The evolution of a slender non-axisymmetric drop in an extensional flow

An asymptotic method for analysing slender non-axisymmetric drops, bubbles and jets in a general straining flow is developed. The method relies on the slenderness of the geometry to reduce the three-dimensional equations to a sequence of weakly coupled, quasi-two-dimensional Stokes flow problems for the cross-sectional evolution. Exact solution techniques for the flow outside a bubble in two-dimensional Stokes flow are generalised to solve for the transverse flow field, allowing large non-axisymmetric deformations to be described. A generalisation to the case where the interior contains a slightly viscous fluid is also presented. Our method is used to compute steady non-axisymmetric solution branches for inviscid bubbles and slightly viscous drops. We also present unsteady numerical solutions showing how the eccentricity of the cross-section adjusts to a non-axisymmetric external flow. Finally, we use our theory to investigate how the pinch-off of a jet of relatively inviscid fluid is affected by a two-dimensional straining cross-flow

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

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

High-temperature thermal storage systems for advanced solar receivers materials selections

Advanced space power systems that use solar energy and Brayton or Stirling heat engines require thermal energy storage (TES) systems to operate continuously through periods of shade. The receiver storage units, key elements in both Brayton and Stirling systems, are designed to use the latent heat of fusion of phase-change materials (PCMs). The power systems under current consideration for near-future National Aeronautics and Space Administration space missions require working fluid temperatures in the 1100 to 1400 K range. The PCMs under current investigation that gave liquid temperatures within this range are the fluoride family of salts. However, these salts have low thermal conductivity, which causes large temperature gradients in the storage systems. Improvements can be obtained, however, with the use of thermal conductivity enhancements or metallic PCMs. In fact, if suitable containment materials can be found, the use of metallic PCMs would virtually eliminate the orbit associated temperature variations in TES systems. The high thermal conductivity and generally low volume change on melting of germanium and alloys based on silicon make them attractive for storage of thermal energy in space power systems. An approach to solving the containment problem, involving both chemical and physical compatibility, preparation of NiSi/NiSi2, and initial results for containment of germanium and NiSi/NiSi2, are presented

Boundary conditions for free surface inlet and outlet\ud problems

We investigate and compare the boundary conditions that are to be applied to free surface problems involving inlet and outlets of Newtonian fluid, typically found in coating processes. The flux of fluid is a priori known at an inlet, but unknown at an outlet, where it is governed by the local behaviour near the film-forming meniscus. In the limit of vanishing capillary number Ca it is well-known that the flux scales with Ca2/3, but this classical result is nonuniform as the contact angle approaches . By examining this limit we find a solution that is uniformly valid for all contact angles. Furthermore, by considering the far-field behaviour of the free surface we show that there exists a critical capillary number above which the problem at an inlet becomes over-determined. The implications of this result for the modelling of coating flows are discussed

Navigation and guidance requirements for commercial VTOL operations

The NASA Langley Research Center (LaRC) has undertaken a research program to develop the navigation, guidance, control, and flight management technology base needed by Government and industry in establishing systems design concepts and operating procedures for VTOL short-haul transportation systems in the 1980s time period. The VALT (VTOL Automatic Landing Technology) Program encompasses the investigation of operating systems and piloting techniques associated with VTOL operations under all-weather conditions from downtown vertiports; the definition of terminal air traffic and airspace requirements; and the development of avionics including navigation, guidance, controls, and displays for automated takeoff, cruise, and landing operations. The program includes requirements analyses, design studies, systems development, ground simulation, and flight validation efforts

On the predictions and limitations of the BeckerDoring model for reaction kinetics in micellar surfactant solutions

We investigate the breakdown of a system of micellar aggregates in a surfactant solution following an order-one dilution. We derive a mathematical model based on the Becker–Döring system of equations, using realistic expressions for the reaction constants fit to Molecular Dynamics simulations. We exploit the largeness of typical aggregation numbers to derive a continuum model, substituting a large system of ordinary differential equations for a partial differential equation in two independent variables: time and aggregate size. Numerical solutions demonstrate that re-equilibration occurs in two distinct stages over well-separated time-scales, in agreement with experiment and with previous theories. We conclude by exposing a limitation in the Becker–Döring theory for re-equilibration and discuss potential resolutions

Nuclear Equation of State from Observations of Short Gamma-Ray Burst Remnants

The favoured progenitor model for short $\gamma$-ray bursts (SGRBs) is the merger of two neutron stars that triggers an explosion with a burst of collimated $\gamma$-rays. Following the initial prompt emission, some SGRBs exhibit a plateau phase in their $X$-ray light curves that indicates additional energy injection from a central engine, believed to be a rapidly rotating, highly magnetised neutron star. The collapse of this `protomagnetar' to a black hole is likely to be responsible for a steep decay in $X$-ray flux observed at the end of the plateau. In this letter, we show that these observations can be used to effectively constrain the equation of state of dense matter. In particular, we show that the known distribution of masses in binary neutron star systems, together with fits to the $X$-ray light curves, provide constraints that exclude the softest and stiffest plausible equations of state. We further illustrate how a future gravitational wave observation with Advanced LIGO/Virgo can place tight constraints on the equation of state, by adding into the picture a measurement of the chirp mass of the SGRB progenitor.Comment: accepted for publication in Phys. Rev.