Granular Flow Lubrication: Continuum Modeling of Shear Behavior

2004 ◽  
Vol 126 (3) ◽  
pp. 499-510 ◽  
Author(s):  
C. Fred Higgs, ◽  
John Tichy
Keyword(s):  
Boundary Conditions ◽  
Energy Transport ◽  
Granular Flows ◽  
Solid Particles ◽  
Numerical Code ◽  
Flow Properties ◽  
Local Flow ◽  
Shear Cell ◽  
Coupled Boundary Conditions ◽  
Lubricating Mechanism

Because at extreme temperatures, conventional liquid lubrication breaks down, researchers have proposed using flows of solid particles as a lubricating mechanism. The particles may be powders, which tend to coalesce and slide over one another in sustained contact, or granules, which collide with one another in fluctuating motion. Distinction between these two regimes is elucidated. The behavior of various granular flows is studied using a granular kinetic lubrication (GKL) model. Our GKL model is a continuum approach that applies proper rheological constitutive equations for stress, conduction and dissipation to thin shearing flows of granular particles, as well as the most rigorous boundary conditions for momentum and energy transport. A robust numerical code, utilizing Newton’s finite differencing method, is developed to apply GKL theory to the problem of simple shearing flow. The code solves two second-order, coupled nonlinear ordinary differential equations with coupled boundary conditions of the first-order. As a result, new parametric curves for the local flow properties of the large-particle granular flows are constructed. Results from the GKL model agree qualitatively with past experiments using glass granules in an annular shear cell.

scholarly journals A Self-Adjoint Coupled System of Nonlinear Ordinary Differential Equations with Nonlocal Multi-Point Boundary Conditions on an Arbitrary Domain

2021 ◽  
Vol 11 (11) ◽  
pp. 4798
Author(s):  
Hari Mohan Srivastava ◽  
Sotiris K. Ntouyas ◽  
Mona Alsulami ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Coupled System ◽  
Contraction Mapping Principle ◽  
Arbitrary Domain ◽  
Banach Contraction ◽  
Coupled Boundary Conditions ◽  
Banach Contraction Mapping Principle ◽  
Banach Contraction Mapping

The main object of this paper is to investigate the existence of solutions for a self-adjoint coupled system of nonlinear second-order ordinary differential equations equipped with nonlocal multi-point coupled boundary conditions on an arbitrary domain. We apply the Leray–Schauder alternative, the Schauder fixed point theorem and the Banach contraction mapping principle in order to derive the main results, which are then well-illustrated with the aid of several examples. Some potential directions for related further researches are also indicated.

scholarly journals Existence results for coupled nonlinear fractional differential equations of different orders with nonlocal coupled boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmed Alsaedi ◽  
Soha Hamdan ◽  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Arbitrary Domain ◽  
Uniqueness Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Coupled Boundary Conditions ◽  
Fractional Differential

AbstractThis paper is concerned with the solvability of coupled nonlinear fractional differential equations of different orders supplemented with nonlocal coupled boundary conditions on an arbitrary domain. The tools of the fixed point theory are applied to obtain the criteria ensuring the existence and uniqueness of solutions of the problem at hand. Examples illustrating the main results are presented.

The Influence of Initial Velocity and Temperature Lag on the Relaxation Zone behind a Shock Wave in a Gas-Solid Flow

1975 ◽  
Vol 189 (1) ◽  
pp. 367-373
Author(s):  
B. N. Cole ◽  
M. R. Baum ◽  
F. R. Mobbs
Keyword(s):  
Shock Wave ◽  
Energy Transfer ◽  
Initial Velocity ◽  
Solid Particles ◽  
Flow Properties ◽  
Equilibrium Conditions ◽  
Solid Flow ◽  
Relaxation Zone ◽  
Nozzle Flows ◽  
Kinetic Energy Transfer

Thermal and velocity lag prior to the gas discontinuity are shown to have a significant effect on the properties of the relaxation zone of a gas-solid flow shock wave. The results obtained by previous workers assuming equilibrium conditions are not therefore applicable to shock waves formed in gas-solid nozzle flows where considerable disequilibrium already exists. The variations of the relevant flow properties in the relaxation zone are interpreted physically in terms of the magnitude and sign of the heat, momentum and kinetic energy transfer between the solid particles and the gas.

scholarly journals Lateral boundary conditions for a local anisotropic ice-flow model

2002 ◽  
Vol 35 ◽  
pp. 503-509 ◽  
Author(s):  
Olivier Gagliardini ◽  
Jacques Meyssonnier
Keyword(s):  
Boundary Conditions ◽  
Flow Model ◽  
Ice Sheet ◽  
Lateral Boundary ◽  
Local Flow ◽  
Ice Flow ◽  
Lateral Boundary Conditions ◽  
Potential Applications ◽  
Two Dimensional Flow ◽  
Spatial Domains

AbstractA local two-dimensional flow model which accounts for the anisotropic behaviour of polar ice and the evolution of its strain-induced anisotropy is briefly reviewed. Due to its complexity, it is not yet possible to use this model to simulate the flow of a whole ice sheet, and its potential applications are presently restricted to limited spatial domains around existing drilling sites. In order to calculate the local flow of ice, boundary conditions must be applied on the lateral edges of the studied domain. Since these limits correspond to fictitious sections of the ice sheet, the type of boundary condition to adopt is not obvious. In the present paper, different kinds of boundary conditions of the Dirichlet type, applied at the lateral boundary of an idealized ice sheet of simplified geometry, are discussed. This will serve as a first step towards the coupling of the local flow model with a global ice-sheet flow model.

Existence of solutions for a system of fractional differential equations with coupled nonlocal boundary conditions

2018 ◽  
Vol 21 (2) ◽  
pp. 423-441 ◽  
Author(s):  
Bashir Ahmad ◽  
Rodica Luca
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Fractional Integrals ◽  
Nonlinear Alternative ◽  
Coupled Boundary Conditions ◽  
Fractional Differential

AbstractWe study the existence of solutions for a system of nonlinear Caputo fractional differential equations with coupled boundary conditions involving Riemann-Liouville fractional integrals, by using the Schauder fixed point theorem and the nonlinear alternative of Leray-Schauder type. Two examples are given to support our main results.

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