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Viscoplastic flow between hinged plates
- Jesse J. Taylor-West, Andrew J. Hogg
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- Journal:
- Journal of Fluid Mechanics / Volume 958 / 10 March 2023
- Published online by Cambridge University Press:
- 09 March 2023, A38
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The incompressible motion of viscoplastic fluid between two semi-infinite rigid plates, hinged at their ends and rotating towards one another at constant angular velocity, generates self-similar flow fields because there is no externally imposed length scale in the absence of inertia. The magnitude of the strain rate scales with the angular velocity of the plates and the dimensionless deviatoric stresses are functions only of the polar angle and a dimensionless measure of the yield stress; they are independent of the radial distance from the corner. These flows feature unyielded regions adjacent to the boundaries for sufficiently large angles between the plates. Moreover, when the dimensionless yield stress is large, there are viscoplastic boundary layers that are attached to the boundary or the plug, the asymptotic structures of which are constructed.
Viscoplastic corner eddies
- Jesse J. Taylor-West, Andrew J. Hogg
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- Journal:
- Journal of Fluid Mechanics / Volume 941 / 25 June 2022
- Published online by Cambridge University Press:
- 10 May 2022, A64
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When viscous fluid in a corner is disturbed, eddies can form in the absence of inertia. Examples of flow configurations in which this motion occurs include flow through an abrupt contraction and over a cavity. Six decades ago, Moffatt (J. Fluid Mech., vol. 18, 1964, pp. 1–18) calculated the slow viscous flow of Newtonian fluids in sharp corners, detailing his eponymous ‘Moffatt eddies’. In this study we examine corner flows of viscoplastic materials, a class of non-Newtonian fluids which exhibit solid-like behaviour for stresses below a yield stress. Specifically, we consider a Bingham fluid, for which the material is perfectly rigid at stresses below the yield stress. While a static unyielded plug forms at the tip of the corner, eddies analogous to those found by Moffatt can also form. We examine these viscoplastic eddies numerically, by computing finite element solutions using the augmented-Lagrangian method, and analytically, by employing a viscoplastic boundary layer formulation and scaling arguments. We measure the depth of the static plug as a function of the Bingham number (dimensionless yield stress), show that the process of a new eddy forming as the Bingham number is decreased is driven by the pressure in the yielded fluid adjacent to the static plug, and provide a heuristic argument for the critical Bingham number at which this occurs.
The converging flow of viscoplastic fluid in a wedge or cone
- Jesse J. Taylor-West, Andrew J. Hogg
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- Journal:
- Journal of Fluid Mechanics / Volume 915 / 25 May 2021
- Published online by Cambridge University Press:
- 17 March 2021, A69
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Converging flows of viscoplastic fluids, driven steadily through wedges and axisymmetric cones, are studied analytically and numerically. When the yield stress is relatively large, the bulk of the fluid flows plastically apart from within thin layers where the fluid is strongly sheared in order to achieve no slip at the boundary. Conversely, when the yield stress is relatively small, the motion is viscously dominated with weak corrections to the velocity and stress fields due to viscoplastic effects. For both regimes, viscoplasticity induces a weak angular velocity, directed away from the boundaries, and purely radial flow is not possible. The structure of the flow is calculated using asymptotic methods, confirmed by finite element numerical simulations. Flows of both Bingham and Herschel–Bulkley fluids are analysed, and both planar and axisymmetric geometries are considered. Although these cases differ in their details, they share the same qualitative structure. In particular, the viscoplastic boundary layers that emerge when the yield stress is relatively large, ensure not only that no slip is enforced, but also, through an intermediate matching layer, that the shear rates remain bounded.
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- The Cambridge Dictionary of Christianity
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- 05 August 2012
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- 20 September 2010, pp xi-xliv
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