Yongqi Wang

PERISTALTIC TRANSPORT OF A THIRD-ORDER FLUID IN A CIRCULAR CYLINDRICAL TUBE

The effect of a third-order fluid on the peristaltic transport is analysed in a circular cylindrical tube, such as some organs in the living body. The third-order flow of an incompressible fluid in a circular cylindrical tube, on which an axisymmetric travelling sinusoidal wave is imposed, is considered. The wavelength of the peristaltic waves is assumed to be large compared to the tube average radius, whereas the amplitude of the wave need not be small compared to the average radius. Both analytic (perturbation) and numerical solutions are given. For the perturbation solution, a systematic approach based on an asymptotic expansion of the solution in terms of a small Deborah number is used and solutions up to the first order are presented in closed forms. The numerical solution, valid for any Deborah number, represents a new approach to peristaltic flows, and its features illuminate the physical behaviour much more than the analytical research on this problem. Comparison is made between the analytic (perturbation) and numerical results. Furthermore, the obtained results could also have applications to a range of peristaltic flows for a variety of non-Newtonian fluids such as aqueous solutions of high-molecular weight polyethylene oxide and polyacrylamide.

Peristaltic transport of an Oldroyd-B fluid in a planar channel

The effects of an Oldroyd-B fluid on the peristaltic mechanism are examined under the long wavelength assumption. Analytical expressions for the stream function, the axial velocity, and the pressure rise per wavelength are obtained up to the second order in the dimensionless wave number. The effects of the various parameters of interest on the flow are shown and discussed.

Peristaltic motion of a Johnson-Segalman fluid in a planar channel

This paper is devoted to the study of the two-dimensional flow of a Johnson-Segalman fluid in a planar channel having walls that are transversely displaced by an infinite, harmonic travelling wave of large wavelength. Both analytical and numerical solutions are presented. The analysis for the analytical solution is carried out for small Weissenberg numbers. (A Weissenberg number is the ratio of the relaxation time of the fluid to a characteristic time associated with the flow.) Analytical solutions have been obtained for the stream function from which the relations of the velocity and the longitudinal pressure gradient have been derived. The expression of the pressure rise over a wavelength has also been determined. Numerical computations are performed and compared to the perturbation analysis. Several limiting situations with their implications can be examined from the presented analysis.

Hall effects on the unsteady hydromagnetic oscillatory flow of a second-grade fluid

An exact solution of an oscillatory flow is constructed in a rotating fluid under the influence of an uniform transverse magnetic field. The fluid is considered as second-grade (non-Newtonian). The influence of Hall currents and material parameters of the second-grade fluid is investigated. The hydromagnetic flow is generated in the uniformly rotating fluid bounded between two rigid non-conducting parallel plates by small amplitude oscillations of the upper plate. The exact solutions of the steady and unsteady velocity fields are constructed. It is found that the steady solution depends on the Hall parameter but is independent of the material parameter of the fluid. The unsteady part of the solution depends upon both (Hall and material) parameters. Attention is focused upon the physical nature of the solution, and the structure of the various kinds of boundary layers is examined. Several results of physical interest have been deduced in limiting cases.

Rapid flow of dry granular materials down inclined chutes impinging on rigid walls

We performed laboratory experiments of dry granular chute flows impinging an obstructing wall. The chute consists of a 10cm wide rectangular channel, inclined by 50° relative to the horizontal, which, 2m downslope abruptly changes into a horizontal channel of the same width. 15l of quartz chips are released through a gate with the same width as the chute and a gap of 6cm height, respectively. Experiments are conducted for two positions of the obstructing wall, (i) 2m below the exit gate and perpendicular to the inclined chute, and (ii) 0.63m into the horizontal runout and then vertically oriented. Granular material is continuously released by opening the shutter of the silo. The material then moves rapidly down the chute and impinges on the obstructing wall. This leads to a sudden change in the flow regime from a fast moving supercritical thin layer to a stagnant thick heap with variable thickness and a surface dictated by the angle of repose typical for the material. We conducted particle image velocimet...

The Savage–Hutter avalanche model: how far can it be pushed?

The Savage–Hutter (SH) avalanche model is a depth-averaged dynamical model of a fluid-like continuum implementing the following simplifying assumptions: (i) density preserving, (ii) shallowness of the avalanche piles and small topographic curvatures, (iii) Coulomb-type sliding with bed friction angle δ and (iv) Mohr–Coulomb behaviour in the interior with internal angle of friction φ≥δ and an ad hoc assumption reducing the number of Mohrs circles in three-dimensional stress states to one. We scrutinize the available literature on information regarding these assumptions and thus delineate the ranges of validity of the proposed model equations. The discussion is limited to relatively large snow avalanches with negligible powder snow component and laboratory sand avalanches starting on steep slopes. The conclusion of the analysis is that the SH model is a valid model for sand avalanches, but its Mohr–Coulomb sliding law may have to be complemented for snow avalanches by a second velocity-dependent contribution. For very small snow avalanches and for laboratory avalanches starting on moderately steep and bumpy slopes it may not be adequate.

Velocity measurements in dry granular avalanches using particle image velocimetry technique and comparison with theoretical predictions

Velocity and depth are crucial field variables to describe the dynamics of avalanches of sand or soil or snow and to draw conclusions about their flow behavior. In this paper we present new results about velocity measurements in granular laboratory avalanches and their comparison with theoretical predictions. Particle image velocimetry measurement technique is introduced and used to measure the dynamics of the velocity distribution of free surface and unsteady flows of avalanches of non-transparent quartz particles down a curved chute merging into a horizontal plane from initiation to the runout zone. Velocity distributions at the free surface are determined and in one case also at the bottom from below. Also measured is the settlement of the avalanche in the deposit. For the theoretical prediction we consider the model equations proposed by Pudasaini and Hutter [J. Fluid Mech. 495, 193 (2003)]. A nonoscillatory central differencing total variation diminishing scheme is implemented to integrate these mode...

Rapid motions of free-surface avalanches down curved and twisted channels and their numerical simulation.

This paper presents a new model and discussions about the motion of avalanches from initiation to run-out over moderately curved and twisted channels of complicated topography and its numerical simulations. The model is a generalization of a well established and widely used depth-averaged avalanche model of Savage & Hutter and is published with all its details in Pudasaini & Hutter (Pudasaini & Hutter 2003 J. Fluid Mech. 495, 193–208). The intention was to be able to describe the flow of a finite mass of snow, gravel, debris or mud, down a curved and twisted corrie of nearly arbitrary cross-sectional profile. The governing equations for the distribution of the avalanche thickness and the topography-parallel depth-averaged velocity components are a set of hyperbolic partial differential equations. They are solved for different topographic configurations, from simple to complex, by applying a high-resolution non-oscillatory central differencing scheme with total variation diminishing limiter. Here we apply the model to a channel with circular cross-section and helical talweg that merges into a horizontal channel which may or may not become flat in cross-section. We show that run-out position and geometry depend strongly on the curvature and twist of the talweg and cross-sectional geometry of the channel, and how the topography is shaped close to run-out zones.

SHEARING FLOWS IN A GOODMAN-COWIN TYPE GRANULAR MATERIAL—THEORY AND NUMERICAL RESULTS

Goodman and Cowin (1972) proposed a continuum theory of a dry cohesionless granular material in which the solid volume fraction ” is treated as an independent kinematic fleld for which an additional balance law of equilibrated forces is postulated. By adopting the M˜ uller-Liu approach to the exploitation of the entropy inequality we show that in a constitutive model containing ”, _ ” and grad” as independent variables results agree with the classical Coleman-Noll approach only provided the Helmholtz free energy does not depend on _ ”, for which the Goodman-Cowin equations are reproduced. This reduced theory is then applied to analyses of steady fully-developed horizontal shearing ∞ow and gravity ∞ows of granular materials down an inclined plane and between vertical parallel plates. It is demonstrated that the equations and numerical results, presented by Passman et al. (1980) are false, and they are corrected. The results show that the dynamical behaviour of these materials is quite difierent from that of a viscous ∞uid. In some cases the dilatant shearing layers exist only in the narrow zones near the boundaries.

Continuum Mechanics and Applications in Geophysics and the Environment

I Applied Continuum Mechanics.- Numerical Investigation of Shock Waves in a Radiating Gas Described by a Variable Eddington Factor.- Anisotropic Fluids: From Liquid Crystals to Granular Materials.- Integration and Segregation in a Population - A Thermodynamicistss View.- Asymptotic and Other Properties of Some Nonlinear Diffusion Models.- The Binary Mixtures of Euler Fluids: A Unified Theory of Second Sound Phenomena.- Continuously Distributed Control of Plates by Electric Networks with PZT Actuators.- II Soil Mechanics and Porous Media.- Hydraulic Theory for a Frictional Debris Flow on a Collisional Shear Layer.- The Beavers and Joseph Condition for Velocity Slip at the Surface of a Porous Medium.- Porous Convection, the Chebyshev Tau Method, and Spurious Eigenvalues.- Mechanics of Multiphase Porous Media - Application to Unsaturated Soils.- III Glacier and Ice Dynamics.- Modelling Iceberg Drift and Ice-Rafted Sedimentation.- Modelling the Flow of Glaciers and Ice Sheets.- Notes on Basic Glaciological Computational Methods and Algorithms.- Constitutive Modelling and Flow Simulation of Anisotropic Polar Ice.- Influence of Bed Topography on Steady Plane Ice Sheet Flow.- IV Climatology and Lake Physics.- Glacial Isostasy: Models for the Response of the Earth to Varying Ice Loads.- Arctic Sea Ice and Its Role in Climate Variability and Change.- The Role of Simple Models in Understanding Climate Change.- Comparing Different Numerical Treatments of Advection Terms for Wind-Induced Circulations in Lake Constance.