Slow Steady Rotation of an Approximate Sphere in an Approximate Spherical Container with Slip Surfaces

Prasad, M. Krishna; Kaur, Manpreet; Srinivasacharya, D.

doi:10.1007/s40819-016-0151-1

Cited by 8 publications

(4 citation statements)

References 24 publications

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“…In many technical applications, slip particles are not isolated. Thus, it is imperative to determine if the attendance of adjoining particles [21,22] or the proximity of confining walls [23][24][25] meaningfully affects the particle movement. Through an exact representation in spherical bipolar coordinates, the axisymmetric slow translation of two slip spherical particles was investigated semi-analytically and numerical results were calculated for the cases of identical spheres with equal magnitude of velocities [26] and arbitrary spheres with arbitrary velocities [27].…”

Section: Introductionmentioning

confidence: 99%

Slow Rotation of Coaxial Slip Colloidal Spheres about Their Axis

Tsai,

Keh

2023

Colloids and Interfaces

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The flow field around a straight chain of multiple slip spherical particles rotating steadily in an incompressible Newtonian fluid about their line of centers is analyzed at low Reynolds numbers. The particles may vary in radius, slip coefficient, and angular velocity, and they are permitted to be unevenly spaced. Through the use of a boundary collocation method, the Stokes equation governing the fluid flow is solved semi-analytically. The interaction effects among the particles are found to be noteworthy under appropriate conditions. For the rotation of two spheres, our collocation results for their hydrodynamic torques are in good agreement with the analytical asymptotic solution in the literature obtained by using a method of twin multipole expansions. For the rotation of three spheres, the particle interaction effect indicates that the existence of the third particle can influence the torques exerted on the other two particles noticeably. The interaction effect is stronger on the smaller or less slippery particles than on the larger or more slippery ones. Torque results for the rotation of chains of many particles visibly show the shielding effect among the particles.

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Section: Introductionmentioning

confidence: 99%

Slow Rotation of Coaxial Slip Colloidal Spheres about Their Axis

Tsai,

Keh

2023

Colloids and Interfaces

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“…The steady and transient creeping rotations of a spherical particle inside a concentric spherical cavity, where the fluid slips on the particle and cavity surfaces, were analytically studied and explicit formulas for the torque exerted by the fluid on the particle were derived (Keh and Chang 1998, Krishna Prasad et al 2017, Li and Keh 2021. Furthermore, the slow rotations of a slip sphere in an eccentric slip spherical cavity about an axis along or perpendicular to their common diameter Keh 2013, Chou andKeh 2021) and about a diameter lying along the axis of a slip circular cylinder (Lee and Keh 2021b) were semi-analytically examined by using a boundary collocation method.…”

Section: Introductionmentioning

confidence: 99%

Slow rotation of a sphere about its diameter normal to two planes with slip surfaces

Liao¹,

Keh²

2022

Fluid Dyn. Res.

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The steady creeping flow of an incompressible Newtonian fluid around a slip spherical particle rotating about its diameter perpendicular to one or two slip plane walls is analyzed. To satisfy the Stokes equation for fluid velocity, the general solution consists of the sum of the essential solutions in spherical and cylindrical coordinates. Boundary conditions are implemented first on the plane walls by means of the Hankel transforms and then on the particle surface through a collocation method. The hydrodynamic torque exerted on the particle is obtained with excellent convergence for various values of the pertinent geometrical and stick-slip parameters, and the effect of the slip planes on the rotational motion of the slip particle is interesting. The torque increases with an increase in the stickiness of the walls from the limit of full slip to the limit of no slip. When the stick parameters of the plane walls are larger than some critical values, the hydrodynamic torque is more than that on an identical particle in the unbounded fluid and an increasing function of the stickiness of the particle surface and ratio of the particle radius to distance from the walls. When the stick parameters of the plane walls are smaller than the critical values, on the contrary, the torque is less than that on the particle in the unbounded fluid and a decreasing function of the surface stickiness and relative radius of the particle.

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“…where b and 1/β w are the radius and slip coefficient, respectively, of the cavity, and this equation reduces to equation (1) as a/b = 0. Subsequently, the slow rotations of a spherical particle about a diameter inside an eccentric or approximate spherical cavity with slip surfaces were analyzed (Faltas and Saad 2012, Lee and Keh 2013, Krishna Prasad et al 2017, Chou and Keh 2021.…”

Section: Introductionmentioning

confidence: 99%

Transient rotation of a spherical particle in a concentric cavity with slip surfaces

Keh

2021

Fluid Dyn. Res.

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Slow Steady Rotation of an Approximate Sphere in an Approximate Spherical Container with Slip Surfaces

Cited by 8 publications

References 24 publications

Slow Rotation of Coaxial Slip Colloidal Spheres about Their Axis

Slow Rotation of Coaxial Slip Colloidal Spheres about Their Axis

Slow rotation of a sphere about its diameter normal to two planes with slip surfaces

Transient rotation of a spherical particle in a concentric cavity with slip surfaces

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