Stokes flow caused by the motion of a rigid sphere close to a viscous interface

• Published in: Chemical engineering science Vol. 53; no. 19; pp. 3413 - 3434
• Main Authors: Danov, K.D., Gurkov, T.D., Raszillier, H., Durst, F.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.10.1998; Elsevier
• Subjects: creeping flow; drag and torque on sphere; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Interface; Laminar flows; Laminar flows in cavities; Laminar suspensions; Physics; surface viscosity; surface viscosity; Interface; drag and torque on sphere; creeping flow; Torque; Digital simulation; Creeping flow; Pressure distribution; Boundary conditions; Velocity distribution; Surfactants; Surface viscosity; Fluid-fluid interfaces; Rotating sphere; Spherical particle; Drag coefficient; Moving body; Stokes flow
• ISSN: 0009-2509; 1873-4405
• DOI: 10.1016/S0009-2509(98)00137-7

The subject of this work is the creeping motion of liquid caused by steady translation and rotation of a solid sphere close to an interface between two fluid phases. The case of vanishingly small Reynolds and capillary numbers is considered. We account for the intrinsic viscous properties of the liquid boundary, characterised by dilatational and shear surface viscosities, in the frame of the Boussinesq–Scriven model. Numerical computations are presented for the velocity and pressure distributions throughout the flow domain. The drag force and the torque exerted on the particle are obtained by means of analytical integration of the stresses over the spherical surface. At small distances of separation between the rigid sphere and the wall, the role of the surface viscosity becomes quite substantial: the drag and the toque can be several times bigger than those which correspond to motion in an unbounded fluid. For steady rotation the flow around the solid particle is restrained in a relatively narrow region, whereas with translation the velocity field extends to large distances. Consequently, the rotating sphere should be closer in order to start ‘feeling’ the wall. Our results are relevant for systems which contain surfactant laden interfaces. We showed that even with low molecular weight surfactants such interfaces can behave much like solid ones. This is particularly true for fluid boundaries covered by proteins, as they turn out to be completely immobilised.