and Takasue and with similar measurements on very off-critical mixtures of 2-6 lutidine plus water reported by Min et al. However, as the composition gets closer to the critical composition significant differences arise. The main feature is that the measured suppression in temperature peaks at an off-critical composition which is dependent on the stirring frequency. A simple, analytical calculation is found to show the same feature

Study of the Effect of Relativistic Time Dilation on Cosmic Ray Muon Flux - Undergraduate Modern Physics Experiment

An experiment to study the effect of relativistic time dilation on secondary muon fluxes observed at different altitudes is described in this article. Muons, produced as secondary particles from the interaction of primary cosmic rays with the upper atmosphere, form a natural and abundant source of subatomic ``clocks\u27\u27 moving at very high speeds. The measured muon flux on a mountain relative to that measured at sea level can be compared to predictions from calculations that take into account the relativistic time dilation in the muon frame. Situations under which such an experiment can be successfully performed are explored with a day-long field trip to a nearby mountain. This experiment has been developed at Smith College as a module in the Five College cooperative undergraduate advanced laboratory course (other participating institutions are Amherst College, Mount Holyoke College, and the University of Massachusetts)

Turbulent Suppression of Spinodal Decomposition

Light scattering experiments reveal a strong suppression of phase separation near the critical point of a vigorously stirred binary liquid mixture. For stirring Reynolds numbers R ranging from 6.0 × 103 to 4.5 × 103, the apparent critical temperature is depressed by ∼1 mK to ∼50 mK. This temperature depression ΔTc can be fitted to a power law ΔTc∼Rλ where λ∼2. The magnitude of ΔTc is consistent with simple models which attribute the effect to the suppression of composition fluctuations by shear; however, these models predict λ≃0.80 in contrast to the observed value of ∼2. Below the apparent critical temperature the turbidity τ changes significantly throughout a temperature range of tens of millikelvin following a power law τ∝(Tc−T)ζ where ζ increases from ∼1 to ∼6 as R is increased

A Demonstration of Phonons That Implements the Linear Theory

Beads on a vibrating wire are used to simulate the discrete structure of a solid-state material. The novel idea of the experiment is to use very small oscillation amplitudes of the wire to avoid nonlinearities in the interaction. We achieve a good signal-to-noise ratio using a lock-in technique. We find quantitative agreement between theory and experiment for not only a mono- and a diatomic chain, but also for the bare wire. The latter agreement is the crucial aspect that distinguishes our experiment from previous ones. This agreement assures that the fundamental assumption of the theory ~Hooke’s law! is satisfied. We show that the properties of phonon dispersion curves are not special, and that the same band structures occur when the wavelength of any wave becomes comparable to the length scale of a discrete periodicity