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On local solutions to non-Newtonian slow viscous flows
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In this paper, the eigenfunction expansion method is used to obtain local solutions to some non-Newtonian slow viscous flows, including power-law fluids, and the critical corner angle for eddy formation is obtained.Abstract:
The eigenfunction expansion method is used to obtain local solutions to some non-Newtonian slow viscous flows. The forms of viscosity variation amenable to such analysis are restricted but do include power-law fluids. Power-law flow near a sharp corner between plane boundaries is analysed and results are obtained for the critical corner angle for eddy formation. Flows near a 90° corner with either a moving boundary or a finite flow rate at the corner are also considered. The “stick-slip” behaviour of a power-law fluid at a plane solid boundary is shown to obey a simple law.read more
Citations
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Mantle flow pressure and the angle of subduction: Non-Newtonian corner flows
TL;DR: In this paper, the authors used a mixture of Newtonian and non-Newtonian fluids to model the flow in a subduction zone which is viscously driven by the motions of the converging plates and the descending slab.
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Some boundary value problems for the Bingham model
Colin Atkinson,K. El-Ali +1 more
TL;DR: In this paper, the authors study the behavior of Bingham materials near the apex of a corner for different external flows: Poiseuille flow due to an applied external pressure or other axially moving boundaries, creeping plane flow around wedges, and three dimensional flow in the neighbourhood of the corner of the base of a right circular cylinder.
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The wedge subjected to tractions: a paradox resolved
TL;DR: In this paper, the authors derived conditions which pre-determine the form of the necessary Airy stress function, and showed that inhomogeneous boundary conditions can induce stresses of O(r−ω), O( r−ω ln r), or O(ρ−ω rn2r) as r→0, depending on which conditions are satisfied.
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A continuum model of continental deformation above subduction zones - Application to the Andes and the Aegean
TL;DR: In this article, a model of continental deformation above subduction zones was developed that combines the viscous sheet and the corner flow models; the continental lithosphere is described by a two-dimensional sheet model that considers basal drag resulting from viscous asthenosphere flow underneath, and a corner flow model with a deforming overlying plate and a rigid subducting plate is used to calculate the shear traction that acts on the base of the lithosphere above a subduction zone.
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The effect of the slip condition on flows of an Oldroyd 6-constant fluid
TL;DR: In this paper, the steady flows of a non-Newtonian fluid are considered when the slippage between the plate and the fluid is valid and the constitutive equations of the fluid are modeled by those for an Oldroyd 6-constant fluid.
References
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On the Stress Distribution at the Base of a Stationary Crack
TL;DR: In this article, it was shown that at the base of the crack in the direction of its prolongation, the principal stresses are equal, thus tending toward a two-dimensional (two-dimensional) hydrostatic tension.
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Singular behaviour at the end of a tensile crack in a hardening material
TL;DR: In this paper, a total deformation theory of plasticity, in conjunction with two hardening stress-strain relations, is used to determine the dominant singularity at the tip of a crack in a tension field.
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Viscous and resistive eddies near a sharp corner
TL;DR: In this paper, it was shown that when either or both of the boundaries is a rigid wall and when the angle between the planes is less than a certain critical angle, any flow sufficiently near the corner must consist of a sequence of eddies of decreasing size and rapidly decreasing intensity.
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Analytical and numerical studies of the structure of steady separated flows
TL;DR: In this paper, an analytical solution, based on a linearized model, is obtained for an eddy bounded by a circular streamline, which reveals the flow development from a completely viscous eddy at low Reynolds number to an inviscid rotational core at high Reynolds number, in the manner envisaged by Batchelor.
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