arXiv subjects

Devaraj van der Meer

Publications and source records attributed to Devaraj van der Meer.

69 records · Page 4Linked to original sources

arXiv2009

Collapse of Non-Axisymmetric 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.

physics.flu-dyn↗

arXiv2009

Approach to Universality in Axisymmetric Bubble Pinch-Off

The pinch-off of an axisymmetric air bubble surrounded by an inviscid fluid is compared in four physical realizations: (i) cavity collapse in the wake of an impacting disc, (ii) gas bubbles injected through a small orifice, (iii) bubble rupture in a straining flow, and (iv) a bubble with an initially necked shape. Our boundary-integral simulations suggest that all systems eventually follow the universal behavior characterized by slowly varying exponents predicted in [Eggers et al., PRL 98, 094502 (2007)]. However, the time scale for the onset of this final regime is found to vary by orders of magnitude depending on the system in question: while for the impacting disc it is well in the millisecond range, for the gas injection needle universal behavior sets in only a few microseconds before pinch-off. These findings reconcile the different views expressed in recent literature about the universal nature of bubble pinch-off.

physics.flu-dyn↗

arXiv2008

High-speed Jet Formation after Solid Object Impact

A circular disc impacting on a water surface creates a remarkably vigorous jet. Upon impact an axisymmetric air cavity forms and eventually pinches off in a single point halfway down the cavity. Immediately after closure two fast sharp-pointed jets are observed shooting up- and downwards from the closure location, which by then has turned into a stagnation point surrounded by a locally hyperbolic flow pattern. This flow, however, is {\it not} the mechanism feeding the two jets. Using high-speed imaging and numerical simulations we show that jetting is fed by the local flow around the base of the jet, which is forced by the colliding cavity walls. Based on this insight, we then show how the analytical description of a collapsing void (using a line of sinks along the axis of symmetry) can be continued beyond the time of pinch-off to obtain a quantitative model for jet formation which is in good agreement with the numerical and experimental data.

physics.flu-dyn↗

arXiv2008

Controlled impact of a disk on a water surface: Cavity dynamics

In this paper we study the transient surface cavity which is created by the controlled impact of a disk of radius h0 on a water surface at Froude numbers below 200. The dynamics of the transient free surface is recorded by high speed imaging and compared to boundary integral simulations. An excellent agreement is found between both. The flow surrounding the cavity is measured with high speed particle image velocimetry and is found to also agree perfectly with the flow field obtained from the simulations. We present a simple model for the radial dynamics of the cavity based on the collapse of an infinite cylinder. This model accounts for the observed asymmetry of the radial dynamics between the expansion and contraction phase of the cavity. It reproduces the scaling of the closure depth and total depth of the cavity which are both found to scale roughly proportional to Fr^{1/2} with a weakly Froude number dependent prefactor. In addition, the model accurately captures the dynamics of the minimal radius of the cavity, the scaling of the volume Vbubble of air entrained by the process, namely Vbubble/h0^3 proportional (1 + 0.26Fr^{1/2})Fr^{1/2}, and gives insight into the axial asymmetry of the pinch-off process.

physics.flu-dyn↗

arXiv2006

Non-continuous Froude number scaling for the closure depth of a cylindrical cavity

A long, smooth cylinder is dragged through a water surface to create a cavity with an initially cylindrical shape. This surface void then collapses due to the hydrostatic pressure, leading to a rapid and axisymmetric pinch-off in a single point. Surprisingly, the depth at which this pinch-off takes place does not follow the expected Froude$^{1/3}$ power-law. Instead, it displays two distinct scaling regimes separated by discrete jumps, both in experiment and in numerical simulations (employing a boundary integral code). We quantitatively explain the above behavior as a capillary waves effect. These waves are created when the top of the cylinder passes the water surface. Our work thus gives further evidence for the non-universality of the void collapse.

cond-mat.soft↗

arXiv2006

Phase Diagram of Vertically Shaken Granular Matter

A shallow, vertically shaken granular bed in a quasi 2-D container is studied experimentally yielding a wider variety of phenomena than in any previous study: (1) bouncing bed, (2) undulations, (3) granular Leidenfrost effect, (4) convection rolls, and (5) granular gas. These phenomena and the transitions between them are characterized by dimensionless control parameters and combined in a full experimental phase diagram.

physics.flu-dyn↗

arXiv2006

Leaping shampoo and the stable Kaye effect

Shear-thinning fluids exhibit surprisingly rich behaviour. One example is the Kaye effect which occurs when a thin stream of a solution of polyisobutylene in Decalin is poured into a dish of the fluid. As pouring proceeds, a small stream of liquid occasionally leaps upward from the heap. This surprising effect, which lasts only a second or so, is named after its first observer A. Kaye, who could offer no explanation for this behaviour. Later, Collyer and Fischer suggested from 250 frames per second cine recordings that the fluid must be highly shear thinning as well as elastic and 'pituitous'. In addition, they concluded that a rigid surface is required to back the reflected liquid stream. While the words bouncing and reflection are associated with non-continuous and elastic effects, we will show here that the Kaye effect is in fact a continuous flow phenomenon. We show that the Kaye effect works for many common fluids, including shampoos and liquid soaps. We reveal its physical mechanism (formation, stability and disruption) through high-speed imaging. The measurements are interpreted with a simple theoretical model including only the shear thinning behaviour of the liquid; elastic properties of the liquid play no role. We show that the Kaye effect can be stable and that it can be directed. We even demonstrate a stable Kaye effect on a thin soap film excluding the necessity of a rigid backing surface.

physics.flu-dyn↗

arXiv2006

Giant bubble pinch-off

Self-similarity has been the paradigmatic picture for the pinch-off of a drop. Here we will show through high-speed imaging and boundary integral simulations that the inverse problem, the pinch-off of an air bubble in water, is not self-similar in a strict sense: A disk is quickly pulled through a water surface, leading to a giant, cylindrical void which after collapse creates an upward and a downward jet. Only in the limiting case of large Froude number the neck radius $h$ scales as $h(-\log h)^{1/4} \propto τ^{1/2}$, the purely inertial scaling. For any finite Froude number the collapse is slower, and a second length-scale, the curvature of the void, comes into play. Both length-scales are found to exhibit power-law scaling in time, but with different exponents depending on the Froude number, signaling the non-universality of the bubble pinch-off.

physics.flu-dyn↗

arXiv2004

Temperature Anisotropy in a Driven Granular Gas

When smooth granular material is fluidized by vertically shaking a container, we find that the temperature in the direction of energy input always exceeds the temperature in the other directions. An analytical model is presented which shows how the anisotropy can be traced back to the inelasticity of the interparticle collisions and the collisions with the wall. The model compares very well with molecular dynamics simulations. It is concluded that any non-isotropic driving of a granular gas in a steady state necessarily causes anisotropy of the granular temperature.

cond-mat.stat-mech↗

arXiv2004

Impact

According to Shoemaker, the "impact of solid bodies is the most fundamental process that has taken place on the terrestrial planets", as they shape the surfaces of all solar system bodies. A lot of information on this process has been extracted from remote observations of impact craters on planetary surfaces. However, the nature of the geophysical impact events is that they are non-reproducible. Moreover, their scale is enormous and direct observations are not possible. Therefore, we choose an alternate and of course downscaled experimental approach in order to guarantee reproducible results: We prepare very fine sand in a well defined and fully decompactified state by letting gas bubble through it. After turning off the gas stream, we let a steel ball fall on the sand. The series of events in the experiments and corresponding discrete particle simulations is as follows: On impact of the ball, sand is blown away in all directions ("splash") and an impact crater forms. When this cavity collapses, a granular jet emerges and is driven straight into the air. A second jet goes downwards into the air bubble entrained during the process, thus pushing surface material deep into the ground. The air bubble rises slowly towards the surface, causing a granular eruption. In addition to the experiments and the discrete particle simulations we present a simple continuum theory to account for the void collapse leading to the formation of the upward and downward jets. We show that the phenomenon is robust and even works for oblique impacts: the upward jet is then shooting backwards, in the direction where the projectile came from.

cond-mat.other↗

arXiv2004

Spontaneous Ratchet Effect in a Granular Gas

The spontaneous clustering of a vibrofluidized granular gas is employed to generate directed transport in two different compartmentalized systems: a "granular fountain" in which the transport takes the form of convection rolls, and a "granular ratchet" with a spontaneous particle current perpendicular to the direction of energy input. In both instances, transport is not due to any system-intrinsic anisotropy, but arises as a spontaneous collective symmetry breaking effect of many interacting granular particles. The experimental and numerical results are quantitatively accounted for within a flux model.

cond-mat.soft↗

arXiv2002

Competitive Clustering in a Bi-disperse Granular Gas

A bi-disperse granular gas in a compartmentalized system is experimentally found to cluster competitively: Depending on the shaking strength, the clustering can be directed either towards the compartment initially containing mainly small particles, or to the one containing mainly large particles. The experimental observations are quantitatively explained within a flux model.

cond-mat.soft↗

arXiv2002

Sudden Collapse of a Granular Cluster

Single clusters in a vibro-fluidized granular gas in N connected compartments become unstable at strong shaking. They are experimentally shown to collapse very abruptly. The observed cluster lifetime (as a function of the driving intensity) is analytically calculated within a flux model, making use of the self-similarity of the process. After collapse, the cluster diffuses out into the uniform distribution in a self-similar way, with an anomalous diffusion exponent 1/3.

cond-mat.soft↗

arXiv2001

Bifurcation Diagram for Compartmentalized Granular Gases

The bifurcation diagram for a vibro-fluidized granular gas in N connected compartments is constructed and discussed. At vigorous driving, the uniform distribution (in which the gas is equi-partitioned over the compartments) is stable. But when the driving intensity is decreased this uniform distribution becomes unstable and gives way to a clustered state. For the simplest case, N=2, this transition takes place via a pitchfork bifurcation but for all N>2 the transition involves saddle-node bifurcations. The associated hysteresis becomes more and more pronounced for growing N. In the bifurcation diagram, apart from the uniform and the one-peaked distributions, also a number of multi-peaked solutions occur. These are transient states. Their physical relevance is discussed in the context of a stability analysis.

nlin.CD↗

arXiv2001

Hysteretic clustering in granular gas

Granular material is vibro-fluidized in N=2 and N=3 connected compartments, respectively. For sufficiently strong shaking the granular gas is equi-partitioned, but if the shaking intensity is lowered, the gas clusters in one compartment. The phase transition towards the clustered state is of 2nd order for N=2 and of 1st order for N=3. In particular, the latter is hysteretic. The experimental findings are accounted for within a dynamical model that exactly has the above properties.

nlin.CD↗