scholarly journals The motion of a deformable drop in a second-order fluid

1979 ◽  
Vol 92 (1) ◽  
pp. 131-170 ◽  
Author(s):  
P. C.-H. Chan ◽  
L. G. Leal
Keyword(s):  
Experimental Data ◽  
Shear Flow ◽  
Particle Velocity ◽  
Simple Shear ◽  
Poiseuille Flow ◽  
Second Order ◽  
Simple Shear Flow ◽  
Stream Migration ◽  
The Cross ◽  
Viscoelastic Rheology

The cross-stream migration of a deformable drop in a unidirectional shear flow of a second-order fluid is considered. Expressions for the particle velocity due to the separate effects of deformation and viscoelastic rheology are obtained. The direction and magnitude of migration are calculated for the particular cases of Poiseuille flow and simple shear flow and compared with experimental data.

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.

scholarly journals The slow motion of slender rod-like particles in a second-order fluid

1975 ◽  
Vol 69 (2) ◽  
pp. 305-337 ◽  
Author(s):  
L. G. Leal
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Fluid Model ◽  
Slow Motion ◽  
Second Order ◽  
Reciprocal Theorem ◽  
Simple Shear Flow ◽  
Shear Rates ◽  
Stable Orientation ◽  
The Reciprocal Theorem

The motion of a slender axisymmetric rod-like particle is investigated theoretically for translation through a quiescent second-order fluid and for rotation in a simple shear flow of the same material. The analysis consists of an asymptotic expansion about the limit of rheologically slow flow, coupled with an application of a generalized form of the reciprocal theorem of Lorentz to calculate the force and torque on the particle. It is shown that an arbitrarily oriented particle with fore-aft symmetry translates, to a first approximation, at the same rate as in an equivalent Newtonian fluid, but that the motion of particles with no fore-aft symmetry may be modified at the same level of approximation. In addition, it is found that freely translating particles with fore-aft symmetry exhibit a single stable orientation with the axis of revolution vertical. In simple shear flow at small and moderate shear rates, the non-Newtonian nature of the suspending fluid causes a drift through Jeffery orbits to the equilibrium orbit C = 0 in which the particle rotates about its axis of revolution. At larger shear rates, the particle aligns itself in the direction of flow and ceases to rotate. Comparison with the available experimental data indicates that the measured rate of orbit drift may be used to determine the second normal stress difference parameter of the second-order fluid model. Finally, in an appendix, some preliminary observations are reported of the motion of slender rod-like particles falling through a quiescent viscoelastic fluid.

Emulsification of particle loaded drops in simple shear flow

2015 ◽  
Vol 470 ◽  
pp. 179-187 ◽  
Author(s):  
Tobias Merkel ◽  
Julius Henne ◽  
Lena Hecht ◽  
Volker Gräf ◽  
Elke Walz ◽  
...  
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Simple Shear Flow

scholarly journals Do Protein Molecules Unfold in a Simple Shear Flow?

2006 ◽  
Vol 91 (9) ◽  
pp. 3415-3424 ◽  
Author(s):  
Juan Jaspe ◽  
Stephen J. Hagen
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Protein Molecules

Numerical study of electric field effects on the deformation of two-dimensional liquid drops in simple shear flow at arbitrary Reynolds number

2009 ◽  
Vol 626 ◽  
pp. 367-393 ◽  
Author(s):  
STEFAN MÄHLMANN ◽  
DEMETRIOS T. PAPAGEORGIOU
Keyword(s):  
Steady State ◽  
Shear Flow ◽  
Electric Field ◽  
Electric Fields ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Two Dimensional ◽  
Liquid Drops

The effect of an electric field on a periodic array of two-dimensional liquid drops suspended in simple shear flow is studied numerically. The shear is produced by moving the parallel walls of the channel containing the fluids at equal speeds but in opposite directions and an electric field is generated by imposing a constant voltage difference across the channel walls. The level set method is adapted to electrohydrodynamics problems that include a background flow in order to compute the effects of permittivity and conductivity differences between the two phases on the dynamics and drop configurations. The electric field introduces additional interfacial stresses at the drop interface and we perform extensive computations to assess the combined effects of electric fields, surface tension and inertia. Our computations for perfect dielectric systems indicate that the electric field increases the drop deformation to generate elongated drops at steady state, and at the same time alters the drop orientation by increasing alignment with the vertical, which is the direction of the underlying electric field. These phenomena are observed for a range of values of Reynolds and capillary numbers. Computations using the leaky dielectric model also indicate that for certain combinations of electric properties the drop can undergo enhanced alignment with the vertical or the horizontal, as compared to perfect dielectric systems. For cases of enhanced elongation and alignment with the vertical, the flow positions the droplets closer to the channel walls where they cause larger wall shear stresses. We also establish that a sufficiently strong electric field can be used to destabilize the flow in the sense that steady-state droplets that can exist in its absence for a set of physical parameters, become increasingly and indefinitely elongated until additional mechanisms can lead to rupture. It is suggested that electric fields can be used to enhance such phenomena.

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