Falling liquid films with blowing and suction

Flow of a thin viscous film down a flat inclined plane becomes unstable to long wave interfacial fluctuations when the Reynolds number based on the mean film thickness becomes larger than a critical value (this value decreases as the angle of inclination with the horizontal increases, and in particular becomes zero when the plate is vertical). Control of these interfacial instabilities is relevant to a wide range of industrial applications including coating processes and heat or mass transfer systems. This study considers the effect of blowing and suction through the substrate in order to construct from first principles physically realistic models that can be used for detailed passive and active control studies of direct relevance to possible experiments. Two different long-wave, thin-film equations are derived to describe this system; these include the imposed blowing/suction as well as inertia, surface tension, gravity and viscosity. The case of spatially periodic blowing and suction is considered in detail and the bifurcation structure of forced steady states is explored numerically to predict that steady states cease to exist for sufficiently large suction speeds since the film locally thins to zero thickness giving way to dry patches on the substrate. The linear stability of the resulting nonuniform steady states is investigated for perturbations of arbitrary wavelengths, and any instabilities are followed into the fully nonlinear regime using time-dependent computations. The case of small amplitude blowing/suction is studied analytically both for steady states and their stability. Finally, the transition between travelling waves and non-uniform steady states is explored as the suction amplitude increases

Arc Phenomena in low-voltage current limiting circuit breakers

Circuit breakers are an important safety feature in most electrical circuits, and they act to prevent excessive currents caused by short circuits, for example. Low-voltage current limiting circuit breakers are activated by a trip solenoid when a critical current is exceeded. The solenoid moves two contacts apart to break the circuit. However, as soon as the contacts are separated an electric arc forms between them, ionising the air in the gap, increasing the electrical conductivity of air to that of the hot plasma that forms, and current continues to flow. The currents involved may be as large as 80,000 amperes. Critical to the success of the circuit breaker is that it is designed to cause the arc to move away from the contacts, into a widening wedge-shaped region. This lengthens the arc, and then moves it onto a series of separator plates called an arc divider or splitter. The arc divider raises the voltage required to sustain the arcs across it, above the voltage that is provided across the breaker, so that the circuit is broken and the arcing dies away. This entire process occurs in milliseconds, and is usually associated with a sound like an explosion and a bright ash from the arc. Parts of the contacts and the arc divider may melt and/or vapourise. The question to be addressed by the Study Group was to mathematically model the arc motion and extinction, with the overall aim of an improved understanding that would help the design of a better circuit breaker. Further discussion indicated that two key mechanisms are believed to contribute to the movement of the arc away from the contacts, one being self-magnetism (where the magnetic field associated with the arc and surrounding circuitry acts to push it towards the arc divider), and the other being air flow (where expansion of air combined with the design of the chamber enclosing the arc causes gas flow towards the arc divider). Further discussion also indicated that a key aspect of circuit breaker design was that it is desirable to have as fast a quenching of the arc as possible, that is, the faster the circuit breaker can act to stop current flow, the better. The relative importance of magnetic and air pressure effects on quenching speed is of central interest to circuit design

A5: Grafton Notch State Park: Glacial Gorges and Streams Under Pressure in the Mahoosic Range, Maine

Guidebook for field trips in Western Maine and Northern New Hampshire: New England Intercollegiate Geological Conference, p. 95-104

High magnetic field pulsars and magnetars: a unified picture

We propose a unified picture of high magnetic field radio pulsars and magnetars by arguing that they are all rotating high-field neutron stars, but have different orientations of their magnetic axes with respective to their rotation axes. In strong magnetic fields where photon splitting suppresses pair creation near the surface, the high-field pulsars can have active inner accelerators while the anomalous X-ray pulsars cannot. This can account for the very different observed emission characteristics of the anomalous X-ray pulsar 1E 2259+586 and the high field radio pulsar PSR J1814-1744. A predicted consequence of this picture is that radio pulsars having surface magnetic field greater than about $2\times 10^{14}$ G should not exist.Comment: 5 pages, emulateapj style, accepted for publication in the ApJ Letter

Bifurcations of drops and bubbles propagating in variable-depth Hele-Shaw channels

From Springer Nature via Jisc Publications RouterHistory: received 2020-11-30, registration 2021-05-30, accepted 2021-05-30, pub-electronic 2021-07-18, online 2021-07-18, pub-print 2021-08Publication status: PublishedFunder: Engineering and Physical Sciences Research Council; doi: http://dx.doi.org/10.13039/501100000266; Grant(s): EP/T021365/1, EP/P026044/1Abstract: The steady propagation of air bubbles through a Hele-Shaw channel with either a rectangular or partially occluded cross section is known to exhibit solution multiplicity for steadily propagating bubbles, along with complicated transient behaviour where the bubble may visit several edge states or even change topology several times, before typically reaching its final propagation mode. Many of these phenomena can be observed both in experimental realisations and in numerical simulations based on simple Darcy models of flow and bubble propagation in a Hele-Shaw cell. In this paper, we investigate the corresponding problem for the propagation of a viscous drop (with viscosity ν relative to the surrounding fluid) using a Darcy model. We explore the effect of drop viscosity on the steady solution structure for drops in rectangular channels or with imposed height variations. Under the Darcy model in a uniform channel, steady solutions for bubbles map directly on to those for drops with any internal viscosity ν≠1. Hence, the solution multiplicity predicted for bubbles also occurs for drops, although for ν>1, the interface shape is reversed with inflection points appearing at the rear rather than the front of the drop. The equivalence between bubbles and drops breaks down for transient behaviour, at the introduction of any height variation, for multiple bodies of different viscosity ratios and for more detailed models which produce a more complicated flow in the interior of the drop. We show that the introduction of topography variations affects bubbles and drops differently, with very viscous drops preferentially moving towards more constricted regions of the channel. Both bubbles and drops can undergo transient behaviour which involves breakup into two almost equal bodies, which then symmetry break before either recombining or separating indefinitely

Surface-tension-driven coalescence

When fluid droplets coalesce, the flow is initially controlled by a balance between surface tension and viscosity. For low viscosity fluids such as water, the viscous lengthscale is quickly reached, yielding a new balance between surface tension and inertia. Numerical and asymptotic calculations have shown that there is no simply connected solution for the coalescence of inviscid fluid drops surrounded by a void, as large amplitude capillary waves cause the free surface to pinch off. We analyse in detail a linearised version of this free boundary problem. For zero density surrounding fluid, we find asymptotic solutions to the leading order linear problem for small and large contact point displacement. In both cases, this requires the solution of a mixed type boundary value problem via complex variable methods. For the large displacement solution, we match this to a WKB analysis for capillary waves away from the contact point. The composite solution shows that the interface position becomes self intersecting for sufficiently large contact point displacement. We identify a distinguished density ratio for which flows in the coalescing drops and surrounding fluid are equally important in determining the interface shape. We find a large displacement solution to the leading order two-fluid problem with a multiple-scales analysis, using a spectral method to solve the leading order periodic oscillator problem for capillary waves. This is matched to a single-parameter inner problem, which we solve numerically to obtain the correct boundary conditions for the secularity equations. We find that the composite solution for the two-fluid problem is simply connected for arbitrarily large contact-point displacement, and so zero density surrounding fluid is a singular limit

Surface-tension-driven coalescence

When fluid droplets coalesce, the flow is initially controlled by a balance between surface tension and viscosity. For low viscosity fluids such as water, the viscous lengthscale is quickly reached, yielding a new balance between surface tension and inertia. Numerical and asymptotic calculations have shown that there is no simply connected solution for the coalescence of inviscid fluid drops surrounded by a void, as large amplitude capillary waves cause the free surface to pinch off. We analyse in detail a linearised version of this free boundary problem. For zero density surrounding fluid, we find asymptotic solutions to the leading order linear problem for small and large contact point displacement. In both cases, this requires the solution of a mixed type boundary value problem via complex variable methods. For the large displacement solution, we match this to a WKB analysis for capillary waves away from the contact point. The composite solution shows that the interface position becomes self intersecting for sufficiently large contact point displacement. We identify a distinguished density ratio for which flows in the coalescing drops and surrounding fluid are equally important in determining the interface shape. We find a large displacement solution to the leading order two-fluid problem with a multiple-scales analysis, using a spectral method to solve the leading order periodic oscillator problem for capillary waves. This is matched to a single-parameter inner problem, which we solve numerically to obtain the correct boundary conditions for the secularity equations. We find that the composite solution for the two-fluid problem is simply connected for arbitrarily large contact-point displacement, and so zero density surrounding fluid is a singular limit

Robust low-dimensional modelling of falling liquid films subject to variable wall heating

Accurate low-dimensional models for the dynamics of falling liquid films subject to localized or time-varying heating are essential for applications that involve patterning or control. However, existing modelling methodologies either fail to respect fundamental thermodynamic properties or else do not accurately capture the effects of advection and diffusion on the temperature profile. We argue that the best-performing long-wave models are those that give the surface temperature implicitly as the solution of an evolution equation in which the wall temperature alone (and none of its derivatives) appears as a source term. We show that, for both flat and non-uniform films, such a model can be rationally derived by expanding the temperature field about its free-surface values. We test this model in linear and nonlinear regimes, and show that its predictions are in remarkable quantitative agreement with full Navier–Stokes calculations regarding the surface temperature, the internal temperature field and the surface displacement that would result from temperature-induced Marangoni stresses

Magnetic Photon Splitting: Computations of Proper-time Rates and Spectra

The splitting of photons in the presence of an intense magnetic field has recently found astrophysical applications in polar cap models of gamma-ray pulsars and in magnetar scenarios for soft gamma repeaters. Numerical computation of the polarization-dependent rates of this third order QED process for arbitrary field strengths and energies below pair creation threshold is difficult: thus early analyses focused on analytic developments and simpler asymptotic forms. The recent astrophysical interest spurred the use of the S-matrix approach by Mentzel, Berg and Wunner to determine splitting rates. In this paper, we present numerical computations of a full proper-time expression for the rate of splitting that was obtained by Stoneham, and is exact up to the pair creation threshold. While the numerical results derived here are in accord with the earlier asymptotic forms due to Adler, our computed rates still differ by as much as factors of 3 from the S-matrix re-evaluation of Wilke and Wunner, reflecting the extreme difficulty of generating accurate S-matrix numerics for fields below about \teq{4.4\times 10^{13}}Gauss. We find that our proper-time rates appear very accurate, and exceed Adler's asymptotic specializations significantly only for photon energies just below pair threshold and for supercritical fields, but always by less than a factor of around 2.6. We also provide a useful analytic series expansion for the scattering amplitude valid at low energies.Comment: 13 pages, AASTeX format, including 3 eps figures, ApJ in pres