Straining flow of a micellar surfactant solution

We present a mathematical model describing the distribution of monomer and micellar surfactant in a steady straining flow beneath a fixed free surface. The model includes adsorption of monomer surfactant at the surface and a single-step reaction whereby $n$ monomer molecules combine to form each micelle. The equations are analysed asymptotically and numerically and the results are compared with experiments. Previous studies of such systems have often assumed equilibrium between the monomer and micellar phases, i.e. that the reaction rate is effectively infinite. Our analysis shows that such an approach inevitably fails under certain physical conditions and also cannot accurately match some experimental results. Our theory provides an improved fit with experiments and allows the reaction rates to be estimated

Mathematical modelling of the overflowing cylinder experiment

The overflowing cylinder (OFC) is an experimental apparatus designed to generate a controlled straining flow at a free surface, whose dynamic properties may then be investigated. Surfactant solution is pumped up slowly through a vertical cylinder. On reaching the top, the liquid forms a flat free surface which expands radially before overflowing down the side of the cylinder. The velocity, surface tension and surfactant concentration on the expanding free surface are measured using a variety of non-invasive techniques. A mathematical model for the OFC has been previously derived by Breward, Darton, Howell and Ockendon and shown to give satisfactory agreement with experimental results. However, a puzzling indeterminacy in the model renders it unable to predict one scalar parameter (e.g. the surfactant concentration at the centre of the cylinder), which must be therefore be taken from the experiments. In this paper we analyse the OFC model asymptotically and numerically. We show that solutions typically develop one of two possible singularities. In the first, the surface concentration of surfactant reaches zero a finite distance from the cylinder axis, while the surface velocity tends to infinity there. In the second, the surfactant concentration is exponentially large and a stagnation point forms just inside the rim of the cylinder. We propose a criterion for selecting the free parameter, based on the elimination of both singularities, and show that it leads to good agreement with experimental results

The drainage of a foam lamella

We present a mathematical model for the drainage of a surfactant-stabilised foam lamella, including capillary, Marangoni and viscous effects and allowing for diffusion, advection and adsorption of the surfactant molecules. We use the slender geometry of a lamella to formulate the model in the thin-film limit and perform an asymptotic decomposition of the liquid domain into a capillary-static Plateau border, a time-dependent thin film and a transition region between the two. By solving a quasi-steady boundary-value problem in the transition region, we obtain the flux of liquid from the lamella into the Plateau border and thus are able to determine the rate at which the lamella drains. Our method is illustrated initially in the surfactant-free case. Numerical results are presented for three particular parameter regimes of interest when surfactant is present. Both monotonic profiles and those exhibiting a dimple near the Plateau border are found, the latter having been previously observed in experiments. The velocity field may be uniform across the lamella or of parabolic Poiseuille type, with fluid either driven out along the centre-line and back along the free surfaces or vice versa. We find that diffusion may be negligible for a typical real surfactant, although this does not lead to a reduction in order because of the inherently diffusive nature of the fluid-surfactant interaction. Finally, we obtain the surprising result that the flux of liquid from the lamella into the Plateau border increases as the lamella thins, approaching infinity at a finite lamella thickness

Graphical techniques to assist in pointing and control studies of orbiting spacecraft

Computer generated graphics are developed to assist in the modeling and assessment of pointing and control systems of orbiting spacecraft. Three-dimensional diagrams are constructed of the Earth and of geometrical models which resemble the spacecraft of interest. Orbital positioning of the spacecraft model relative to the Earth and the orbital ground track are then displayed. A star data base is also available which may be used for telescope pointing and star tracker field-of-views to visually assist in spacecraft pointing and control studies. A geometrical model of the Hubble Space Telescope (HST) is constructed and placed in Earth orbit to demonstrate the use of these programs. Simulated star patterns are then displayed corresponding to the primary mirror's FOV and the telescope's star trackers for various telescope orientations with respect to the celestial sphere

Effects of simulated lightning on composite and metallic joints

The effects of simulated lightning strikes and currents on aircraft bonded joints and access/inspection panels were investigated. Both metallic and composite specimens were tested. Tests on metal fuel feed through elbows in graphite/epoxy structures were evaluated. Sparking threshold and residual strength of single lap bonded joints and sparking threshold of access/inspection panels and metal fuel feed through elbows are reported

Speed control with low armature loss for very small sensorless brushed DC motors

A method for speed control of brushed dc motors is presented. It is particularly applicable to motors with armatures of less than 1 cm3. Motors with very small armatures are difficult to control using the usual pulsewidth-modulation (PWM) approach and are apt to overheat if so driven. The technique regulates speed via the back electromotive force but does not require current-discontinuous drives. Armature heating in small motors under PWM drive is explained and quantified. The method is verified through simulation and measurement. Control is improved, and armature losses are minimized. The method can expect to find application in miniature mechatronic equipment

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

A Computer Simulation Model of Waterhyacinth and Weevil Interactions

A personal computer simulation model termed INSECT has been developed to evaluate biological control of waterhyacinth (Eichhornia crassipes (Mart.) Solms.) by two species of weevil (Neochetina eichhorniae Warner, and N. bruchi Hustache). The model results were compared with the data from three different locations. For each data set, the simulated plant biomass, adult and larva populations were plotted aqainst the 95% confidence intervals of the actual field observations. In many cases, the simulation results were within the 95% confidence intervals, and especially during the growing season, they indicated trends similar to those seen in the field data. However, there were discrepancies in both the magnitude and the trend for early and the late periods of the year. These initial results suggest that development of a model to simulate the impact of a biocontrol agent on waterhyacinth populations is a feasible approach to better understand the interactions within this control system

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