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

Fusi, Lorenzo; Farína, Angiolo; Rosso, Fábio; Roscani, Sabrina

doi:10.1016/j.jnnfm.2015.04.005

Cited by 40 publications

(52 citation statements)

References 14 publications

(35 reference statements)

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“…In a recent study, 1 we have extended a lubrication approximation method proposed by Fusi et al 2 for solving pressure-driven flow of a Bingham-plastic in a symmetric channel, in order to solve the flow of a Herschel-Bulkley fluid with pressure-dependent consistency index k * and yield stress τ * y . Thus, we have employed the following constitutive equation…”

Section: Introductionmentioning

confidence: 99%

“…Fusi et al presented a novel technique for modeling the lubrication flow of a Bingham plastic (with constant rheological parameters) in a two-dimensional channel of non-uniform thickness. 2 This is based on the application of Reynolds transport theorem over the unyielded core. The advantage of the method is that it avoids the lubrication paradox and predicts at zero order the correct shape of the yield surface, whose behavior is opposite to that of the wall function, i.e., the width of the unyielded core increases when the channel width is reduced and vice versa.…”

Section: Introductionmentioning

confidence: 99%

“…With other lubrication-approximation methods, the correct shape of the yield surface is obtained only at higher orders. 6,7 A limitation of the method of Fusi et al, 2 however, is that it applies only when the unyielded region (plug) extends continuously from the inlet to the outlet plane, i.e., it is not applicable when the plug is broken.…”

Section: Introductionmentioning

confidence: 99%

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Lubrication solution of the flow of a Herschel-Bulkley fluid with pressure-dependent rheological parameters in an asymmetric channel

2019

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A new model for the bouncing regime boundary in binary droplet collisions Physics of Fluids 31, 027105 (2019); https://doi.org/10.1063/1.5085762Post-collision hydrodynamics of droplets on cylindrical bodies of variant convexity and wettability Physics of Fluids 31, 022008 (2019); https://doi. ABSTRACTThe lubrication flow of a Herschel-Bulkley fluid in a long asymmetric channel, the walls of which are described by two arbitrary functions h 1 (x) and h 2 (x) such that h 1 (x) < h 2 (x) and h 1 (x) + h 2 (x) are linear, is solved extending a recently proposed method, which avoids the lubrication paradox approximating satisfactorily the correct shape of the yield surface at zero order [P. Panaseti et al., "Pressure-driven flow of a Herschel-Bulkley fluid with pressure-dependent rheological parameters," Phys. Fluids 30, 030701 (2018)]. Both the consistency index and the yield stress are assumed to be pressure-dependent. Under the lubrication approximation, the pressure at zero order is a function of x only, is decoupled from the velocity components, and obeys a first-order integro-differential equation. An interesting feature of the asymmetric flow is that the unyielded core moves not only in the main flow direction but also in the transverse direction. Explicit expressions for the two yield surfaces defining the asymmetric unyielded core are obtained, and the two velocity components in both the yielded and unyielded regions are calculated by means of closed-form expressions in terms of the calculated pressure and the two yield surfaces. The method is applicable in a range of Bingham numbers where the unyielded core extends from the inlet to the outlet plane of the channel. Semi-analytical solutions are derived in the case of an asymmetric channel with h 1 = 0 and linearly varying h 2 . Representative results demonstrating the effects of the Bingham number and the consistency-index and yield-stress growth numbers are discussed.Published under license by AIP Publishing. https://doi.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Lubrication solution of the flow of a Herschel-Bulkley fluid with pressure-dependent rheological parameters in an asymmetric channel

2019

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“…We have moreover that p (1) = p (1) (x) from (17). Using Equation (16) and the boundary conditions (19) and (20) for u (1) we conclude that…”

Section: Formal Asymptotic Analysismentioning

confidence: 99%

“…Lubrication approximation has been developed in the case of fluids with pressure dependent viscosity by Rajagopal and Szeri [17] and Gustafsson et al [18]. Finally, Fusi et al [19] have studied the lubrication approximation for a Bingham fluid taking into account inertial effects; fluids like the Bingham fluid that have a threshold in the stress for flow to take place are best described by constitutive relations wherein the kinematics is described as a function of the stress rather than expressing the stress in terms of the kinematical variable in the traditional manner (see Rajagopal [20,21] for a discussion of such fluids as well as more general fluids that are described by implicit constitutive relations). As there is a threshold for the stress beyond which the fluid starts to flow, the governing equations are quite different from the lubrication approximation obtained in the case of the other studies that employ fluid models that do not have such a threshold for the flow to take place.…”

Section: Introductionmentioning

confidence: 99%

Lubrication Approximation for Fluids with Shear-Dependent Viscosity

Pereira

Dias

Cal

et al. 2019

Fluids

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We present dimensionally reduced Reynolds type equations for steady lubricating flows of incompressible non-Newtonian fluids with shear-dependent viscosity by employing a rigorous perturbation analysis on the governing equations of motion. Our analysis shows that, depending on the strength of the power-law character of the fluid, the novel equation can either present itself as a higher-order correction to the classical Reynolds equation or as a completely new nonlinear Reynolds type equation. Both equations are applied to two classic problems: the flow between a rolling rigid cylinder and a rigid plane and the flow in an eccentric journal bearing.

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Analytical Approximation Techniques

Huilgol

Georgiou

2022

Fluid Mechanics of Viscoplasticity

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

Cited by 40 publications

References 14 publications

Lubrication solution of the flow of a Herschel-Bulkley fluid with pressure-dependent rheological parameters in an asymmetric channel

Lubrication solution of the flow of a Herschel-Bulkley fluid with pressure-dependent rheological parameters in an asymmetric channel

Lubrication Approximation for Fluids with Shear-Dependent Viscosity

Analytical Approximation Techniques

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