Creeping flow of a Herschel–Bulkley fluid with pressure-dependent material moduli

Fusi, Lorenzo; Rosso, Fábio

doi:10.1017/s0956792517000183

Cited by 9 publications

(2 citation statements)

References 21 publications

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“…Ali et al [12] presented a numerical study creeping flow of Herschel-Bulkley fluids in collapsible channels. Creeping flow of a Herschel-Bulkley fluid with pressure-dependent material moduli is discussed by Fusi and Rosso [13]. In this paper we consider the flow of Herschel -Bulkley fluid in a plane analogue with elastic walls.…”

Section: Introductionmentioning

confidence: 96%

Flow of a Herschel-Bulkley Fluid in a Channel with Elastic Walls

Sreenadh

Sumalatha²,

Srinivas³

2018

IJET

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In order to model the blood flow through an artery in presence of catheter, we considered a steady, laminar, incompressible, Poiseuille flow of a Herschel-Bulkley fluid between two horizontal parallel elastic walls. The power law index ( ) and yield stress ( ) are the two parameters of the Herschel - Bulkley fluid. By giving different values for the above mentioned parameters, we get the Newtonian, Bingham and Power-law fluids as special cases. The exact solutions for the flow quantities such as velocity, plug flow velocity and flux are derived. The flux is determined as a function of inlet, outlet, external pressures and the elastic property of the channel. The effect of elastic parameters on flux variation is analyzed. Further when and our results qualitatively agree with those of Rubinow and Keller [2]. In addition, velocity of the Herschel- Bulkley fluid flow is expressed in terms of elastic parameters.

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Section: Introductionmentioning

confidence: 96%

Flow of a Herschel-Bulkley Fluid in a Channel with Elastic Walls

Sreenadh

Sumalatha²,

Srinivas³

2018

IJET

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“…When the constitutive response exhibits a yield stress the fluid is called viscoplastic, meaning that a critical value of the stress must be exceeded to start the flow. Among visco-plastic models we mention the Bingham model [2], the Herschel-Bulkley model [12], the Casson model [3] and the Heinz-Casson model [10] and [16] we assume that the latter may depend on the pressure.…”

Section: Introductionmentioning

confidence: 99%

Lubrication flow of a generalized Casson fluid with pressure-dependent rheological parameters

Fusi

2019

Journal of Non-Newtonian Fluid Mechanics

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A spectral collocation scheme for the flow of a piezo-viscous fluid in ducts with slip conditions

Fusi,

Giovinetto

2024

Theor. Comput. Fluid Dyn.

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In this paper we present a numerical scheme based on spectral collocation methods to investigate the flow of a piezo-viscous fluid, i.e., a fluid in which the rheological parameters depend on the pressure. In particular, we consider an incompressible Navier–Stokes fluid with pressure dependent viscosity flowing in: (i) a two-dimensional non-symmetric planar channel; (ii) a three-dimensional axisymmetric non-straight conduit. For both cases we impose the Navier slip boundary conditions that can be reduced to the classical no-slip condition for a proper choice of the slip parameter. We assume that the dependence of the viscosity on the pressure is of exponential type (Barus law), even though the model can be replaced by any other viscosity function. We write the mathematical problem (stress based formulation) and discretize the governing equations through a spectral collocation scheme. The advantage of this numerical procedure, which to the authors’ knowledge has never been used before for this class of fluids, lies in in the ease of implementation and in the accuracy of the solution. To validate our model we compare the numerical solution with the one that can be obtained in the case of small aspect ratio, i.e., the leading order lubrication solution. We perform some numerical simulation to investigate the effects of the pressure-dependent viscosity on the flow. We consider different wall functions to gain insight also on the role played by the channel/duct geometry. In both cases (i), (ii) we find that the increase of the coefficient appearing in the viscosity function results in a global reduction of the flow, as physically expected.

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Creeping flow of a Herschel–Bulkley fluid with pressure-dependent material moduli

Cited by 9 publications

References 21 publications

Flow of a Herschel-Bulkley Fluid in a Channel with Elastic Walls

Flow of a Herschel-Bulkley Fluid in a Channel with Elastic Walls

Lubrication flow of a generalized Casson fluid with pressure-dependent rheological parameters

A spectral collocation scheme for the flow of a piezo-viscous fluid in ducts with slip conditions

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