The steady, spreading flow of a rivulet of mud

Wilson, S. D. R.; Burgess, S.L.

doi:10.1016/s0377-0257(98)00079-2

Cited by 39 publications

(28 citation statements)

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“…The Bingham plastic model ͑i.e., F 1 ϰ ‫ץ‬V / ‫ץ‬y͒ appears to be well suited to some sediment-laden flows with large concentrations of fine particles ͑e.g., Wan and Wang 1994;Julien 1995͒. A more advanced rheological model is the Herschel-Bulkley fluid model for which F 1 ϰ ͑‫ץ‬V / ‫ץ‬y͒ m , where 0 Ͻ m ഛ 1 ͑e.g., Huang and Garcia 1998;Wilson and Burgess 1998͒. Various models have been proposed to describe the behavior of thixotropic fluids ͑e.g., Mewis 1979;Usui 1995;Toorman 1997͒. Most have a similar structure consisting of an equation of the form ͑2͒ now with parameters depending upon some structure parameter͑s͒, associated with some kinetic equation͑s͒ giving the time evolution of the͑se͒ structure parameter͑s͒ as function͑s͒ of time and shear rate.…”

Section: Fluid Rheologymentioning

confidence: 99%

Dam Break Wave of Thixotropic Fluid

2006

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Abstract:Thixotropy is the characteristic of a fluid to form a gelled structure over time when it is not subjected to shearing, and to liquefy when agitated. Thixotropic fluids are commonly used in the construction industry ͑e.g., liquid concrete and drilling fluids͒, and related applications include some forms of mud flows and debris flows. This paper describes a basic study of dam break wave with thixotropic fluid. Theoretical considerations were developed based upon a kinematic wave approximation of the Saint-Venant equations down a prismatic sloping channel. A very simple thixotropic model, which predicts the basic rheological trends of such fluids, was used. It describes the instantaneous state of fluid structure by a single parameter. The analytical solution of the basic flow motion and rheology equations predicts three basic flow regimes depending upon the fluid properties and flow conditions, including the initial "degree of jamming" of the fluid ͑related to its time of restructuration at rest͒. These findings were successfully compared with systematic bentonite suspension experiments. The present work is the first theoretical analysis combining the basic principles of unsteady flow motion with a thixotropic fluid model and systematic laboratory experiments.

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Section: Fluid Rheologymentioning

confidence: 99%

Dam Break Wave of Thixotropic Fluid

2006

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“…While much of the earlier work has focused on time-dependent flows of viscous fluids over a rigid boundary [14][15][16][17], a growing attention has been paid to the corresponding problem with viscoplastic fluids from the theoretical point of view [18][19][20][21][22][23][24][25][26][27][28][29]. On rare occasions, exact or asymptotic analytical solutions to the governing equations can be worked out [10,21,[30][31][32][33][34], but most of the time, solutions must be computed numerically using flow-depth averaged equations of motion (the equivalent of the shallow-water equations in hydraulics) [35][36][37], nonlinear diffusion equations when inertial terms are negligible [19,21], or the full set of equations of motion (using a finite-element approach or smooth-particle-hydrodynamics techniques).…”

Section: Introductionmentioning

confidence: 99%

Experimental investigation of the spreading of viscoplastic fluids on inclined planes

Cochard

Ancey

2009

Journal of Non-Newtonian Fluid Mechanics

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a b s t r a c tWe report experimental results related to the dam-break problem for viscoplastic fluids. Using image processing techniques, we were able to accurately reconstruct the free-surface evolution of fixed volumes of fluid suddenly released a plane. We used Carbopol Ultrez 10 as a viscoplastic material; its rheological behavior was closely approximated by a Herschel-Bulkley model for a fairly wide range of shear-rates. Varying the Carbopol concentration allowed us to change the yield stress and bulk viscosity. The yield stress ranged from 78 to 109 Pa, producing Bingham numbers in the 0.07-0.35 range. We investigated the behavior of a 43-kg mass released on a plane, whose inclination ranged from 0 • to 18 • . For each run, we observed that the behavior was nearly the same: at short times, the mass accelerated vigorously on gate opening and very quickly reached a nearly constant velocity. At time t = 1 s, independently of plane inclination and yield stress, the mass reached a near-equilibrium regime, where the front position varied as a power function of time over several decades. We did not observe any run-out phase, during which the mass would have gradually come to a halt. The similarity in the flow behavior made it possible to derive an empirical scaling for the front position in the form x f = t 0.275(sin˛) 1/3 (sin˛) 5/4 , where˛and t denote plane inclination and time, respectively, and which holds for sloping beds (˛> 0).

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“…We did this in two stages, first by using a shooting method to solve (36) subject to (25) to determine the value of η 0 in (26) 1 for a given value of H 0 , and then by using the condition C = 0 to select the physically realisable solutions from this family of solutions;…”

Section: A Rivuletmentioning

confidence: 99%

“…Smith [35] obtained a similarity solution describing steady flow of a sessile rivulet issuing from a point source on an inclined plane, and this was generalised by Wilson and Burgess [36] to the case of a power-law fluid. Perazzo and Gratton [37] obtained a wide class of steady two-dimensional solutions for flow of a power-law fluid on an inclined plane.…”

Section: Introductionmentioning

confidence: 99%

Similarity solutions for unsteady shear-stress-driven flow of Newtonian and power-law fluids: slender rivulets and dry patches

2011

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This version is available at https://strathprints.strath.ac.uk/34258/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output.Similarity solutions for unsteady shear-stress-driven flow of Abstract. Unsteady flow of a thin film of a Newtonian fluid or a non-Newtonian power-law fluid with power-law index N driven by a constant shear stress applied at the free surface, on a plane inclined at an angle α to the horizontal, is considered. Unsteady similarity solutions representing flow of slender rivulets and flow around slender dry patches are obtained. Specifically, solutions are obtained for converging sessile rivulets (0 < α < π/2) and converging dry patches in a pendent film (π/2 < α < π), as well as for diverging pendent rivulets and diverging dry patches in a sessile film. These solutions predict that at any time t the rivulet and dry patch widen or narrow according to |x| 3/2 and the film thickens or thins according to |x|, where x denotes distance down the plane, and that at any station x the rivulet and dry patch widen or narrow like |t| −1 and the film thickens or thins like |t| −1 , independent of N.

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The steady, spreading flow of a rivulet of mud

Cited by 39 publications

References 5 publications

Dam Break Wave of Thixotropic Fluid

Dam Break Wave of Thixotropic Fluid

Experimental investigation of the spreading of viscoplastic fluids on inclined planes

Similarity solutions for unsteady shear-stress-driven flow of Newtonian and power-law fluids: slender rivulets and dry patches

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