A mixer design for the pigtail braid

The stirring of a body of viscous fluid using multiple stirring rods is known to be particularly effective when the rods trace out a path corresponding to a nontrivial mathematical braid. The optimal braid is the so-called "pigtail braid", in which three stirring rods execute the usual "over-under" motion associated with braiding plaiting) hair. We show how to achieve this optimal braiding motion straightforwardly: one stirring rod is driven in a figure-of-eight motion, while the other two rods are baffles, which rotate episodically about their common centre. We also explore the extent to which the physical baffles may be replaced by flow structures (such as periodic islands).

Anisotropic Assembly of Colloidal Nanoparticles: Exploiting Substrate Crystallinity

We show that the crystal structure of a substrate can be exploited to drive the anisotropic assembly of colloidal nanoparticles. Pentanethiol-passivated Au particles of approximately 2 nm diameter deposited from toluene onto hydrogen-passivated Si(111) surfaces form linear assemblies (rods) with a narrow width distribution. The rod orientations mirror the substrate symmetry, with a high degree of alignment along principal crystallographic axes of the Si(111) surface. There is a strong preference for anisotropic growth with rod widths substantially more tightly distributed than lengths. Entropic trapping of nanoparticles provides a plausible explanation for the formation of the anisotropic assemblies we observe.

Two-dimensional Stokes flow driven by elliptical paddles

A fast and accurate numerical technique is developed for solving the biharmonic equation in a multiply connected domain, in two dimensions. We apply the technique to the computation of slow viscous flow (Stokes flow) driven by multiple stirring rods. Previously, the technique has been restricted to stirring rods of circular cross section; we show here how the prior method fails for noncircular rods and how it may be adapted to accommodate general rod cross sections, provided only that for each there exists a conformal mapping to a circle. Corresponding simulations of the flow are described, and their stirring properties and energy requirements are discussed briefly. In particular the method allows an accurate calculation of the flow when flat paddles are used to stir a fluid chaotically.