Point torque representations of ciliary flows

Ciliary flows are generated by a vast array of eukaryotic organisms, from unicellular algae to mammals, and occur in a range of different geometrical configurations. We employ a point torque -- or `rotlet' -- model to capture the time-averaged ciliary flow above a planar rigid wall. We demonstrate the advantages (i.e. accuracy and computational efficiency) of using this, arguably simpler approach compared to other singularity-based models in Stokes flows. Then, in order to model ciliary flows in confined spaces, we extend the point torque solution to a bounded domain between two plane parallel no-slip walls. The flow field is resolved using the method of images and Fourier transforms, and we analyze the role of confinement by comparing the resultant fluid velocity to that of a rotlet near a single wall. Our results suggest that the flow field of a single cilium is not changed significantly by the confinement, even when the distance between the walls is commensurate with the cilium's length.Comment: 20 pages, 13 figure

Instabilities in Blistering

Blistering occurs when a thin solid layer locally separates from an underlying substrate through cracking of a bulk material, delamination of a composite material, or peeling of a membrane adhered to the substrate by a thin layer of viscous fluid. In this last scenario, the expansion of the newly formed blister by fluid injection occurs via a displacement flow, which peels apart the adhered surfaces through a two-way interaction between flow and deformation. Such blisters are prone to fluid and solid mechanical instabilities. If the injected fluid is less viscous than the fluid already occupying the gap, patterns of short and stubby fingers form on the propagating fluid interface. This process is regulated by membrane compliance, which if increased delays the onset of fingering to higher flow rates and reduces finger amplitude. Suppression is mediated by the locally tapered geometry of the blister near the fluid interface, which is imposed by the underlying blistering flow. Buckling/wrinkling instabilities of the delaminated layer arise for sufficiently thin membranes and can interact with the fluid mechanical fingering instability. </jats:p

Dynamics of inertialess sedimentation of a rigid U-shaped disk

Abstract When particles sediment in a viscous fluid, the character of their trajectories depends sensitively on the particles’ shape. Here we study the sedimentation of U-shaped rigid disks in a regime where inertia can be neglected. We show that, unlike the case of planar disks which settle in a fixed orientation relative to the direction of gravity, U-shaped disks tend to perform a periodic sequence of pitching and rolling motions which cause their centre of mass to sediment along complex trajectories that range from quasi-periodic spirals to helices. Thus, we demonstrate that particles of achiral shape can sediment along chiral paths whose handedness is determined by their initial orientation rather than their geometry. Our analysis provides a framework in which to interpret the motion of sedimenting particles of arbitrary shape

Trapping and escape of viscous fingers in a soft Hele-Shaw cell

Viscous flow in the narrow gap between a rigid plate and a confined elastic solid has been observed to ‘choke’ at high flow rates, due to the deforming solid making contact with the plate and sealing the gap. When the viscous flow is driven by injection of a gas bubble, the advancing meniscus is susceptible to the viscous-fingering instability. By comparing fingering experiments with axisymmetric numerical simulations, we demonstrate that, depending on the width of the fingers, the fingering instability can either promote or suppress choking, i.e. cause the system to choke when an axisymmetric system would not, or vice versa