Pressure-driven flow of a rate-type fluid with stress threshold in an infinite channel

Fusi, Lorenzo; Farína, Angiolo

doi:10.1016/j.ijnonlinmec.2011.04.015

Cited by 8 publications

(3 citation statements)

References 13 publications

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“…We recall from the previous section that the condition |ξ 1 t | < 1 is guaranteed if dt dφ 1 The latter is automatically satisfied, under assumption H3 , recalling that φ 1 ξ o . So, also for the first order we have local uniqueness and existence of the solution ξ 1 t φ 1 t t, where φ 1 t is obtained inverting 4.28 .…”

Section: 28mentioning

confidence: 92%

On the Solution of a Hyperbolic One‐Dimensional Free Boundary Problem for a Maxwell Fluid

Fusi

Farína

2011

Advances in Mathematical Physics

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We study a hyperbolic (telegrapher's equation) free boundary problem describing the pressure-driven channel flow of a Bingham-type fluid whose constitutive model was derived in the work of Fusi and Farina (2011). The free boundary is the surface that separates the inner core (where the velocity is uniform) from the external layer where the fluid behaves as an upper convected Maxwell fluid. We present a procedure to obtain an explicit representation formula for the solution. We then exploit such a representation to write the free boundary equation in terms of the initial and boundary data only. We also perform an asymptotic expansion in terms of a parameter tied to the rheological properties of the Maxwell fluid. Explicit formulas of the solutions for the various order of approximation are provided.

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Section: 28mentioning

confidence: 92%

On the Solution of a Hyperbolic One‐Dimensional Free Boundary Problem for a Maxwell Fluid

Fusi

Farína

2011

Advances in Mathematical Physics

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“…Another way to smooth the singularities arising from the classical viscoplastic models is to take into account possible deformations of the plug, a procedure first suggested by Oldroyd [19]. Regarding the latter approach, the authors have carried out in the last ten years a series of papers in which they have relaxed the hypothesis of a perfectly rigid unyielded region assuming that the plug may undergo elastic deformations [7], [8] [9], [10], [11], [12].…”

Section: Introductionmentioning

confidence: 99%

Flow of a Bingham fluid in a non symmetric inclined channel

Fusi

Farína

2016

Journal of Non-Newtonian Fluid Mechanics

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“…; see e.g. [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15]) 616 L. FUSI, A. FARINA, AND F. ROSSO otherwise. We also refer the reader to [4], where interesting experimental investigations on these kinds of materials are reported.…”

Section: Introductionmentioning

confidence: 99%

Ill posedness of Bingham-type models for the downhill flow of a thin film on an inclined plane

2015

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In this paper we consider the flow of a thin layer of a Bingham-type material over an inclined plane with “small” tilt angle. A Bingham-type continuum is a material which behaves as a viscous fluid above a certain threshold (tied to the shear stress) and as a solid below such a threshold. We consider creeping flow and that the ratio between the thickness and the length of the layer is small, so that the lubrication approach is suitable. The unknowns of the model are the layer thickness, the position of the yield surface and the position of the advancing front. We first show that, though diverging in a neighborhood of the wetting front, the shear stress is integrable so that total dissipation is bounded. We then prove that the mathematical problem is inherently ill posed independently on the constitutive model selected for the solid domain. We therefore conclude that either the Bingham-type models are inappropriate to describe the thin film motion on an inclined surface or the lubrication technique fails in approximating such flows.

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Pressure-driven flow of a rate-type fluid with stress threshold in an infinite channel

Cited by 8 publications

References 13 publications

On the Solution of a Hyperbolic One‐Dimensional Free Boundary Problem for a Maxwell Fluid

On the Solution of a Hyperbolic One‐Dimensional Free Boundary Problem for a Maxwell Fluid

Flow of a Bingham fluid in a non symmetric inclined channel

Ill posedness of Bingham-type models for the downhill flow of a thin film on an inclined plane

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