arXiv subjects

Ko van der Weele

Publications and source records attributed to Ko van der Weele.

9 recordsLinked to original sources

arXiv2020

Continuous hydraulic jumps in laminar channel flow

On the basis of the viscous Saint-Venant equations, hydraulic jumps in laminar open channel flow are obtained as continuous shock structures. Thanks to the inclusion of viscosity, the jumps are not abrupt, rendering the classic patchwork via the Rankine-Hugoniot shock relations unnecessary. The jumps arise as stable stationary solutions of the governing equations and lend themselves excellently to a Dynamical Systems analysis, manifesting themselves as near-parabolic trajectories in phase space. Based on this, we derive an analytic expression for the jump length as a function of the Froude and Reynolds numbers, reflecting the fact that both gravity and viscosity contribute to the balance of forces that shape the jump. The paper concludes with a numerical experiment confirming the stability of the jumps.

physics.flu-dyn↗

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↗

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↗