Combined effects of compressibility and slip in flows of a Herschel–Bulkley fluid

Damianou, Yiolanda; Georgiou, Georgios C.; Moulitsas, Irene

doi:10.1016/j.jnnfm.2012.09.004

Cited by 49 publications

(26 citation statements)

References 29 publications

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“…It also emulates the Newtonian fluids when both the yield-stress is zero and the flow behavior index is unity. [34] The Herschel-Bulkley model contains six classes: (1) shear-thinning without yield-stress [n < 1.0, τ o = 0], which is the power-law fluid in shear-thinning mode, For Herschel-Bulkley fluids, the volumetric flow rate as a function of the pressure drop in a circular cylindrical tube with a fixed radius assuming a laminar incompressible flow with no wall slip [31,35] is given by the following relation [9,32,33] :…”

Section: Herschel-bulkley Modelmentioning

confidence: 99%

Flow of non‐Newtonian fluids in converging–diverging rigid tubes

Sochi

2015

Asia-Pacific J Chem Eng

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A residual‐based lubrication method is used to find the flow rate and pressure field in converging‐diverging rigid tubes for the flow of time‐independent category of non‐Newtonian fluids. Five converging‐diverging prototype geometries were used in this investigation in conjunction with two fluid models: Ellis and Herschel‐Bulkley. The method was validated by convergence behavior sensibility tests, convergence to analytical solutions for the straight tubes as special cases for the converging‐diverging tubes, convergence to analytical solutions found earlier for the flow in converging‐diverging tubes of Newtonian fluids as special cases for non‐Newtonian, and convergence to analytical solutions found earlier for the flow of power‐law fluids in converging‐diverging tubes. A brief investigation was also conducted on a sample of diverging‐converging geometries. The method can in principle be extended to the flow of viscoelastic and thixotropic/rheopectic fluid categories. The method can also be extended to geometries varying in size and shape in the flow direction, other than the perfect cylindrically‐symmetric converging‐diverging ones, as long as characteristic flow relations correlating the flow rate to the pressure drop on the discretized elements of the lubrication approximation can be found. These relations can be analytical, empirical and even numerical and hence the method has a wide applicability range. © 2015 Curtin University of Technology and John Wiley & Sons, Ltd.

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Section: Herschel-bulkley Modelmentioning

confidence: 99%

Flow of non‐Newtonian fluids in converging–diverging rigid tubes

Sochi

2015

Asia-Pacific J Chem Eng

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“…The case of Herschel-Bulkley flow with Navier slip (B c =0 and s=1) has been discussed in detail by Damianou et al [9], who, however, employed a different definition of the slip number (A 1 in their paper corresponds to 1/(2B)). Here we consider first Bingham flow (n=1) with zero slip yield stress (B c =0).…”

Section: State -State Herschel-bulkley Flows With Slipmentioning

confidence: 99%

“…As discussed in Section 3, in the case of Bingham flow, steady-state plug velocity profiles are admissible when Navier slip is allowed [9]. The critical slip number for attaining a uniform steady-state velocity profile in axisymmetric Poiseuille flow is B crit =Bn-B c .…”

Section: Time-dependent Bingham Flows With Slipmentioning

confidence: 99%

Cessation Flows of Bingham Plastics With Slip at the Wall

Damianou¹,

Philippou²,

Kaoullas³

et al. 2014

Proceedings of the 3rd South-East European Conference on Computational Mechanics (SEECCM III)

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“…In this context we assume a no-slip at wall condition where the velocity of the fluid at the interface is identical to the velocity of the solid [40][41][42]. This NavierStokes system is normally supported by a constitutive relation that links the cross sectional area at a certain axial location to the corresponding axial pressure in a distensible tube, to close the system in the three variables Q, A and and hence provide a complete mathematical description for such a flow in such a conduit.…”

Section: One-dimensional Navier-stokes Modelmentioning

confidence: 99%

The yield condition in the mobilization of yield-stress materials in distensible tubes

Sochi

2014

Open Physics

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Abstract:In this paper we investigate the yield condition in the mobilization of yield-stress materials in distensible tubes. We discuss the two possibilities for modeling the yield-stress materials prior to yield: solid-like materials and highly-viscous fluids and identify the logical consequences of these two approaches on the yield condition. Our results reveal that these two modeling approaches have far reaching consequences on the yield bottleneck and hence should be critically examined in the light of experimental evidence. As part of this investigation we derive an analytical expression for the pressure field inside a distensible tube with a Newtonian flow using a one-dimensional Navier-Stokes flow model in conjunction with a pressurearea constitutive relation based on elastic tube wall characteristics. This analytical expression has wider applicability than in the identification of the yield condition of yield-stress material.

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Combined effects of compressibility and slip in flows of a Herschel–Bulkley fluid

Cited by 49 publications

References 29 publications

Flow of non‐Newtonian fluids in converging–diverging rigid tubes

Flow of non‐Newtonian fluids in converging–diverging rigid tubes

Cessation Flows of Bingham Plastics With Slip at the Wall

The yield condition in the mobilization of yield-stress materials in distensible tubes

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