Particle motion near and inside an interface

• Published in: Journal of fluid mechanics Vol. 575; pp. 333 - 357
• Main Author: POZRIKIDIS, C.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.03.2007
• Subjects: Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Laminar flows; Laminar suspensions; Physics; Reynolds number; Traction; Velocity; Interfaces; Low Reynolds number; Shear flow; Particle motion; Digital simulation; Modelling; Spherical particle; Particle suspension; Immiscible fluid; Viscous fluids
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112006004046

The motion of a spherical particle near the interface between two immiscible viscous fluids undergoing simple shear flow is considered in the limit of small Reynolds and capillary numbers where the interface exhibits negligible deformation. Taking advantage of the rotational symmetry of the boundaries of the flow with respect to the axis that is normal to the interface and passes through the particle centre, the problem is formulated as a system of one-dimensional integral equations for the first Fourier coefficients of the unknown components of the traction and velocity along the particle and interface contours. The results document the particle translational and angular velocities, and reveal that the particle slips while rolling over the interface under the influence of a simple shear flow, for any viscosity ratio. In the second part of the investigation, the motion of an axisymmetric particle straddling a planar interface is considered. The results confirm a simple exact solution when a particle with top-down symmetry is immersed half-way in each fluid and translates parallel to the interface, reveal a similar simple solution for a particle that is held stationary in simple shear flow, and document the force and torque exerted on a spherical particle for more general arrangements. The onset of a non-integrable singularity of the traction at the contact line prohibits the computation of the translational and angular velocities of a freely suspended particle convected under the action of a shear flow.