Effect of surface slip on Stokes flow past a spherical particle in infinite fluid and near a plane wall |
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Authors: | Haoxiang Luo C Pozrikidis |
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Affiliation: | (1) Department of Mechanical Engineering, Vanderbilt University, 2301 Vanderbilt Pl., Nashville, TN 37235-1592, USA;(2) Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093-0411, USA |
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Abstract: | The motion of a spherical particle in infinite linear flow and near a plane wall, subject to the slip boundary condition on
both the particle surface and the wall, is studied in the limit of zero Reynolds number. In the case of infinite flow, an
exact solution is derived using the singularity representation, and analytical expressions for the force, torque, and stresslet
are derived in terms of slip coefficients generalizing the Stokes–Basset–Einstein law. The slip velocity reduces the drag
force, torque, and the effective viscosity of a dilute suspension. In the case of wall-bounded flow, advantage is taken of
the axial symmetry of the boundaries of the flow with respect to the axis that is normal to the wall and passes through the
particle center to formulate the problem in terms of a system of one-dimensional integral equations for the first sine and
cosine Fourier coefficients of the unknown traction and velocity along the boundary contour in a meridional plane. Numerical
solutions furnish accurate predictions for (a) the force and torque exerted on a particle translating parallel to the wall
in a quiescent fluid, (b) the force and torque exerted on a particle rotating about an axis that is parallel to the wall in
a quiescent fluid, and (c) the translational and angular velocities of a freely suspended particle in simple shear flow parallel
to the wall. For certain combinations of the wall and particle slip coefficients, a particle moving under the influence of
a tangential force translates parallel to the wall without rotation, and a particle moving under the influence of a tangential
torque rotates about an axis that is parallel to the wall without translation. For a particle convected in simple shear flow,
minimum translational velocity is observed for no-slip surfaces. However, allowing for slip may either increase or decrease
the particle angular velocity, and the dependence on the wall and particle slip coefficients is not necessarily monotonic. |
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Keywords: | Boundary-integral method Particle motion Stokes flow Surface slip Suspension |
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