The motion of a piezoviscous fluid under a surface load

Janečka, Adam; Průša, Vít

doi:10.1016/j.ijnonlinmec.2013.12.006

Cited by 5 publications

(2 citation statements)

References 42 publications

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“…Therefore the constraint of the rigid motion is fulfilled in the unyielded region and no "lubrication paradox" arises. These results are also extended to the case of fluids with constant density and pressure dependent viscosity (see [10] and the reference therein for an overview of these kind of fluids).…”

Section: Introductionmentioning

confidence: 89%

Pressure driven lubrication flow of a Bingham fluid in a channel: A novel approach

Fusi¹,

Farína²,

Rosso³

et al. 2015

Journal of Non-Newtonian Fluid Mechanics

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Section: Introductionmentioning

confidence: 89%

Pressure driven lubrication flow of a Bingham fluid in a channel: A novel approach

Fusi¹,

Farína²,

Rosso³

et al. 2015

Journal of Non-Newtonian Fluid Mechanics

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“…This desired behaviour has been guaranteed rigorously in [22] after making additional requirements which, however, do not cover realistic viscosity (15) at large pressures. The result in [22] stems from intensive research devoted to the notion and existence of a weak solution for incompressible fluids with pressureand shear rate-dependent viscosity, see [11,12,16,28] (see also [13,24,25,37] and the references therein). One of the assumptions embodied in the theoretical framework requires in particular that for certain constant C, see the concerned results for details 5 .…”

Section: Numerical Solutionmentioning

confidence: 99%

Numerical simulations of an incompressible piezoviscous fluid flowing in a plane slider bearing

2017

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The boundary conditions prescribing the constant traction or the so-called do-nothing conditions are frequently taken on artificial boundaries in the numerical simulations of steady flow of incompressible fluids, despite the fact that they do not facilitate a well-posed problem, not allowing to establish the standard energy estimates. In a pursuit to understand better the possible consequences of using these conditions, we present a particular set of examples of flow problems, where we find none or two analytical or numerical solutions. Namely, we consider problems where the flow connects two such artificial boundaries. In the simple case of the isotropic radial flows where both steady and unsteady analytical solutions are derived easily, we demonstrate that while for some (large) boundary data all unsteady solutions blow up in finite time, for other data (including small or trivial) the unsteady flows either converge asymptotically to one of two steady solutions, or blow up in finite time, depending on the initial state. We then document the very same behavior of the numerical solutions for planar flow in a diverging channel. Finally, we provide an illustrative example of two steady numerical solutions to the flow in a three-dimensional bifurcating tube, where the inflow velocity is prescribed at the inlet, while the two outlets are treated by the do-nothing boundary condition.

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Squeeze flow of a piezoviscous fluid

Řehoř¹,

Průša²

2016

Applied Mathematics and Computation

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The motion of a piezoviscous fluid under a surface load

Cited by 5 publications

References 42 publications

Pressure driven lubrication flow of a Bingham fluid in a channel: A novel approach

Pressure driven lubrication flow of a Bingham fluid in a channel: A novel approach

Numerical simulations of an incompressible piezoviscous fluid flowing in a plane slider bearing

Squeeze flow of a piezoviscous fluid

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