Squeeze plane flow of viscoplastic Bingham material

Muravleva, Larisa

doi:10.1016/j.jnnfm.2015.01.012

Cited by 30 publications

(19 citation statements)

References 49 publications

(56 reference statements)

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“…Numerical studies using the Bingham constitutive law have been found to be in good agreement with experimental work using Carbopol 940 gels, developing drag correlations and stability criteria (with respect to sedimentation) [4,7,9,10]. Viscoplastic squeeze flow between coaxial cylindrical disks has been studied analytically for both planar [11] and axisymmetric [12,13] configurations. The configuration of collinearly approaching bodies in a viscoplastic flow has received only cursory attention in numerical studies, eg Yu and Wachs [8], Tokpavi et al [9], with no examination of the interstitial squeeze flow.…”

Section: Introductionmentioning

confidence: 57%

“…Instead, we use an iterative method based on the variational form of the Bingham problem, established by Duvaut and Lions [25], which forms the basis for the widely used augmented Lagrangian (AL) first proposed by Glowinski [26]. This formulation is commonly known as ALG2 and is used extensively in the literature, see Yu and Wachs [8], Muravleva [11], Chaparian and Frigaard [27] and references therein, so we do not give details here. For its solution we use the Uzawa type algorithm of Olshanskii [28] and Muravleva and Olshanskii [29].…”

Section: B Computational Methodsmentioning

confidence: 99%

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Viscoplastic squeeze flow between two identical infinite circular cylinders

Koblitz¹,

Lovett

Nikiforakis³

2018

Phys. Rev. Fluids

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Direct numerical simulations of closely interacting infinite circular cylinders in a Bingham fluid are presented, and results compared to asymptotic solutions based on lubrication theory in the gap. Unlike for a Newtonian fluid, the macroscopic flow outside of the gap between the cylinders is shown to have a large effect on the pressure profile within the gap and the resulting lubrication force on the cylinders. The presented results indicate that the asymptotic lubrication solution can be used to predict the lubrication pressure only if the surrounding viscoplastic matrix is yielded by a macroscopic flow. This has implications for the use of sub-grid-scale lubrication models in simulations of non-colloidal particulate suspensions in viscoplastic fluids.

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Section: Introductionmentioning

confidence: 57%

Section: B Computational Methodsmentioning

confidence: 99%

Viscoplastic squeeze flow between two identical infinite circular cylinders

Koblitz¹,

Lovett

Nikiforakis³

2018

Phys. Rev. Fluids

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“…In a recent paper by Muravleva [18] the planar squeeze flow of a Bingham fluid is studied exploiting the asymptotic technique introduced in [16], [17], [19]. Besides, the results of computations in [18] show presence of unyielded regions near the two stagnation points of flow close to centers of plates (that was found earlier by many researchers) and new additional unyielded regions at the outer edge of the material (both for short and long plates). More recently Fusi at all [20] investigated these unyielded regions, adjacent to the outer edge exploiting the integral formulation of the linear momentum balance.…”

Section: Introductionmentioning

confidence: 88%

Squeeze Flow of Viscoplastic Bingham Material

Muravleva¹

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. We consider both planar and axisymmetric squeeze flows of a viscoplastic medium. Firstly we deal with no-slip boundary conditions. The asymptotic and the numerical solutions are developed. Previous theoretical analysis of this problem, using the standard lubrication approximation, has led to conflicting results, whereby the material around the plane of symmetry must both behaves as unyielded solid and translates in the main direction with a nonuniform velocity. This variation of the velocity implies that the plug region cannot be truly unyielded. Our solutions show that this region is a pseudo-plug region in which the leading order equation predicts a plug, but really it is weakly yielded at higher order. We follow the asymptotic technique suggested earlier by Balmforth, Craster (1999) and Frigaad, Ryan (2004). The obtained analytical expressions and numerical results are in a very good agreement with the earlier works. For numerical simulations we apply Augmented Lagrangian method (ALM) that yields superior results regarding the location of the yieldsurface. Finite-difference method on staggered grids is used as a discretization technique.Secondly we consider squeeze flow of a Bingham fluid subject to wall slip. If the wall shearstress is smaller than the threshold value (the slip yield stress), the fluid adherence to the boundary is imposed and we have no-slip condition. When the wall shear stress reaches the slip yield stress, the fluid slips along the boundary. We solve numerically this problem also by ALM. The different flow regimes can be observed depending on the relative values of the yield stress and the slip yield stress. More precisely, for the case when the yield stress is smaller than the slip yield stress, there exists a particular value T crit such that when the slip yield stress is greater or equal to T crit ,the material fully sticks at the wall. When the slip yield stress is less than T crit and bigger than the yield stress, the fluid sticks in the central region of the wall and slips close to the outer edges of discsorplates. For the case when the yield stress is bigger than the slip yield stress the material slips on the whole boundary.1215

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“…According to this method, originally developed by Safronchik [14], the unyielded region is treated as a rigid body of variable mass whose dynamics is governed by the cardinal equations. We remark that the yield surface can be determined using other methods, such as the ones illustrated in [8,[15][16][17].…”

Section: Introductionmentioning

confidence: 99%

On a Casson Fluid Motion: Nonuniform Width Symmetric Channel and Peristaltic Flows

Guadagli

Palade

Fusi

et al. 2021

Fluids

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Widely used for modeling biological fluids flows—in particular, blood vessel flows—a Casson flow is studied in a symmetric channel for which the aspect ratio enables one to use the lubrication approximation. Two flow driving conditions are prescribed: inlet–outlet pressure difference and peristaltic oscillations of the vessel walls. In both cases, starting from mass and momentum balance and using lubrication approximation, we investigate the conditions to be imposed on the driving mechanisms so that the inner plug does not come in touch with the walls. The study of the peristaltic flow is of great importance in view of its applications in physiology (including microcirculation applications).

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Squeeze plane flow of viscoplastic Bingham material

Cited by 30 publications

References 49 publications

Viscoplastic squeeze flow between two identical infinite circular cylinders

Viscoplastic squeeze flow between two identical infinite circular cylinders

Squeeze Flow of Viscoplastic Bingham Material

On a Casson Fluid Motion: Nonuniform Width Symmetric Channel and Peristaltic Flows

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