Time development of small disturbances to plane Couette Flow

The question of linear sheared-disturbance evolution in constant-shear parallel flow is here reexamined with regard to the temporary-amplification phenomenon noted first by Orr in 1907. The results apply directly to Rossby waves on a beta-plane, and are also relevant to the Eady model of baroclinic instability. It is shown that an isotropic initial distribution of standing waves maintains a constant energy level throughout the shearing process, the amplification of some waves being precisely balanced by the decay of the others. An expression is obtained for the energy of a distribution of disturbances whose wavevectors lie within a given angular wedge and an upper bound derived. It is concluded that the case for ubiquitous amplification made in recent studies may have been somewhat overstated: while carefully-chosen individual Fourier components can amplify considerably before they decay. a general distribution will tend to exhibit little or no amplification.

2D hexagonal mesoporous platinum films exhibiting biaxial, in-plane pore alignment

The synthesis of 2D hexagonal mesoporous platinum films with biaxial, in-plane pore alignment is demonstrated by electrodeposition through an aligned lyotropic liquid crystal templating phase. Shear force is used to align a hexagonal lyotropic liquid crystalline templating phase of an inexpensive and a commercially available surfactant, C16EO10, at the surface of an electrode. Electrodeposition and subsequent characterisation of the films produced shows that the orientation and alignment of the phase is transferred to the deposited material. Transmission electron microscopy confirms the expected nanostructure of the films, whilst transmission and grazing incidence small angle X-ray scattering analysis confirms biaxial, in plane alignment of the pore structure. In addition further electrochemical studies in dilute sulfuric acid and methanol show that the pores are accessible to electrolyte solution as indicated by a large current flow; the modified electrode therefore has a high surface area, that catalyses methanol oxidation, and the pores have a very large aspect ratio (of theoretical maximum 2 × 105). Films with such aligned mesoporosity will advance the field of nanotechnology where the control of pore structure is paramount. The method reported is sufficiently generic to be used to control the structure and order of many materials, thus increasing the potential for the development of a wide range of novel electronic and optical devices.