Cessation of viscoplastic Poiseuille flow in a square duct with wall slip

Damianou, Yiolanda; Kaoullas, George; Georgiou, Georgios C.

doi:10.1016/j.jnnfm.2015.11.002

Cited by 22 publications

(7 citation statements)

References 14 publications

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“…Five flow regimes were identified in a master curve: full slip, full stick, partial slip and stick at the wall, block translation and stopped material. investigated the time-dependent problem and the stopping time for a Poiseuille flow with a circular or square (Damianou et al, 2016) cross section with yield slip at the wall by using the regularization approach for both the viscoplastic model and the yield slip equation .…”

Section: Yield Slip Boundary Conditionsmentioning

confidence: 99%

Progress in numerical simulation of yield stress fluid flows

2017

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Numerical simulations of viscoplastic fluid flows have provided a better understanding of fundamental properties of yield stress fluids in many applications relevant of natural and engineering sciences. In the first part of this paper, we review the classical numerical methods for the solution of the non-smooth viscoplastic mathematical models, highlight their advantages and drawbacks, and discuss more recent numerical methods that show promises for fast algorithms and accurate solutions. In the second part, we present and analyze a variety of applications and extensions involving viscoplastic flow simulations: yield slip at the wall, heat transfer, thixotropy, granular materials, combining elasticity, with multiple phases and shallow flow approximations. We illustrate from a physical viewpoint how fascinating the corresponding rich phenomena pointed out by these simulations are.

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Section: Yield Slip Boundary Conditionsmentioning

confidence: 99%

Progress in numerical simulation of yield stress fluid flows

2017

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“…to address the Poiseuille flow of viscoplastic fluids in ducts with wall slip (Damianou et al. 2014; Damianou & Georgiou 2014; Damianou, Kaoullas & Georgiou 2016); in these works, the yield surfaces appearing at the centre and corners of the duct have been accurately captured.…”

Section: Introductionmentioning

confidence: 99%

Poiseuille flow of a Bingham fluid in a channel with a superhydrophobic groovy wall

Rahmani

Taghavi

2022

J. Fluid Mech.

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Plane Poiseuille flow of a Bingham fluid in a channel armed with a superhydrophobic (SH) lower wall is analysed via a semi-analytical model, accompanied by complementary direct numerical simulations (DNS). The SH surface represents a groovy structure with air trapped inside its cavities. Therefore, the fluid adjacent to the wall undergoes stick–slip conditions. The model is developed based on introducing infinitesimal wall-induced perturbations into the motion equations, followed by Fourier series expansions, and solving the resulting equations as a boundary value problem. The Navier slip law accounts for the slip at the liquid/air interface (assuming the Cassie state). The presented analysis is fairly comprehensive, covering the creeping and inertial regimes for thick channels (via the semi-analytical and DNS solutions). The main dimensionless numbers are the Reynolds ( $Re$ ), Bingham ( $Bi$ ) and slip ( $b$ ) numbers, as well as the groove periodicity length ( $\ell$ ) and the slip area fraction ( $\varphi$ ). By increasing $Bi$ , the perturbation and slip velocity fields grow. As $Re$ increases, the perturbation and slip velocity fields become asymmetric. For certain flow parameters, an unyielded plug zone may appear on the SH wall liquid/air interface, while its formation is accelerated by inertial effects. The results classify the regimes of creeping and inertial flows via predicting the onset of the unyielded plug zone formation at the SH wall.

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“…Before dealing with the case of Herschel-Bulkley luids, the case of a Bingham luids is irst considered. The low of such luids in rectilinear capillaries of square cross-section was extensively discussed in several previous works (Saramito and Roquet 2001;Roquet and Saramito 2008;Damianou et al 2016). Therefore, to evaluate the results provided by the present empirical relationship (Eq.…”

Section: Case Of Bingham Fluidsmentioning

confidence: 88%

Empirical Flow Rate/Pressure Drop Relationships for Capillaries of Triangular and Rectangular Cross-Sections to be Used in Yield Stress Fluid Porosimetry

et al. 2021

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The aim of the present work is to investigate the low rate/pressure gradient relationship for the low of yield stress luids through rectilinear capillaries of non-circular cross-sections. These capillaries very often serve as basic elements in the modeling of porous media as bundles of capillaries or pore-network models. Based on the notions of shape coeicient and critical Bingham number, empirical low rate/pressure gradient relationships have been proposed for both Bingham and Herschel-Bulkley luids. The reliability of these relationships has been assessed by performing numerical simulations with the open-source Computational Fluid Dynamics (CFD) package OpenFOAM. For the considered cross-sectional shapes (equilateral triangle and square), and for a wide range of Bingham numbers, the predictions of the proposed empirical relationships have shown to be in very good agreement with the results of the current numerical simulations, as well as with previous results from the literature. An interesting feature of the proposed empirical relationships is the possibility to easily predict the total low rate under a given imposed pressure gradient in a bundle of non-circular capillaries having any random distribution of inscribed circle radii. Furthermore, in the context of the yield stress luid porosimetry method (YSM), experimental data may now be processed based upon bundles of capillaries with non-circular cross-sections.

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Cessation of viscoplastic Poiseuille flow in a square duct with wall slip

Cited by 22 publications

References 14 publications

Progress in numerical simulation of yield stress fluid flows

Progress in numerical simulation of yield stress fluid flows

Poiseuille flow of a Bingham fluid in a channel with a superhydrophobic groovy wall

Empirical Flow Rate/Pressure Drop Relationships for Capillaries of Triangular and Rectangular Cross-Sections to be Used in Yield Stress Fluid Porosimetry

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