Dense mixture of granules and liquid often shows a sever shear thickening and is called a dilatant fluid. We construct a fluid dynamics model for the dilatant fluid by introducing a phenomenological state variable for a local state of dispersed particles. With simple assumptions for an equation of the state variable, we demonstrate that the model can describe basic features of the dilatant fluid such as the stress-shear rate curve that represents discontinuous severe shear thickening, hysteresis upon changing shear rate, instantaneous hardening upon external impact. Analysis of the model reveals that the shear thickening fluid shows an instability in a shear flow for some regime and exhibits the shear thickening oscillation, i.e. the oscillatory shear flow alternating between the thickened and the relaxed states. Results of numerical simulations are presented for one and two-dimensional systems.

We investigate the condition for the bounce of circular disks which obliquely impacts on fluid surface. An experiment [ Clanet, C., Hersen, F. and Bocquet, L., Nature 427, 29 (2004) ] revealed that there exists a "magic angle" of 20• between a disk's face and water surface in which condition the required speed for bounce is minimized. We perform three-dimensional simulation of the diskwater impact by means of the Smoothed Particle Hydrodynamics (SPH). Futhermore, we analyze the impact with a model of ordinal differential equation (ODE). Our simulation is in good agreement with the experiment. The analysis with the ODE model gives us a theoretical insight for the "magic angle" of stone skipping.PACS numbers: 45.50. Tn, 47.11.+j, 47.90.+a Problem of impacts and ricochets of solid bodies against water surface have been received a considerable amount of attention [1,2,3,4,5,6]. In the early stage, the problem was of importance in naval engineering concerning the impacts of canon balls on sea-surface [7]. Investigations then revealed that there exists a maximum angle of incidence θ max for impacts of spheres, above which the rebound does not occur [8]. Besides, it was empirically found that the θ max relates to specific gravity of sphere σ as θ max = 18/ √ σ. This relation was theoretically explained using a simple model of an ordinal differential equation (ODE) [8,9]. In military engineering today, the problem of water impacts may be not as important as that of a century ago, however, recently it attracts renewed interest under the studies of locomotion of basilisk lizards [10] and stone-skip [11].This study is motivated by experimental study of stone-skip -bounce of a stone against water surfaceby C. Clanet et. al. [12]. They investigated impacts of a circular disk (stone) on water surface and found that an angle about φ = 20• between the disk's face and water surface would be the "magic angle" which minimizes required velocity for bounce. In this paper, we study theoretically and numerically the oblique impact of disks and water surface. Our simulation successfully agrees with the experiment. Moreover, we apply an ODE model [17] to the disk-water impact and obtain an analytical form of the required velocity v min and maximum angle θ max as a function of initial disk conditions.To perform a numerical simulation of the disk-water impact, we solve the Navier-Stokes equation using the technique of Smoothed Particle Hydrodynamics (SPH) [13,14]. Fig. 1 is the snapshots of our simulation. The SPH method is based on Lagrangian description of fluid and has an advantage to treat free surface motion. Several representation of the viscous term have been proposed for this method. In this work, we adopt an artificial viscous term [15] which is simple for computation * Electronic address: nagahiro@cmpt.phys.tohoku.ac.jp and sufficiently examined with Couette flow [16]. In our simulation, we neglect surface tension and put the velocity of sound of the fluid, at least, 25 times larger than the incident velocity of the disk.In ...

We perform experiments and numerical simulations to investigate spatial distribution of pressure in a sheared dilatant fluid of the Taylor-Couette flow under a constant external shear stress. In a certain range of shear stress, the flow undergoes the shear thickening oscillation around 20 Hz. We find that, during the oscillation, a localized thickened band rotates around the axis with the flow. Based upon experiments and numerical simulations, we show that a major part of the thickened band is under negative pressure even in the case of discontinuous shear thickening, which indicates that the thickening is caused by Reynolds dilatancy; the dilatancy causes the negative pressure in interstitial fluid, which generates contact structure in the granular medium., then frictional resistance hinders rearrangement of the structure and solidifies the medium.

This corrects the article DOI: 10.1103/PhysRevE.94.062614.

We investigate one-dimensional collisions of unharmonic chains and a rigid wall. We find that the coefficient of restitution (COR) is strongly dependent on the velocity of colliding chains and has a minimum value at a certain velocity. The relationship between COR and collision velocity is derived for low-velocity collisions using perturbation methods. We found that the velocity dependence is characterized by the exponent of the lowest unharmonic term of interparticle potential energy.

A simple model is proposed for the buckling and coiling instability of a viscous "fluid rope" falling on a plane. By regarding a fluid rope as a one-dimensional flow, this model accounts for only the axial and shared viscous forces. Our model successfully reproduces several experiments with no adjustable parameters, such as the existence of three distinct coiling regimes reported in Phys. Rev. Lett. 93, 214502 (2004). Our model allows for the discussion of unsteady motion.An expression for the critical fall height at which the coiling frequency changes from a decrease to increase was phenomenologically derived. It was found that the coil-uncoil transition shows remarkable hysteresis only for weak gravity condition.

A numerical model is presented to describe both the transient and steady-state dynamics of viscous threads falling onto a plane. The steady-state coiling frequency Ω is calculated as a function of fall height H. In the case of weak gravity, Ω ∝ H −1 and Ω ∝ H are obtained for lower and higher fall heights respectively. When the effect of gravity is significant, the relation Ω ∝ H 2 is observed. These results agree with the scaling laws previously predicted.The critical Reynolds number for coil-uncoil transition is discussed. When the gravity is weak, the transition occurs with hysteresis effects. If the plane moves horizontally at a constant speed, a variety of meandering oscillation modes can be observed experimentally. The present model also can describe this phenomenon. The numerically obtained state diagram for the meandering modes qualitatively agrees with the results of experiment.