Shock waves in two-dimensional granular flow: effects of rough walls and polydispersity

Critical role of friction for a single particle falling through a funnel

We investigate a single frictional, inelastic, spherical particle falling under gravity through a symmetric funnel. A recent study showed that, for a frictionless particle in such a system, several anomalous phenomena occur: The particle can stay longer, lose more energy, and exert more impulsive force in a funnel with steeper walls. For frictionless particles, such phenomena exist for many small ranges of funnel angles and are a consequence of the many possible repeated patterns in particle trajectories. However, in reality, friction always exists and it is a natural question whether the anomalous phenomena still exist for frictional particles in such systems. We show that, surprisingly, the inclusion of friction in the dynamics actually dramatically enhances the anomalous phenomena. For frictional particles, the anomalous phenomena exist for all funnel angles steeper than 45^{°} and are thus more robust than the frictionless case. Furthermore, instead of many possible complicated repeated patterns in particle trajectories, there is a unique repeated pattern for frictional particles. Moreover, this is the simplest possible repeated pattern. We derive an analytical expression for this unique repeated pattern and provide a theoretical explanation for the anomalous phenomena observed in frictional particle systems. We further show that the friction, no matter how small, plays a critical role in the dynamics, that is, the dynamics of the frictionless particle system is singular.

Velocity oscillations in microfluidic flows of concentrated colloidal suspensions

We study the pressure-driven flow of concentrated colloids confined in glass microchannels at the single-particle level using fast confocal microscopy. For channel to particle size ratios 2a/D[over ] less, similar30, the flow rate of the suspended particles shows fluctuations. These turn into regular oscillations for higher confinements (2a/D[over ] approximately 20). We present evidence to link these oscillations with the relative flow of solvent and particles (permeation) and the effect of confinement on shear thickening.

Anomalous behavior of a single particle falling through a funnel

We show several surprising phenomena that occur in an extremely simple system of a single frictionless, inelastic, spherical particle falling under gravity through a symmetric funnel. One might naively expect that particles would fall through funnels with steeper sides more quickly, exert a smaller total impulse on the funnel walls, and lose less energy. However, we show that there are special ranges of angles of the funnel walls for which exactly the opposite occurs. Typically, the particle will experience a sequence of collisions that is highly sensitive to the location at which it enters the funnel and nearby particle trajectories become widely dispersed. However, in the special angular ranges this is not the case and the particle can experience sequences of collisions that have a highly coherent structure. We provide a theoretical analysis that can predict and explain this surprising behavior.