Showing papers by "Sidney R. Nagel published in 2014"

Coalescence of bubbles and drops in an outer fluid.

Abstract: When two liquid drops touch, a microscopic connecting liquid bridge forms and rapidly grows as the two drops merge into one. Whereas coalescence has been thoroughly studied when drops coalesce in vacuum or air, many important situations involve coalescence in a dense surrounding fluid, such as oil coalescence in brine. Here we study the merging of gas bubbles and liquid drops in an external fluid. Our data indicate that the flows occur over much larger length scales in the outer fluid than inside the drops themselves. Thus, we find that the asymptotic early regime is always dominated by the viscosity of the drops, independent of the external fluid. A phase diagram showing the crossovers into the different possible late-time dynamics identifies a dimensionless number that signifies when the external viscosity can be important.

Fingering versus stability in the limit of zero interfacial tension

Abstract: The invasion of one fluid into another of higher viscosity in a quasi-two dimensional geometry typically produces complex fingering patterns. Because interfacial tension suppresses short-wavelength fluctuations, its elimination by using pairs of miscible fluids would suggest an instability producing highly ramified singular structures. Previous studies focused on wavelength selection at the instability onset and overlooked the striking features appearing more globally. Here we investigate the non-linear growth that occurs after the instability has been fully established. We find a rich variety of patterns that are characterized by the viscosity ratio between the inner and the outer fluid, η(in)/η(out), as distinct from the most-unstable wavelength, which determines the onset of the instability. As η(in)/η(out) increases, a regime dominated by long highly-branched fractal fingers gives way to one dominated by blunt stable structures characteristic of proportionate growth. Simultaneously, a central region of complete outer-fluid displacement grows until it encompasses the entire pattern at η(in)/η(out)≈0.3.

Jamming in finite systems: stability, anisotropy, fluctuations, and scaling.

Abstract: Athermal packings of soft repulsive spheres exhibit a sharp jamming transition in the thermodynamic limit. Upon further compression, various structural and mechanical properties display clean power-law behavior over many decades in pressure. As with any phase transition, the rounding of such behavior in finite systems close to the transition plays an important role in understanding the nature of the transition itself. The situation for jamming is surprisingly rich: the assumption that jammed packings are isotropic is only strictly true in the large-size limit, and finite-size has a profound effect on the very meaning of jamming. Here, we provide a comprehensive numerical study of finite-size effects in sphere packings above the jamming transition, focusing on stability as well as the scaling of the contact number and the elastic response.

Solids between the mechanical extremes of order and disorder

Abstract: Jammed systems are typically thought of as being amorphous. Simulations of packings with varying disorder reveal a crossover from crystalline behaviour, which suggests the physics of jamming also applies to highly ordered systems—providing a new framework for understanding amorphous solids.

Multiple Transient Memories in Experiments on Sheared Non-Brownian Suspensions

Abstract: In line with previous theoretical predictions, noise is shown experimentally to stabilize memory retention in sheared particle suspensions.

Comparison of splashing in high- and low-viscosity liquids.

Abstract: We explore the evolution of a splash when a liquid drop impacts a smooth dry surface. There are two splashing regimes that occur when the liquid viscosity is varied as is evidenced by its dependence on ambient gas pressure. A high-viscosity drop splashes by emitting a thin sheet of liquid from a spreading liquid lamella long after the drop has first contacted the solid. Likewise, we find that there is also a delay in the ejection of a thin sheet when a low-viscosity drop splashes. We show how the ejection time of the thin sheet depends on liquid viscosity and ambient gas pressure.

Contact nonlinearities and linear response in jammed particulate packings.

Abstract: Packings of frictionless athermal particles that interact only when they overlap experience a jamming transition as a function of packing density. Such packings provide the foundation for the theory of jamming. This theory rests on the observation that, despite the multitude of disordered configurations, the mechanical response to linear order depends only on the distance to the transition. We investigate the validity and utility of such measurements that invoke the harmonic approximation and show that, despite particles coming in and out of contact, there is a well-defined linear regime in the thermodynamic limit.

Impact dynamics of granular jets with noncircular cross sections.

Abstract: Using high-speed photography, we investigate two distinct regimes of the impact dynamics of granular jets with noncircular cross sections. In the steady-state regime, we observe the formation of thin granular sheets with anisotropic shapes and show that the degree of anisotropy increases with the aspect ratio of the jet's cross section. Our results illustrate the liquidlike behavior of granular materials during impact and demonstrate that a collective hydrodynamic flow emerges from strongly interacting discrete particles. We discuss the analogy between our experiments and those from the Relativistic Heavy Ion Collider, where similar anisotropic ejecta from a quark-gluon plasma have been observed in heavy-ion impact.

Comment on "Repulsive contact interactions make jammed particulate systems inherently nonharmonic".

Abstract: In their Letter, Schreck, Bertrand, O'Hern and Shattuck [Phys. Rev. Lett. 107, 078301 (2011)] study nonlinearities in jammed particulate systems that arise when contacts are altered. They conclude that there is "no harmonic regime in the large system limit for all compressions" and "at jamming onset for any system size." Their argument rests on the claim that for finite-range repulsive potentials, of the form used in studies of jamming, the breaking or forming of a single contact is sufficient to destroy the linear regime. We dispute these conclusions and argue that linear response is both justified and essential for understanding the nature of the jammed solid.

An island of stability in a sea of fingers: emergent large-scale features of the viscous flow instability

Abstract: The displacement of a more viscous fluid by a less viscous one in a quasi-two dimensional geometry leads to the formation of complex fingering patterns. This fingering has been characterized by a most unstable wavelength, $\lambda_c$, which depends on the viscosity difference between the two immiscible fluids and sets the characteristic width of the fingers. How the finger length grows after the instability occurs is an equally important, but previously overlooked, aspect that characterizes the global features of the patterns. As the lower viscosity fluid is injected, we show that there is a stable inner region where the outer fluid is completely displaced. The ratio of the finger length to the radius of this stable region depends only on the viscosity ratio of the fluids and is decoupled from $\lambda_c$.

Disordered surface vibrations in jammed sphere packings

Abstract: We study the vibrational properties near a free surface of disordered spring networks derived from jammed sphere packings. In bulk systems, without surfaces, it is well understood that such systems have a plateau in the density of vibrational modes extending down to a frequency scale $\omega^*$. This frequency is controlled by $\Delta Z = \langle Z \rangle - 2d$, the difference between the average coordination of the spheres and twice the spatial dimension, $d$, of the system, which vanishes at the jamming transition. In the presence of a free surface we find that there is a density of disordered vibrational modes associated with the surface that extends far below $\omega^*$. The total number of these low-frequency surface modes is controlled by $\Delta Z$, and the profile of their decay into the bulk has two characteristic length scales, which diverge as $\Delta Z^{-1/2}$ and $\Delta Z^{-1}$ as the jamming transition is approached.