Cross-sectional river shapes: A variational discharge-resistance formulation

Cross-sectional river shapes were obtained from a variational principle: minimizing the bed friction for a given discharge and a given maximum lateral bed slope (angle of repose). The optimal shape is found to be independent of both the exponent in the friction law adopted and the value of the discharge, but it does depend on the angle of repose. The optimal profile is a single stream; for braided rivers the solution is suboptimal

Use of elastic stability analysis to explain the stress-dependent nature of soil strength

The peak and critical state strengths of sands are linearly related to the stress level, just as the frictional resistance to sliding along an interface is related to the normal force. The analogy with frictional sliding has led to the use of a ‘friction angle’ to describe the relationship between strength and stress for soils. The term ‘friction angle’ implies that the underlying mechanism is frictional resistance at the particle contacts. However, experiments and discrete element simulations indicate that the material friction angle is not simply related to the friction angle at the particle contacts. Experiments and particle-scale simulations of model sands have also revealed the presence of strong force chains, aligned with the major principal stress. Buckling of these strong force chains has been proposed as an alternative to the frictional-sliding failure mechanism. Here, using an idealized abstraction of a strong force chain, the resistance is shown to be linearly proportional to the magnitude of the lateral forces supporting the force chain. Considering a triaxial stress state, and drawing an analogy between the lateral forces and the confining pressure in a triaxial test, a linear relationship between stress level and strength is seen to emerge from the failure-by-buckling hypothesis

Effect of the tool tilt angle on the heat generation and the material flow in friction stir welding

This work studies the effect of the tool tilt angle on the generated heat and the material flow in the work pieces joint by Friction Stir Welding (FSW). An apropos kinematic framework together with a two-stage speed-up strategy is adopted to simulate the FSW problem. The effect of tilt angle on the FSWelds is modeled through the contact condition by modifying an enhanced friction model. A rotated friction shear stress is proposed, the angle of rotation depending on the process parameters and the tilt angle. The proposed rotation angle is calibrated by the experimental data provided for a tilt angle 2.5°. The differences of generated heat and material flow for the cases of tool with tilt angle of 0° and 2.5° are discussed. It is concluded that due to the higher temperature, softer material and greater frictional force in the trailing side of the tool, the material flow in the rear side of the FSW tool with the title angle is considerably enhanced, which assists to prevent the generation of defect.Peer ReviewedPostprint (published version

Energy Dissipation and Trapping of Particles Moving on a Rough Surface

We report an experimental, numerical and theoretical study of the motion of a ball on a rough inclined surface. The control parameters are $D$, the diameter of the ball, $\theta$, the inclination angle of the rough surface and $E_{ki}$, the initial kinetic energy. When the angle of inclination is larger than some critical value, $\theta>\theta_{T}$, the ball moves at a constant average velocity which is independent of the initial conditions. For an angle $\theta < \theta_{T}$, the balls are trapped after moving a certain distance. The dependence of the travelled distances on $E_{ki}$, $D$ and $\theta$. is analysed. The existence of two kinds of mechanisms of dissipation is thus brought to light. We find that for high initial velocities the friction force is constant. As the velocity decreases below a certain threshold the friction becomes viscous.Comment: 8 pages RevTeX, 12 Postscript figure

Relativistic Dynamical Friction in the Weak Scattering Limit

A test mass, $M$, moving through an ambient medium of light particles with lower average kinetic energy than itself suffers a deceleration caused by its scattering of the light particles. The phenomenon is usually referred to as dynamical friction. The velocity, \v, of the test mass decays on a timescale independent of \v in the non-relativistic case. We derive expressions for dynamical friction in the case that the test mass and the light particles are relativistic, and that the scattering is weak (with impact parameter, $b\gg M$). In the case that the light particles are ultra-relativistic, and isotropic in the frame in which $M$ moves with velocity $v$, we find an explicit expression for the dynamical friction. The well known factor of 2 correcting the Newtonian scattering of photons to give the Einstein angle, $4M/b$, has the largest effect on the resulting friction, which is modified by a factor of roughly $16 / 3\gamma_v$ over the simple non-relativistic case. In the non-relativistic case, the largest contribution to the friction comes from light particles moving slower than $v$. We find that this is not the case for ultra-relativistic scattering, essentially because the scattering angle is independent of \v. Some astrophysical implications are discussed. (Accepted for publication in Monthly Notices.)Comment: 10 pages (no figures), self-unpacking uuencoded PostScript (uufiles), RDF#

Translational and rotational friction on a colloidal rod near a wall

We present particulate simulation results for translational and rotational friction components of a shish-kebab model of a colloidal rod with aspect ratio (length over diameter) $L/D = 10$ in the presence of a planar hard wall. Hydrodynamic interactions between rod and wall cause an overall enhancement of the friction tensor components. We find that the friction enhancements to reasonable approximation scale inversely linear with the closest distance $d$ between the rod surface and the wall, for $d$ in the range between $D/8$ and $L$. The dependence of the wall-induced friction on the angle $\theta$ between the long axis of the rod and the normal to the wall is studied and fitted with simple polynomials in $\cos \theta$.Comment: 8 pages, 8 figure

Research of a fibrous layer at refining in the refiners

A subject of research-a fibrous layer in the refiners at refining. By means of the tension compression chart it is shown that parameters of a fibrous layer are adequately described by Maxwell-Thompson's model for liquid friction and the Hooke model for boundary friction of a plate. Deborah's number of a fibrous layer is also investigated. Deborah's number of a fibrous layer at refining changes in the range from 7 to 2.1•106 and depends on a nature and concentration of the refining material, the angle of knife crossing, the frequency of rotation of rotor and width of the platform of contact. For decrease in power consumption at refining both chips and pulp of high concentration it is recommended to increase the speed of sliding of knife of rotor along stator knife. It is possible to reach by increase in frequency of rotation of rotor and by decrease of an angle of crossing of knife. At refining of pulp of low concentration for decrease in power consumption of refining it is recommended to reduce the frequency of rotation of rotor and to increase the angle of crossing of knife of rotor and stator. At the high density of contact of plate knife in the range from 5 to 106 of Deborah number the deformation component of friction coefficient decreases together with power consumption of refining process. © 2019 IOP Publishing Ltd. All rights reserved