Particle motion in Stokes flow near a plane fluid-fluid interface. Part 1. Slender body in a quiescent fluid

The present study examines the motion of a slender body in the presence of a plane fluid–fluid interface with an arbitrary viscosity ratio. The fluids are assumed to be at rest at infinity, and the particle is assumed to have an arbitrary orientation relative to the interface. The method of analysis is slender-body theory for Stokes flow using the fundamental solutions for singularities (i.e. Stokeslets and potential doublets) near a flat interface. We consider translation and rotation, each in three mutually orthogonal directions, thus determining the components of the hydrodynamic resistance tensors which relate the total hydrodynamic force and torque on the particle to its translational and angular velocities for a completely arbitrary translational and angular motion. To illustrate the application of these basic results, we calculate trajectories for a freely rotating particle under the action of an applied force either normal or parallel to a flat interface, which are relevant to particle sedimentation near a flat interface or to the processes of particle capture via drop or bubble flotation

Particle motion in Stokes flow near a plane fluid-fluid interface. Part 2. Linear shear and axisymmetric straining flows

We consider the motion of a sphere or a slender body in the presence of a plane fluid–fluid interface with an arbitrary viscosity ratio, when the fluids undergo a linear undisturbed flow. First, the hydrodynamic relationships for the force and torque on the particle at rest in the undisturbed flow field are determined, using the method of reflections, from the spatial distribution of Stokeslets, rotlets and higher-order singularities in Stokes flow. These fundamental relationships are then applied, in combination with the corresponding solutions obtained in earlier publications for the translation and rotation through a quiescent fluid, to determine the motion of a neutrally buoyant particle freely suspended in the flow. The theory yields general trajectory equations for an arbitrary viscosity ratio which are in good agreement with both exact-solution results and experimental data for sphere motions near a rigid plane wall. Among the most interesting results for motion of slender bodies is the generalization of the Jeffrey orbit equations for linear simple shear flow

Photonic Bandgap Structures of Core-Shell Simple Cubic Crystals from Holographic Lithography

We report the investigation of photonic bandgap properties of a core-shell simple cubic structure (air core with a dielectric shell) using a two-parameter level-set approach. The proposed structure can be obtained by partially backfilling high refractive index materials into a polymeric template fabricated by multi-beam interference lithography. We find that the shell formation in the inverted simple cubic structure increases the complete photonic bandgap width by 10–20% in comparison to that of a completely filled structure. The bandgap between the 5th and 6th bands begins to appear at a refractive index contrast of 2.7. This study suggests the importance to investigate the core-shell formation in three-dimensional photonic crystals through backfilling, which may offer an additional control over their photonic bandgap properties