Unsteady shear flow of a viscoplastic material

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

doi:10.1016/s0377-0257(97)00018-9

Cited by 8 publications

(3 citation statements)

References 7 publications

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“…At early time, immediately following start-up, the material dynamics possess two key properties: (i) the velocity field is non-negligible only in the immediate neighbourhood of the plate; and (ii) the yield surface remains close to the plate (Burgess & Wilson 1997). These properties imply that the free surface cannot yet influence the material dynamics.…”

Section: Early Timementioning

confidence: 99%

“…Moreover, it has been reported that Poiseuille flow of a viscoplastic material comes to rest in finite time when the forcing is removed (Huilgol, Mena & Piau 2002;Chatzimina et al 2005). Transient viscoplastic and bi-viscous flows in pipes, with a time-dependent pressure gradient or wall velocity, have also been well studied, with detailed mathematical solutions developed for the evolution of the yield surface (Safronchik 1959a(Safronchik , 1960Comparini 1992;Burgess & Wilson 1997). The flow exterior to a cylinder with general applied angular velocity has also been considered (Safronchik 1959b).…”

Section: Introductionmentioning

confidence: 99%

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A layer of yield-stress material on a flat plate that moves suddenly

2022

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The flow of an unbounded Newtonian fluid above a flat solid plate, set into motion suddenly with uniform velocity, is a canonical problem investigated by Stokes (On the effect of the internal friction of fluids on the motion of pendulums, Trans. Camb. Phil. Soc., vol. 9, 1851) and Rayleigh (Lond. Edinb. Dubl. Philos. Mag. J. Sci., vol. 21, issue 126, 1911, pp. 697–711). We tackle the same problem but with the fluid replaced by a yield-stress material of finite height with a free surface; the latter ensures both yielded (fluid-like) and rigid behaviour. The interface between the yielded and rigid regions – the so-called ‘yield surface’ – always emerges from the plate at a rate faster than that for momentum diffusion. The rigid region, adjacent to the free surface, is accelerated by the constant yield stress acting at this yield surface. As the velocity of this region increases following start-up, its acceleration climaxes and subsequently diminishes. In this latter period, the thickness of the rigid region increases owing to relaxation of the velocity gradients and the stress. The yield surface eventually collides with the plate in finite time, after which the entire material moves in concert with the plate as a rigid body. Analytical and numerical results are presented that can form the basis for practical applications. This includes the development of a ‘rheological microscope’ to directly detect and measure the yield stress. The analysis focuses on exploring the flow physics of a Bingham material. This is shown to be similar to that of a general Herschel–Bulkley material with shear-thinning or shear-thickening rheology.

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Section: Early Timementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A layer of yield-stress material on a flat plate that moves suddenly

2022

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“…The study of fully dynamic flows of yield-stress materials is intrinsically more challenging owing to the nonlinear interactions of yield stress, inertia, viscosity and the flow geometry. The creation and destruction of yield surfaces is a dynamic process, and the yield surfaces can move through the material, driven by inertia (Burgess & Wilson 1997; Huilgol 2004). Hinton, Collis & Sader (2022) studied the dynamics of the viscoplastic Stokes’ first problem where a yield-stress material sits atop a solid plate that moves suddenly.…”

Section: Introductionmentioning

confidence: 99%

The motion of a layer of yield-stress material on an oscillating plate

2023

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The motion of a finite layer of Bingham material on a solid plate that executes in-plane oscillations was reported previously by Balmforth et al. (J. Non-Newtonian Fluid Mech., vol. 158, issue 1–3, 2009, pp. 46–53). There, it was suggested that multiple yielded regions may arise within the material; this contrasts to start-up flow of the same material for which only one yielded region is generated. Here, we explore quantitatively the fluid physics of this oscillatory flow problem through analytical approximations and further numerical computation. Four new key topological properties concerning the generation and termination of the yielded regions are reported. It is shown that the existence of multiple yielded regions is equivalent to the layer never becoming entirely rigid during the periodic motion. For small inertia, the flow is approximately time-reversible with only a single yielded region generated at the plate. For large inertia, shear stress in the material decays rapidly as a function of distance from the plate. A thin zone of yielded material detaches periodically from the plate, and subsequently terminates within the layer. At high oscillation frequency, there can be any number $N$ of distinct rigid regions, satisfying $N= \lfloor 1- {\rm \pi}^{-1} \log B \rfloor$ where $B$ is the Bingham number. It is also shown that for $B>0.5370$ , there are at most one yielded region and one rigid region throughout the motion. These theoretical results can be used as a basis for oscillatory rheometry, allowing for measurement of the yield stress using existing apparatus.

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