Transient squeeze flow of viscoplastic materials

Karapetsas, George; Tsamopoulos, John

doi:10.1016/j.jnnfm.2005.10.010

Cited by 53 publications

(49 citation statements)

References 35 publications

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“…This fact was confirmed numerically in further papers [15,19,20]. The results for the squeeze flow between parallel plates (planar geometry) reveal some significant differences from their axisymmetric counterparts.…”

Section: Effects Of Geometry and Yield Stresssupporting

confidence: 53%

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Squeeze plane flow of viscoplastic Bingham material

Muravleva

2015

Journal of Non-Newtonian Fluid Mechanics

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Section: Effects Of Geometry and Yield Stresssupporting

confidence: 53%

“…Shear stresses τ 0 xy has the constant sign in the domain x > 0, y > 0 (20). Derivative of the velocity has the same sign (22).…”

Section: Shear Regionmentioning

confidence: 97%

Squeeze plane flow of viscoplastic Bingham material

Muravleva

2015

Journal of Non-Newtonian Fluid Mechanics

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“…Through numerous tests, it was determined that setting R ∞ = 30 was more than sufficient to guarantee that the outflow boundary did not affect our results in any measurable way. This method has been applied successfully to a number of free-or moving-boundary problems (Dimakopoulos & Tsamopoulos 2003;Karapetsas & Tsamopoulos 2006;Foteinopoulou et al 2006;Tsamopoulos et al 2008). In Tsamopoulos et al (2008), the steady rise and deformation of a bubble in a Newtonian or a viscoplastic material was studied and the accuracy of the present code was demonstrated, because its predictions for the bubble shape and rise velocity and the various geometric characteristics of the vortex behind it were found to be in excellent agreement with results of numerous earlier experimental and theoretical studies.…”

Section: Numerical Solutionmentioning

confidence: 99%

Viscous effects on the oscillations of two equal and deformable bubbles under a step change in pressure

2011

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According to linear theory and assuming the liquids to be inviscid and the bubbles to remain spherical, bubbles set in oscillation attract or repel each other with a force that is proportional to the product of their amplitude of volume pulsations and inversely proportional to the square of their distance apart. This force is attractive, if the forcing frequency lies outside the range of eigenfrequencies for volume oscillation of the two bubbles. Here we study the nonlinear interaction of two deformable bubbles set in oscillation in water by a step change in the ambient pressure, by solving the Navier–Stokes equations numerically. As in typical experiments, the bubble radii are in the range 1–1000 μm. We find that the smaller bubbles (~5 μm) deform only slightly, especially when they are close to each other initially. Increasing the bubble size decreases the capillary force and increases bubble acceleration towards each other, leading to oblate or spherical cap or even globally deformed shapes. These deformations may develop primarily in the rear side of the bubbles because of a combination of their translation and harmonic or subharmonic resonance between the breathing mode and the surface harmonics. Bubble deformation is also promoted when they are further apart or when the disturbance amplitude decreases. The attractive force depends on the Ohnesorge number and the ambient pressure to capillary forces ratio, linearly on the radius of each bubble and inversely on the square of their separation. Additional damping either because of liquid compressibility or heat transfer in the bubble is also examined.

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“…Lawal and Kalyon [] considered Herschel-Bulkley materials with Navier slip boundary conditions following the lubrication approximation,and obtained numerical solutions. Karapetsas and Tsamopoulos [25] examined the transient squeeze flow of a viscoplastic material between two parallel coaxial disks. The Papanastasiou model was used.…”

Section: Introductionmentioning

confidence: 99%

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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Transient squeeze flow of viscoplastic materials

Cited by 53 publications

References 35 publications

Squeeze plane flow of viscoplastic Bingham material

Squeeze plane flow of viscoplastic Bingham material

Viscous effects on the oscillations of two equal and deformable bubbles under a step change in pressure

Squeeze Flow of Viscoplastic Bingham Material

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