Shear banding structure in viscoelastic micellar solutions

 Theoretically, it has been shown that worm-like micellar solutions of surfactant can, for a shear rate γ˙ greater than a critical value γ˙_c, undergo a transition giving a plateau evolution (σ=σ_c) of the shear stress σ against shear rate γ˙. We report here on a experimental study of the linear and nonlinear rheological behaviour of aqueous CTAB solutions with NaNO₃ as added salt. With this system, it is possible to observe the evolution of the fundamental characteristics of the flow curve, i.e., the shear rate γ˙_1c at which a shear banding structure appears and the second critical shear rate γ˙_2c characterizing the end of the shear stress plateau followed by a new increased shear stress. For the first time, experimentally, we obtained evidence for the existence and the evolution of γ˙_2c against CTAB and salt concentrations and temperature variations. Experimental results are compared to theoretical predictions correlating σ_c, γ˙_1c and G ₀ (the shear modulus) for Maxwellian micellar solutions. Received: 4 July 1996 Accepted: 19 November 1996     

Using Vorticity as an Indicator for the Generation of Optimal Coarse Grid Distribution

An improved vorticity-based gridding technique is presented and applied to create optimal non-uniform Cartesian coarse grid for numerical simulation of two-phase flow. The optimal coarse grid distribution (OCGD) is obtained in a manner to capture variations in both permeability and fluid velocity of the fine grid using a single physical quantity called “vorticity”. Only single-phase flow simulation on the fine grid is required to extract the vorticity. Based on the fine-scale vorticity information, several coarse grid models are generated for a given fine grid model. Then the vorticity map preservation error is used to predict how well each coarse grid model reproduces the fine-scale simulation results. The coarse grid model which best preserves the fine-scale vorticity, i.e. has the minimum vorticity map preservation error is recognized as an OCGD. The performance of vorticity-based optimal coarse grid is evaluated for two highly heterogeneous 2D formations. It is also shown that two-phase flow parameters such as mobility ratio have only minor impact on the performance of the predicted OCGD.     

Analysis of an immersed boundary method for three-dimensional flows in vorticity formulation

This article presents numerical analysis and practical considerations for three-dimensional flow computation using an implicit immersed boundary method. The Euler equations, or half a step of the Navier–Stokes equations when using fractional step algorithms, are investigated in their vorticity formulation. The context of flow computation around an arbitrarily shaped body is especially investigated.In conventional immersed boundary methods using vorticity, singular vortex are dispatched over the body surface. In the present study, one prefers using sources of potential velocity field, dispatched on the body, whose nature is not vorticity. Such a formulation is compatible to the Euler equations. In practice, these sources of potential flow produce a velocity through this surface, aiming in practice at cancelling a flow-through velocity.This article focuses on the use of the source-to-flow-through linear application, its properties being the key points for fast convergence. Its self-adjointness, or lack thereof, conditioning and preconditioning aspects are investigated. It follows that computing a velocity field with no-flow-through conditions in complex geometry, when using the source-to-flow-through linear application, can be achieved for 4/3 of the computational cost of standard Poisson equation in a Cartesian box.The robustness of immersed boundaries is especially interesting when used together with vortex-in-cell methods, well known for their robustness in time and their ability to compute accurately convective effects. A few examples, based on real-world geometries, illustrate the method capabilities.     

Magnetic Field Effects on Axis-Switching and Instabilities in Rectangular Plasma Jets

The effect of an external magnetic field on the evolution of rectangular plasma jets is examined. Specifically investigated is the influence of a primarily axial magnetic field on the uniquely characteristic axis-switching phenomenon of rectangular jets and flow instabilities. The results indicate that the magnetic field decelerates the jet (more rapid spreading), prevents axis-switching and inhibits instabilities. The key physical mechanisms underlying the changes are (1) the ability of the magnetic field to reverse the direction of vorticity and (2) transfer of energy from kinetic to magnetic forms. This study has important implications for magneto-hydro-dynamic flow control and propulsion applications.     

Self-organization of adiabatic shear bands in OFHC copper and HY-100 steel

We study the self-organization process of adiabatic shear bands in OFHC copper and HY-100 steel taking into account strain hardening factor. Starting from mathematical model we present a new numerical approach, which is based on Courant–Isaacson–Rees scheme, that allows one to simulate fully localized plastic flow. To prove the accuracy and efficiency of the following method we give solutions of two benchmark problems. Next we apply the proposed method to investigate such quantitative characteristics of self-organization process of ASB as average stress, temperature, localization time and distance between ASB. Then we compare the obtained results with theoretical predictions by other authors.     

FOURIER PSEUDOSPECTRAL－FINITE DIFFERENCE METHOD FOR TWO－DIMENSIONAL VORICITY EQUATION

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Dehn surgeries on strongly invertible knots which yield lens spaces

In this article we show no Dehn surgery on nontrivial strongly invertible knots can yield the lens space for any integer . In order to do that, we determine band attaches to -torus links producing the trivial knot.

     

Convergence of Dirichlet quotients and selective decay of 2D magnetohydrodynamic flows

The selective decay phenomena have been observed by physicists for many dynamic flows such as Navier-Stokes flows, barotropic geophysical flows, and magnetohydrodynamic (MHD) flows in either actual physical experiments or numerical simulations. In the previous paper (M.-Q. Zhan, 2010 [20]), the author showed the validity of the selective decay principle for the 2D magnetohydrodynamic (MHD) flows in the case of small magnetic Prandtl number. In this paper, we shall show the validity of the selective decay principle for the 2D magnetohydrodynamic (MHD) flows for any magnetic Prandtl number with periodic boundary conditions.     

Solution of 2D Navier–Stokes equation by coupled finite difference-dual reciprocity boundary element method

Computation of viscous fluid flow is an area of research where many authors have tried to present different numerical methods for solution of the Navier–Stokes equations. Each of these methods has its own advantages and weaknesses. In the meantime, many researchers have attempted to develop coupled numerical algorithms in order to save storage for computational purposes and to save computational time.