Ivo R. Peters

Direct observation of dynamic shear jamming in dense suspensions

Liquid-like at rest, dense suspensions of hard particles can undergo striking transformations in behaviour when agitated or sheared. These phenomena include solidification during rapid impact, as well as strong shear thickening characterized by discontinuous, orders-of-magnitude increases in suspension viscosity. Much of this highly non-Newtonian behaviour has recently been interpreted within the framework of a jamming transition. However, although jamming indeed induces solid-like rigidity, even a strongly shear-thickened state still flows and thus cannot be fully jammed. Furthermore, although suspensions are incompressible, the onset of rigidity in the standard jamming scenario requires an increase in particle density. Finally, whereas shear thickening occurs in the steady state, impact-induced solidification is transient. As a result, it has remained unclear how these dense suspension phenomena are related and how they are connected to jamming. Here we resolve this by systematically exploring both the steady-state and transient regimes with the same experimental system. We demonstrate that a fully jammed, solid-like state can be reached without compression and instead purely with shear, as recently proposed for dry granular systems. This state is created by transient shear-jamming fronts, which we track directly. We also show that shear stress, rather than shear rate, is the key control parameter. From these findings we map out a state diagram with particle density and shear stress as variables. We identify discontinuous shear thickening with a marginally jammed regime just below the onset of full, solid-like jamming. This state diagram provides a unifying framework, compatible with prior experimental and simulation results on dense suspensions, that connects steady-state and transient behaviour in terms of a dynamic shear-jamming process.

High-speed ultrasound imaging in dense suspensions reveals impact-activated solidification due to dynamic shear jamming

A remarkable property of dense suspensions is that they can transform from liquid-like at rest to solid-like under sudden impact. Previous work showed that this impact-induced solidification involves rapidly moving jamming fronts; however, details of this process have remained unresolved. Here we use high-speed ultrasound imaging to probe non-invasively how the interior of a dense suspension responds to impact. Measuring the speed of sound we demonstrate that the solidification proceeds without a detectable increase in packing fraction, and imaging the evolving flow field we find that the shear intensity is maximized right at the jamming front. Taken together, this provides direct experimental evidence for jamming by shear, rather than densification, as driving the transformation to solid-like behaviour. On the basis of these findings we propose a new model to explain the anisotropy in the propagation speed of the fronts and delineate the onset conditions for dynamic shear jamming in suspensions.

Highly focused supersonic microjets: numerical simulations

By focusing a laser pulse inside a capillary partially filled with liquid, a vapour bubble is created that emits a pressure wave. This pressure wave travels through the liquid and creates a fast, focused axisymmetric microjet when it is reflected at the meniscus. We numerically investigate the formation of this microjet using axisymmetric boundary integral simulations, where we model the pressure wave as a pressure pulse applied on the bubble. We find a good agreement between the simulations and experimental results in terms of the time evolution of the jet and on all parameters that can be compared directly. We present a simple analytical model that accurately predicts the velocity of the jet after the pressure pulse and its maximum velocity

Dynamic jamming of iceberg-choked fjords

We investigate the dynamics of ice melange by analyzing rapid motion recorded by a time-lapse camera and terrestrial radar during several calving events that occurred at Jakobshavn Isbrae, Greenland. During calving events (1) the kinetic energy of the ice melange is 2 orders of magnitude smaller than the total energy released during the events, (2) a jamming front propagates through the ice melange at a rate that is an order of magnitude faster than the motion of individual icebergs, (3) the ice melange undergoes initial compaction followed by slow relaxation and extension, and (4) motion of the ice melange gradually decays before coming to an abrupt halt. These observations indicate that the ice melange experiences widespread jamming during calving events and is always close to being in a jammed state during periods of terminus quiescence. We therefore suspect that local jamming influences longer timescale ice melange dynamics and stress transmission.

Splash wave and crown breakup after disc impact on a liquid surface

In this paper we analyse the impact of a circular disc on a free surface using experiments, potential flow numerical simulations and theory. We focus our attention both on the study of the generation and possible breakup of the splash wave created after the impact and on the calculation of the force on the disc. We have experimentally found that drops are only ejected from the rim located at the top part of the splash – giving rise to what is known as the crown splash – if the impact Weber number exceeds a threshold value Wecrit?140. We explain this threshold by defining a local Bond number Botip based on the rim deceleration and its radius of curvature, with which we show using both numerical simulations and experiments that a crown splash only occurs when Botip?1, revealing that the rim disrupts due to a Rayleigh–Taylor instability. Neglecting the effect of air, we show that the flow in the region close to the disc edge possesses a Weber-number-dependent self-similar structure for every Weber number. From this we demonstrate that Botip?We, explaining both why the transition to crown splash can be characterized in terms of the impact Weber number and why this transition occurs for Wecrit?140. Next, including the effect of air, we have developed a theory which predicts the time-varying thickness of the very thin air cushion that is entrapped between the impacting solid and the liquid. Our analysis reveals that gas critically affects the velocity of propagation of the splash wave as well as the time-varying force on the disc, FD. The existence of the air layer also limits the range of times in which the self-similar solution is valid and, accordingly, the maximum deceleration experienced by the liquid rim, that sets the length scale of the splash drops ejected when We>Wecrit.

Collapse and pinch-off of a non-axisymmetric impact-created air cavity in water

The axisymmetric collapse of a cylindrical air cavity in water follows a universal power law with logarithmic corrections. Nonetheless, it has been suggested that the introduction of a small azimuthal disturbance induces a long-term memory effect, reflecting in oscillations which are no longer universal but remember the initial condition. In this work, we create non-axisymmetric air cavities by driving a metal disc through an initially quiescent water surface and observe their subsequent gravity-induced collapse. The cavities are characterized by azimuthal harmonic disturbances with a single mode number and amplitude . For small initial distortion amplitude (1 or 2 % of the mean disc radius), the cavity walls oscillate linearly during collapse, with nearly constant amplitude and increasing frequency. As the amplitude is increased, higher harmonics are triggered in the oscillations and we observe more complex pinch-off modes. For small-amplitude disturbances we compare our experimental results with the model for the amplitude of the oscillations by Schmidt et al. (Nature Phys., vol. 5, 2009, pp. 343?346) and the model for the collapse of an axisymmetric impact-created cavity previously proposed by Bergmann et al. (J. Fluid Mech., vol. 633, 2009b, pp. 381?409). By combining these two models we can reconstruct the three-dimensional shape of the cavity at any time before pinch-off.

Splashing Onset in Dense Suspension Droplets

We investigate the impact of droplets of dense suspensions onto a solid substrate. We show that a global hydrodynamic balance is unable to predict the splash onset and propose to replace it by an energy balance at the level of the particles in the suspension. We experimentally verify that the resulting, particle-based Weber number gives a reliable, particle size and density dependent splash onset criterion. We further show that the same argument also explains why, in bimodal systems, smaller particles are more likely to escape than larger ones.

Collapse of nonaxisymmetric cavities

A round disk with a harmonic disturbance impacts on a water surface and creates a non-axisymmetric cavity which collapses under the influence of hydrostatic pressure. We use disks deformed with mode m=2 to m=6. For all mode numbers we find clear evidence for a phase inversion of the cavity wall during the collapse. We present a fluid dynamics video showing high speed imaging of different modes, pointing out the characteristic features during collapse.

Dynamic shear jamming in dense granular suspensions under extension

Unlike dry granular materials, a dense granular suspension like cornstarch in water can strongly resist extensional flows. At low extension rates, such a suspension behaves like a viscous fluid, but rapid extension results in a response where stresses far exceed the predictions of lubrication hydrodynamics and capillarity. To understand this remarkable mechanical response, we experimentally measure the normal force imparted by a large bulk of the suspension on a plate moving vertically upward at a controlled velocity. We observe that, above a velocity threshold, the peak force increases by orders of magnitude. Using fast ultrasound imaging we map out the local velocity profiles inside the suspension, which reveal the formation of a growing jammed region under rapid extension. This region interacts with the rigid boundaries of the container through strong velocity gradients, suggesting a direct connection to the recently proposed shear-jamming mechanism.

Non-axisymmetric impact creates pineapple-shaped cavity

We impact a disk on a free water surface at a controlled speed of 1 m=s. The disk is round, with a superimposed mode-20 azimuthal disturbance. The mean disk radius is 20 mm and the amplitude of the disturbance is 0.4 mm. Initially, very close to the disk, the free surface is forced to match the shape of the disk. During the void expansion and subsequent collapse, however, the interface displays rich dynamics, resulting eventually in a pineapple-shaped cavity. If we made a cut-through of the cavity at one specific depth, we would observe an oscillating behavior of the water-air interface just like a standing wave coupled to the fast decreasing mean radius of the cavity. The amplitude of this oscillation remains constant, while the frequency diverges towards the pinch-off—following the prediction made by linear stability analysis of a disconnecting air bubble. Since the absolute amplitude remains constant while the mean radius of the cavity goes to zero, the relative amplitude grows strongly towards the pinch-off; the disturbance thus becomes much more pronounced closer to the pinch-off (e.g., compare Fig. 1(b) with 1(c)). Since the radial flow in this system is much larger than the axial flow, we can approximate each horizontal layer of fluid as being decoupled from the vertical direction. It is, therefore, possible to solve the system at each layer by combining the radial dynamics of an axisymmetric cavity with the model for the oscillations. This was done by Enrı́quez et al., resulting in an almost perfect reproduction of the full pineapple-shaped cavity.