Efficient extraction of oil from droplet microfluidic emulsions.

Droplet microfluidic techniques can perform large numbers of single molecule and cell reactions but often require controlled, periodic flow to merge, split, and sort droplets. Here, we describe a simple method to convert aperiodic flows into periodic ones. Using an oil extraction module, we efficiently remove oil from emulsions to readjust the droplet volume fraction, velocity, and packing, producing periodic flows. The extractor acts as a universal adaptor to connect microfluidic modules that do not operate under identical flow conditions, such as droplet generators, incubators, and merger devices.

Electrical lysis of cells for detergent-free droplet assays.

Efficient lysis is critical when analyzing single cells in microfluidic droplets, but existing methods utilize detergents that can interfere with the assays to be performed. We demonstrate robust cell lysis without the use of detergents or other chemicals. In our method, cells are exposed to electric field immediately before encapsulation in droplets, resulting in cell lysis. We characterize lysis efficiency as a function of control parameters and demonstrate compatibility with enzymatic assays by measuring the catalysis of ß-glucosidase, an important cellulase used in the conversion of biomass to biofuel. Our method enables assays in microfluidic droplets that are incompatible with detergents.

Impact of inlet channel geometry on microfluidic drop formation.

We study the impact of inlet channel geometry on microfluidic drop formation. We show that drop makers with T-junction style inlets form monodisperse emulsions at low and moderate capillary numbers and those with Flow-Focus style inlets do so at moderate and high capillary numbers. At low and moderate capillary number, drop formation is dominated by interfacial forces and mediated by the confinement of the microchannels; drop size as a function of flow-rate ratio follows a simple functional form based on a blocking-squeezing mechanism. We summarize the stability of the drop makers with different inlet channel geometry in the form of a phase diagram as a function of capillary number and flow-rate ratio.

Effective temperatures and activated dynamics for a two-dimensional air-driven granular system on two approaches to jamming.

We present experiments on several distinct effective temperatures in a granular system at a sequence of increasing packing densities and at a sequence of decreasing driving rates. This includes single-grain measurements based on the mechanical energies of both the grains and an embedded oscillator, as well as a collective measurement based on the Einstein relation between diffusivity and mobility, which all probe different time scales. Remarkably, all effective temperatures agree. Furthermore, mobility data along the two trajectories collapse when plotted vs effective temperature and exhibit an Arrhenius form with the same energy barrier as the microscopic relaxation time.

Topological persistence and dynamical heterogeneities near jamming.

We introduce topological methods for quantifying spatially heterogeneous dynamics, and use these tools to analyze particle-tracking data for a quasi-two-dimensional granular system of air-fluidized beads on approach to jamming. In particular, we define two overlap order parameters, which quantify the correlation between particle configurations at different times, based on a Voronoi construction and the persistence in the resulting cells and nearest neighbors. Temporal fluctuations in the decay of the persistent area and bond order parameters define two alternative dynamic four-point susceptibilities chi(A)(tau) and chi(B)(tau), well suited for characterizing spatially heterogeneous dynamics. These are analogous to the standard four-point dynamic susceptibility chi4(l,tau), but where the space dependence is fixed uniquely by topology rather than by discretionary choice of cutoff function. While these three susceptibilities yield characteristic time scales that are somewhat different, they give domain sizes for the dynamical heterogeneities that are in good agreement and that diverge on approach to jamming.

Avalanche statistics and time-resolved grain dynamics for a driven heap.

We probe the dynamics of intermittent avalanches caused by steady addition of grains to a quasi-two-dimensional heap. To characterize the time-dependent average avalanche flow speed v(t) , we image the top free surface. To characterize the grain fluctuation speed deltav(t) , we use speckle-visibility spectroscopy. During an avalanche, we find that the fluctuation speed is approximately one-tenth the average flow speed, deltav approximately equal to 0.1v , and that these speeds are largest near the beginning of an event. We also find that the distribution of event durations is peaked, and that event sizes are correlated with the time interval since the end of the previous event. At high rates of grain addition, where successive avalanches merge into smooth continuous flow, the relationship between average and fluctuation speeds changes to deltav approximately v(1/2) .

Approach to jamming in an air-fluidized granular bed.

Quasi-two-dimensional bidisperse amorphous systems of steel beads are fluidized by a uniform upflow of air, so that the beads roll on a horizontal plane. The short-time ballistic motion of the beads is stochastic, with non-Gaussian speed distributions and with different average kinetic energies for the two species. The approach to jamming is studied as a function of increasing bead area fraction and also as a function of decreasing air speed. The structure of the system is measured in terms of both the Voronoi tessellation and the pair distribution function. The dynamics of the system is measured in terms of both displacement statistics and the density of vibrational states. These quantities all exhibit tell-tale features as the dynamics become more constrained closer to jamming. In particular the pair distribution function and the Voronoi cell shape distribution function both develop split peaks. And the mean-squared displacement develops a plateau of subdiffusive motion separating ballistic and diffusive regimes. Though the system is driven and athermal, this behavior is remarkably reminiscent of that in dense colloidal suspensions and supercooled liquids. One possible difference is that kurtosis of the displacement distribution peaks at the beginning of the subdiffusive regime.

Partition of energy for air-fluidized grains.

The dynamics of one and two identical spheres rolling in a nearly levitating upflow of air obey the Langevin equation and the fluctuation-dissipation relation [Ojha Nature (London) 427, 521 (2004); Phys. Rev. E 71, 016313 (2005)]. To probe the range of validity of this statistical mechanical description, we perturb the original experiments in four ways. First, we break the circular symmetry of the confining potential by using a stadium-shaped trap, and find that the velocity distributions remain circularly symmetric. Second, we fluidize multiple spheres of different density, and find that all have the same effective temperature. Third, we fluidize two spheres of different size, and find that the thermal analogy progressively fails according to the size ratio. Fourth, we fluidize individual grains of aspherical shape, and find that the applicability of statistical mechanics depends on whether or not the grain chatters along its length, in the direction of airflow.

Penetration depth for shallow impact cratering.

We present data for the penetration of a variety of spheres, dropped from rest, into a loose noncohesive granular medium. We improve upon earlier work [J. S. Uehara, Phys. Rev. Lett. 90, 194301 (2003)] in three regards. First, we explore the behavior vs sphere diameter and density more systematically, by holding one of these parameters constant while varying the other. Second, we prepare the granular medium more reproducibly and, third, we measure the penetration depth more accurately. The new data support the previous conclusion that the penetration depth is proportional to the 1/2 power of sphere density, the 2/3 power of sphere diameter, and the 1/3 power of total drop distance.

Statistical characterization of the forces on spheres in an upflow of air.

The dynamics of a sphere fluidized in a nearly levitating upflow of air were previously found to be identical to those of a Brownian particle in a two-dimensional harmonic trap, consistent with a Langevin equation [Ojha et al., Nature (London) 427, 521 (2004)]. The random forcing, the drag, and the trapping potential represent different aspects of the interaction of the sphere with the air flow. In this paper we vary the experimental conditions for a single sphere, and report on how the force terms in the Langevin equation scale with air flow speed, sphere radius, sphere density, and system size. We also report on the effective interaction potential between two spheres in an upflow of air.