Dalton's and Amagat's laws fail in gas mixtures with shock propagation.

A shock propagating through a gas mixture leads to pressure, temperature, and density increases across the shock front. Rankine-Hugoniot relations correlating pre- and post-shock quantities describe a calorically perfect gas but deliver a good approximation for real gases, provided the pre-shock conditions are well characterized with a thermodynamic mixing model. Two classic thermodynamic models of gas mixtures are Dalton's law of partial pressures and Amagat's law of partial volumes. We measure post-shock temperature and pressure in experiments with nonreacting binary mixtures of sulfur hexafluoride and helium (two dramatically disparate gases) and show that neither model can accurately predict the observed values, on time scales much longer than that of the shock front passage, due to the models' implicit assumptions about mixture behavior on the molecular level. However, kinetic molecular theory can help account for the discrepancy. Our results provide starting points for future theoretical work, experiments, and code validation.

Mixing of a continuous flow of two fluids due to unsteady flow.

In many low-Reynolds number mixing applications, the absence of turbulence makes it difficult to achieve proper mixing of two fluids. In this paper, flow visualization is used to obtain quantitative measurements of mixing that occurs when combining two pulsatile fluid streams at a Y-connection. Mixing results from the interface distortion created by the pulsatile flow. This is generated by combining the action a peristaltic pump, which provides the mean flow, with the action of two pinch valves, one on each arm of the Y-connection, to generate strong pulsations. The action of the pinch valves is be controlled via pulse generators. Apparently chaotic conditions were realized in the confluence region, superimposed with the mean flow. The valve action was optimized to maximize mixing, the latter quantified via image analysis. This work demonstrates a low cost, efficient mixing device for low-Reynolds number conditions, which is therefore suitable for miniaturization.

Scaling evolution in shock-induced transition to turbulence.

In this experimental study, a column of heavy gas (SF6) surrounded by light gas (air) is accelerated by a planar Mach 1.2 shock. Richtmyer-Meshkov instability on the initially diffuse air-SF6 interface determines the repeatable large-scale vortex dynamics of the system after the shock passage. Subsequently secondary instabilities form, with the system eventually transitioning to turbulence. We present highly resolved measurements of two components of the instantaneous velocity fields. With these measurements, we investigate the evolution of velocity statistics over a substantial range of scales in terms of structure functions. The latter evolve to exhibit late-time behavior consistent with the Kolmogorov scaling law for fully developed turbulence, despite the transitional character, anisotropy, and inhomogeneity of our flow. Ensemble averaging and comparison with instantaneous results reveal a trend towards the same scaling manifested much earlier by the structure functions of the fluctuating velocity components.

Knots and random walks in vibrated granular chains.

We study experimentally statistical properties of the opening times of knots in vertically vibrated granular chains. Our measurements are in good qualitative and quantitative agreement with a theoretical model involving three random walks interacting via hard-core exclusion in one spatial dimension. In particular, the knot survival probability follows a universal scaling function which is independent of the chain length, with a corresponding diffusive characteristic time scale. Both the large-exit-time and the small-exit-time tails of the distribution are suppressed exponentially, and the corresponding decay coefficients are in excellent agreement with theoretical values.

Validation of an instability growth model using particle image velocimetry measurements

A varicose-profile, thin layer of heavy gas ( SF6) in lighter gas (air) is impulsively accelerated by a planar, Mach 1.2 shock, producing the Richtmyer-Meshkov instability. We present the first measurements of the circulation in the curtain during the vortex-dominated, nonlinear stage of the instability evolution. These measurements, based on particle image velocimetry data, are employed to validate an idealized model of the nonlinear perturbation growth.

Cylinder wakes in flowing soap films.

We present an experimental characterization of cylinder wakes in flowing soap films. From instantaneous velocity and thickness fields, we find the vortex-shedding frequency, mean-flow velocity, and mean-film thickness. Using the empirical relationship between the Reynolds and Strouhal numbers obtained for cylinder wakes in three dimensions, we estimate the effective soap-film viscosity and its dependence on film thickness. We also compare the decay of vorticity with that in a simple Rankine vortex model with a dissipative term to account for air drag.