Anomalous Migration of a Rigid Sphere in Torsional Flow of a Viscoelastic Fluid. II: Effect of Shear Rate

1985 ◽  
Vol 29 (6) ◽  
pp. 639-654 ◽  
Author(s):  
D. C. Prieve ◽  
M. S. Jhon ◽  
T. L. Koenig
Keyword(s):  
Shear Rate ◽  
Viscoelastic Fluid ◽  
Rigid Sphere ◽  
Torsional Flow

Lateral migration of a rigid sphere in torsional flow of a viscoelastic fluid

AIChE Journal ◽  
1984 ◽  
Vol 30 (4) ◽  
pp. 631-636 ◽  
Author(s):  
T. E. Karis ◽  
D. C. Prieve ◽  
S. L. Rosen
Keyword(s):  
Viscoelastic Fluid ◽  
Rigid Sphere ◽  
Lateral Migration ◽  
Torsional Flow

Anomalous Lateral Migration of a Rigid Sphere in Torsional Flow of a Viscoelastic Fluid

1984 ◽  
Vol 28 (4) ◽  
pp. 381-392 ◽  
Author(s):  
T. E. Karis ◽  
D. C. Prieve ◽  
S. L. Rosen
Keyword(s):  
Viscoelastic Fluid ◽  
Rigid Sphere ◽  
Lateral Migration ◽  
Torsional Flow

scholarly journals Migration of rigid spheres in a two-dimensional unidirectional shear flow of a second-order fluid

1976 ◽  
Vol 76 (4) ◽  
pp. 783-799 ◽  
Author(s):  
B. P. Ho ◽  
L. G. Leal
Keyword(s):  
Shear Rate ◽  
Outer Cylinder ◽  
Second Order ◽  
Rigid Sphere ◽  
Cylinder Wall ◽  
Two Dimensional ◽  
Lateral Migration ◽  
Lateral Variation ◽  
Rigid Spheres ◽  
Neutrally Buoyant

The lateral migration of a neutrally buoyant rigid sphere suspended in a second-order fluid is studied theoretically for unidirectional two-dimensional flows. The results demonstrate the existence of migration induced by normal stresses whenever there is a lateral variation of the shear rate in the undisturbed flow. The migration occurs in the direction of decreasing absolute shear rate, which is towards the centre-line for a plane Poiseuille flow and towards the outer cylinder wall for Couette flow. The direction of migration agrees with existing experimental data for a viscoelastic suspending fluid, and qualitative agreement is found between the theoretically predicted and experimentally measured sphere trajectories.

scholarly journals Steady streaming of a viscoelastic fluid within a periodically rotating sphere

2014 ◽  
Vol 761 ◽  
pp. 329-347 ◽  
Author(s):  
Rodolfo Repetto ◽  
Jennifer H. Siggers ◽  
Julia Meskauskas
Keyword(s):  
Viscoelastic Fluid ◽  
Present Model ◽  
Transport Processes ◽  
Rigid Sphere ◽  
Steady Streaming ◽  
Circulation Cell ◽  
Different Types ◽  
Parameter Values ◽  
Streaming Flow ◽  
Axis Passing

AbstractMotivated by understanding mass transport processes occurring in the vitreous chamber of the eye, we consider the steady streaming component of the flow generated in a viscoelastic fluid contained within a hollow, rigid sphere performing small-amplitude, periodic, torsional oscillations about an axis passing through its centre. The problem is solved semi-analytically, assuming that the amplitude of the oscillations is small. The paper extends the work by Repetto et al. (J. Fluid Mech., vol. 608, 2008, pp. 71–80), in which the case of a purely viscous fluid was analysed. However, in reality, in young and healthy subjects, the vitreous humour has complex rheological properties, and so here we model it as a viscoelastic fluid. A similar problem was studied by Nikolakis (Eine Theorie für stationäre Drifterscheinungen viskoelastischer Flüssigkeiten, 1992, VDI). In the present model, the steady streaming flow is governed by four dimensionless parameters. We show that, when we account for the viscoelasticity of the fluid, there is a considerably more complex set of possible flow regimes than was found in the purely viscous case, and the flows can be classified into five qualitatively different types. Whereas there was only one circulation cell in each hemisphere in the viscous case, accounting for viscoelasticity it is possible have either one, two or three circulation cells, with different senses of rotation, depending on the parameter values.

Drag and lift forces acting on a spherical water droplet in homogeneous linear shear air flow

2007 ◽  
Vol 570 ◽  
pp. 155-175 ◽  
Author(s):  
KEN-ICHI SUGIOKA ◽  
SATORU KOMORI
Keyword(s):  
Reynolds Number ◽  
Shear Rate ◽  
Shear Flow ◽  
Rigid Sphere ◽  
Fluid Shear ◽  
Spherical Droplet ◽  
Linear Shear ◽  
Lift Forces ◽  
Drag And Lift ◽  
Homogeneous Linear

Drag and lift forces acting on a spherical water droplet in a homogeneous linear shear air flow were studied by means of a three-dimensional direct numerical simulation based on a marker and cell (MAC) method. The effects of the fluid shear rate and the particle (droplet) Reynolds number on drag and lift forces acting on a spherical droplet were compared with those on a rigid sphere. The results show that the drag coefficient on a spherical droplet in a linear shear flow increases with increasing the fluid shear rate. The difference in the drag coefficient between a spherical droplet and a rigid sphere in a linear shear flow never exceeds 4%. The lift force acting on a spherical droplet changes its sign from a positive to a negative value at a particle Reynolds number of Rep ≃ 50 in a linear shear flow and it acts from the high-speed side to the low-speed side for Rep ≥ 50. The behaviour of the lift coefficient on a spherical droplet is similar to that on a stationary rigid sphere and the change of sign is caused by the decrease of the pressure lift. The viscous lift on a spherical droplet is smaller than that on a rigid sphere at the same Rep, whereas the pressure lift becomes larger. These quantitative differences are caused by the flow inside a spherical droplet.

Inertial migration of a small sphere in linear shear flows

1991 ◽  
Vol 224 ◽  
pp. 261-274 ◽  
Author(s):  
John B. McLaughlin
Keyword(s):  
Reynolds Number ◽  
Shear Rate ◽  
Slip Velocity ◽  
Reynolds Numbers ◽  
Rigid Sphere ◽  
Square Root ◽  
Small Sphere ◽  
Inertial Migration ◽  
Particle Reynolds Number ◽  
Linear Shear

The motion of a small, rigid sphere in a linear shear flow is considered. Saffman's analysis is extended to other asymptotic cases in which the particle Reynolds number based on its slip velocity is comparable with or larger than the square root of the particle Reynolds number based on the velocity gradient. In all cases, both particle Reynolds numbers are assumed to be small compared to unity. It is shown that, as the Reynolds number based on particle slip velocity becomes larger than the square root of the Reynolds number based on particle shear rate, the magnitude of the inertial migration velocity rapidly decreases to very small values. The latter behaviour suggests that contributions that are higher order in the particle radius may become important in some situations of interest.

scholarly journals Processing the Vane Shear Flow Data from Couette Analogy

2008 ◽  
Vol 18 (3) ◽  
pp. 34037-1-34037-6 ◽  
Author(s):  
Patrice Estellé ◽  
Christophe Lanos ◽  
Arnaud Perrot ◽  
Sofiane Amziane
Keyword(s):  
Experimental Data ◽  
Shear Stress ◽  
Shear Rate ◽  
Shear Flow ◽  
Rotational Velocity ◽  
Rheological Behaviour ◽  
Bingham Fluid ◽  
Flow Data ◽  
Velocity Data ◽  
Torsional Flow

Abstract A new procedure is described to convert the vane torque and rotational velocity data into shear stress vs shear rate relationships. The basis of the procedure consists in considering locally the sheared material as a Bingham fluid and computing a characteristic shear rate from Couette analogy. The approach is first applied to experimental vane data of Newtonian fluid, then used to process vane experimental data of non-Newtonian and yield stress materials. Results, which are favourably compared with torsional flow, show that the approach correctly predicts the rheological behaviour of the materials investigated.

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