Anomalous Lateral Migration of a Rigid Sphere in Torsional Flow of a Viscoelastic Fluid—Effect of Polymer Concentration and Solvent Viscosity

1987 ◽  
Vol 31 (4) ◽  
pp. 317-321 ◽  
Author(s):  
H. J. Choi ◽  
D. C. Prieve ◽  
M. S. Jhon
Keyword(s):  
Viscoelastic Fluid ◽  
Polymer Concentration ◽  
Rigid Sphere ◽  
Lateral Migration ◽  
Solvent Viscosity ◽  
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

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

Inertial migration of rigid spheres in two-dimensional unidirectional flows

1974 ◽  
Vol 65 (2) ◽  
pp. 365-400 ◽  
Author(s):  
B. P. Ho ◽  
L. G. Leal
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Poiseuille Flow ◽  
Initial Position ◽  
Rigid Sphere ◽  
Simple Shear Flow ◽  
Two Dimensional ◽  
Lateral Migration ◽  
Rigid Spheres ◽  
Inertial Migration

The familiar Segré-Silberberg effect of inertia-induced lateral migration of a neutrally buoyant rigid sphere in a Newtonian fluid is studied theoretically for simple shear flow and for two-dimensional Poiseuille flow. It is shown that the spheres reach a stable lateral equilibrium position independent of the initial position of release. For simple shear flow, this position is midway between the walls, whereas for Poiseuille flow, it is 0·6 of the channel half-width from the centre-line. Particle trajectories are calculated in both cases and compared with available experimental data. Implications for the measurement of the rheological properties of a dilute suspension of spheres are discussed.

Analysis of the Motion and Deformation of a Bubble Rising in a Viscoelastic Fluid

2006 ◽  
Author(s):  
Shriram Pillapakkam ◽  
Pushpendra Singh ◽  
Denis L. Blackmore ◽  
Nadine Aubry
Keyword(s):  
Velocity Field ◽  
Newtonian Fluid ◽  
Viscoelastic Fluid ◽  
Bubble Radius ◽  
Polymer Concentration ◽  
Deborah Number ◽  
Two Phase ◽  
Bubble Volume ◽  
Recirculation Zones ◽  
Bubble Rising

A finite element code based on the level set method is developed for performing two and three dimensional direct numerical simulations (DNS) of viscoelastic two-phase flow problems. The Oldroyd-B constitutive equation is used to model the viscoelastic liquid and both transient and steady state shapes of bubbles in viscoelastic buoyancy driven flows are studied. The influence of the governing dimensionless parameters, namely the Capillary number (Ca), the Deborah Number (De) and the polymer concentration parameter c, on the deformation of the bubble is also analyzed. Our simulations demonstrate that the rise velocity oscillates before reaching a steady value. The shape of the bubble, the magnitude of velocity overshoot and the amount of damping depend mainly on the parameter c and the bubble radius. Simulations also show that there is a critical bubble volume at which there is a sharp increase in the bubble terminal velocity as the increasing bubble volume increases, similar to the behavior observed in experiments. The structure of the wake of a bubble rising in a Newtonian fluid is strikingly different from that of a bubble rising in a viscoelastic fluid. In addition to the two recirculation zones at the equator of the bubble rising in a Newtonian fluid, two more recirculation zones exist in the wake of a bubble rising in viscoelastic fluids which influence the shape of a rising bubble. Interestingly, the direction of motion of the fluid a short distance below the trailing edge of a bubble rising in a viscoelastic fluid is in the opposite direction to the direction of the motion of the bubble, thus creating a “negative wake”. In this paper, the velocity field in the wake of the bubble, the effect of the parameters on the velocity field and their influence on the shape of the bubble are also investigated.

Direct Numerical Simulation of Drops in Three Dimensional Viscoelastic Simple Shear Flows

2001 ◽  
Author(s):  
Shriram B. Pillapakkam ◽  
Pushpendra Singh
Keyword(s):  
Numerical Simulation ◽  
Shear Flow ◽  
Direct Numerical Simulation ◽  
Viscoelastic Fluid ◽  
Simple Shear ◽  
Polymer Concentration ◽  
Three Dimensional ◽  
Simple Shear Flow ◽  
Splitting Technique

Abstract A three dimensional finite element scheme for Direct Numerical Simulation (DNS) of viscoelastic two phase flows is implemented. The scheme uses the Level Set Method to track the interface and the Marchuk-Yanenko operator splitting technique to decouple the difficulties associated with the governing equations. Using this numerical scheme, the shape of Newtonian drops in a simple shear flow of viscoelastic fluid and vice versa are analyzed as a function of Capillary number, Deborah number and polymer concentration. The viscoelastic fluid is modeled via the Oldroyd-B model. The role of viscoelastic stresses in deformation of a drop subjected to simple shear flow and its effect on the steady state shape is analyzed. Our results compare favorably with existing experimental data and also help in understanding the role of viscoelastic stresses in drop deformation.

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 Three-Dimensional Numerical Simulation of Particle Focusing and Separation in Viscoelastic Fluids

Micromachines ◽  
2020 ◽  
Vol 11 (10) ◽  
pp. 908
Author(s):  
Chen Ni ◽  
Di Jiang
Keyword(s):  
Viscoelastic Fluid ◽  
Rectangular Channel ◽  
Particle Interaction ◽  
Three Dimensional ◽  
Viscoelastic Fluids ◽  
Lateral Migration ◽  
Square Channel ◽  
Particle Focusing ◽  
Aspect Ratios ◽  
Large Particles

Particle focusing and separation using viscoelastic microfluidic technology have attracted lots of attention in many applications. In this paper, a three-dimensional lattice Boltzmann method (LBM) coupled with the immersed boundary method (IBM) is employed to study the focusing and separation of particles in viscoelastic fluid. In this method, the viscoelastic fluid is simulated by the LBM with two sets of distribution functions and the fluid–particle interaction is calculated by the IBM. The performance of particle focusing under different microchannel aspect ratios (AR) is explored and the focusing equilibrium positions of the particles with various elasticity numbers and particle diameters are compared to illustrate the mechanism of particle focusing and separation in viscoelastic fluids. The results indicate that, for particle focusing in the square channel (AR = 1), the centerline single focusing becomes a bistable focusing at the centerline and corners as El increases. In the rectangular channels (AR < 1), particles with different diameters have different equilibrium positions. The equilibrium position of large particles is closer to the wall, and large particles have a faster lateral migration speed and few large particles migrate towards the channel center. Compared with the square channel, the rectangular channel is a better design for particle separation.

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.

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