The surface-tension-driven evolution of a two-dimensional annular viscous tube

We consider the evolution of an annular two-dimensional region occupied by viscous fluid driven by surface tension and applied pressure at the free surfaces. We assume that the thickness of the domain is small compared with its circumference so that it may be described as a thin viscous sheet whose ends are joined to form a closed loop. Analytical and numerical solutions of the resulting model are obtained and we show that it is well posed whether run forwards or backwards in time. This enables us to determine, in many cases explicitly, which initial shapes will evolve into a desired final shape. We also show how the application of an internal pressure may be used to control the evolution. This work is motivated by the production of non-axisymmetric capillary tubing via the Vello process. Molten glass is fed through a die and drawn off vertically, while the shape of the cross-section evolves under surface tension and any applied pressure as it flows downstream. Here the goal is to determine the die shape required to achieve a given desired final shape, typically square or rectangular. We conclude by discussing the role of our two-dimensional model in describing the three-dimensional tube-drawing process

Silicon carbide diode for increased light output

Transition metals improve the overall light output and the output in particular regions of the electroluminescent of a silicon carbide semiconductor device. These metals /impurities/ introduce levels that can be pumped electrically and affect the efficiency of the recombination process involved in emission of radiation

Mathematical modelling of non-axisymmetric capillary tube drawing

This paper concerns the manufacture of non-axisymmetric capillary tubing via the Velloprocess, in which molten glass is fed through a die and drawn off vertically. The shapeof the cross-section evolves under surface tension as it flows downstream. The aim is to achieve a given desired final shape, typically square or rectangular, and our goal is to determine the required die shape. We use the result that, provided the tube is slowly varying in the axial direction, each cross-section evolves like a two-dimensional Stokes flow when expressed in suitably scaled Lagrangian coordinates. This allows us to use a previously derived model for the surface- tension-driven evolution of a thin two-dimensional viscous tube. We thus obtain, and solve analytically, equations governing the axial velocity, thickness and circumference of the tube, as well as its shape. The model is extended to include non-isothermal effects

Solving the characteristic initial value problem for colliding plane gravitational and electromagnetic waves

A method is presented for solving the characteristic initial value problem for the collision and subsequent nonlinear interaction of plane gravitational or gravitational and electromagnetic waves in a Minkowski background. This method generalizes the monodromy transform approach to fields with nonanalytic behaviour on the characteristics inherent to waves with distinct wave fronts. The crux of the method is in a reformulation of the main nonlinear symmetry reduced field equations as linear integral equations whose solutions are determined by generalized (``dynamical'') monodromy data which evolve from data specified on the initial characteristics (the wavefronts).Comment: 4 pages, RevTe

Microfluidic immunomagnetic multi-target sorting – a model for controlling deflection of paramagnetic beads

We describe a microfluidic system that uses a magnetic field to sort paramagnetic beads by deflecting them in the direction normal to the flow. Our experiments systematically study the dependence of the beads’ deflection on: bead size and susceptibility, magnet strength, fluid speed and viscosity, and device geometry. We also develop a design parameter that can aid in the design of microfluidic devices for immunomagnetic multi-target sorting

An experimental and theoretical investigation of particle–wall impacts in a T-junction

Understanding the behaviour of particles entrained in a fluid flow upon changes in flow direction is crucial in problems where particle inertia is important, such as the erosion process in pipe bends.We present results on the impact of particles in a T-shaped channel in the laminar-turbulent transitional regime. The impacting event for a given system is described in terms of the Reynolds number and the particle Stokes number. Experimental results for the impact are compared with the trajectories predicted by theoretical particle tracing models for a range of configurations to determine the role of the viscous boundary layer in retarding the particles and reducing the rate of collision with the substrate. In particular a 2D model based on a stagnation point flow is used together with 3D numerical simulations. We show how the simple 2D model provides a tractable way of understanding the general collision behaviour, while more advanced 3D simulation can be helpful in understanding the details of the flow

REGULAR SUPPRESSION OF P,T-VIOLATING NUCLEAR MATRIX ELEMENTS

In heavy nuclei there is a parametrical suppression, $\;\sim A^{-1/3}\;$, of T-odd, P-odd matrix elements as compared to T-even, P-odd ones.Comment: 3 page