Preface to the special issue on "recent developments and new directions in thin-film flow"

Thin films of fluids are of central importance in numerous industrial, biomedical, geophysical and domestic applications, and display a rich and varied range of behaviours, including pattern formation, dewetting, rupture and finite-time blow up. As well as being of great interest in their own right, thin-film flows provide a “test bed” for research into a variety of challenging nonlinear problems in engineering, physics, chemistry, biology, and mathematics. As a consequence, research by a wide range of scientists, using a variety of analytical, numerical and experimental techniques on many different aspects of thin-film flow, has grown significantly in recent years, as novel applications have continued to appear and increasingly sophisticated theoretical and experimental techniques have been developed

Whisker-reinforced ceramic composites for heat engine components

Much work was undertaken to develop techniques of incorporating SiC whiskers into either a Si3N4 or SiC matrix. The result was the fabrication of ceramic composites with ever-increasing fracture toughness and strength. To complement this research effort, the fracture behavior of whisker-reinforced ceramics is studied so as to develop methodologies for the analysis of structural components fabricated from this toughened material. The results, outlined herein, focus on the following areas: the use of micromechanics to predict thermoelastic properties, theoretical aspects of fracture behavior, and reliability analysis

An investigation of Martian atmospheric trace species using laboratory and computer-based simulation

The study of trace gas species in the Martian atmosphere has the potential to shed new light on wide-ranging topics such as the search for life and the history of liquid water on the planet. Investigating the way that molecules such as ozone, water and HCl are cycled in the atmosphere will give insights into the interactions taking place between the atmosphere, lithosphere and any potential biosphere. Numerous missions are currently being planned; for example the NASA/ESA Trace Gas Orbiter which will probe the trace constituents of the Martian atmosphere and to try to explain recent observations such as the Tharsis methane plumes and the presence of perchlorate in the North polar plains. Currently there are two Mars General Circulation Models (MGCMs) that have fully coupled photochemistry modules: the 3D Mars Global Multiscale Model (GM3) and the Laboratoire de Météorologie Dynamique (LMD) MGCM. Both modules focus on odd-hydrogen (HOx) and odd-oxygen (Ox) chemistry and are not yet capable of simulating more complex chemical interactions. However, the benefit of fully-coupled MGCMs is that both the chemistry and the global transport of trace species can be investigated. In the current project we plan to study the more exotic chemical reactions occurring in the Martian atmosphere and to constrain their mechanisms and rates using both laboratory analogues and computerbased simulation

Travelling-wave similarity solutions for an unsteady shear-stress-driven dry patch in a flowing film

We investigate unsteady flow of a thin film of Newtonian fluid around a symmetric slender dry patch moving with constant velocity on an inclined planar substrate, the flow being driven by a prescribed constant shear stress at the free surface of the film (which would be of uniform thickness in the absence of the dry patch). We obtain a novel unsteady travelling-wave similarity solution which predicts that the dry patch has a parabolic shape and that the film thickness increases monotonically away from the dry patch

Pinning, de-pinning and re-pinning of a slowly varying rivulet

The solutions for the unidirectional flow of a thin rivulet with prescribed volume flux down an inclined planar substrate are used to describe the locally unidirectional flow of a rivulet with constant width (i.e. pinned contact lines) but slowly varying contact angle as well as the possible pinning and subsequent de-pinning of a rivulet with constant contact angle and the possible depinning and subsequent re-pinning of a rivulet with constant width as they flow in the azimuthal direction from the top to the bottom of a large horizontal cylinder. Despite being the same locally, the global behaviour of a rivulet with constant width can be very different from that of a rivulet with constant contact angle. In particular, while a rivulet with constant non-zero contact angle can always run from the top to the bottom of the cylinder, the behaviour of a rivulet with constant width depends on the value of the width. Specifically, while a narrow rivulet can run all the way from the top to the bottom of the cylinder, a wide rivulet can run from the top of the cylinder only to a critical azimuthal angle. The scenario in which the hitherto pinned contact lines of the rivulet de-pin at the critical azimuthal angle and the rivulet runs from the critical azimuthal angle to the bottom of the cylinder with zero contact angle but slowly varying width is discussed. The pinning and de-pinning of a rivulet with constant contact angle, and the corresponding situation involving the de-pinning and re-pinning of a rivulet with constant width at a non-zero contact angle which generalises the de-pinning at zero contact angle discussed earlier, are described. In the latter situation, the mass of fluid on the cylinder is found to be a monotonically increasing function of the constant width

Unsteady gravity-driven slender rivulets of a power-law fluid

Unsteady gravity-driven flow of a thin slender rivulet of a non-Newtonian power-law fluid on a plane inclined at an angle α to the horizontal is considered. Unsteady similarity solutions are obtained for both converging sessile rivulets (when 0 0 with t > 0, where x denotes a coordinate measured down the plane and t denotes time. Numerical and asymptotic methods are used to show that for each value of the power-law index N there are two physically realisable solutions, with cross-sectional profiles that are 'single-humped' and 'double-humped', respectively. Each solution predicts that at any time t the rivulet widens or narrows according to |x | (2N+1)/2(N+1) and thickens or thins according to |x | N/(N+1) as it flows down the plane; moreover, at any station x, it widens or narrows according to |t | −N/2(N+1) and thickens or thins according to |t | −N/(N+1). The length of a truncated rivulet of fixed volume is found to behave according to |t | N/(2N+1)

Three-dimensional coating and rimming flow : a ring of fluid on a rotating horizontal cylinder

The steady three-dimensional flow of a thin, slowly varying ring of Newtonian fluid on either the outside or the inside of a uniformly rotating large horizontal cylinder is investigated. Specifically, we study “full-ring” solutions, corresponding to a ring of continuous, finite and non-zero thickness that extends all the way around the cylinder. In particular, it is found that there is a critical solution corresponding to either a critical load above which no full-ring solution exists (if the rotation speed is prescribed) or a critical rotation speed below which no full-ring solution exists (if the load is prescribed). We describe the behaviour of the critical solution and, in particular, show that the critical flux, the critical load, the critical semi-width and the critical ring profile are all increasing functions of the rotation speed. In the limit of small rotation speed, the critical flux is small and the critical ring is narrow and thin, leading to a small critical load. In the limit of large rotation speed, the critical flux is large and the critical ring is wide on the upper half of the cylinder and thick on the lower half of the cylinder, leading to a large critical load. We also describe the behaviour of the non-critical full-ring solution, and, in particular, show that the semi-width and the ring profile are increasing functions of the load but, in general, non-monotonic functions of the rotation speed. In the limit of large rotation speed, the ring approaches a limiting non-uniform shape, whereas in the limit of small load, the ring is narrow and thin with a uniform parabolic profile. Finally, we show that, while for most values of the rotation speed and the load the azimuthal velocity is in the same direction as the rotation of the cylinder, there is a region of parameter space close to the critical solution for sufficiently small rotation speed in which backflow occurs in a small region on the upward-moving side of the cylinder

Travelling-wave similarity solution for unsteady flow around a dry patch driven by gravity and constant surface shear stress

In this paper we use the lubrication approximation to analyse three-dimensional unsteady flow of a thin film of Newtonian fluid around a symmetric slender moving dry patch on an inclined planar substrate. The flow being driven by gravity and a prescribed constant shear stress at the free surface. We obtain a novel unsteady travelling-wave similarity solution for the dry patch of uniform thickness, in which the dry patch travels at constant speed. This solution predicts that the dry patch has a parabolic shape which may be concave up or concave down the substrate. In all cases investigated numerically the film thickness is found to increase monotonically away from the contact line

Time dependent reliability model incorporating continuum damage mechanics for high-temperature ceramics

Presently there are many opportunities for the application of ceramic materials at elevated temperatures. In the near future ceramic materials are expected to supplant high temperature metal alloys in a number of applications. It thus becomes essential to develop a capability to predict the time-dependent response of these materials. The creep rupture phenomenon is discussed, and a time-dependent reliability model is outlined that integrates continuum damage mechanics principles and Weibull analysis. Several features of the model are presented in a qualitative fashion, including predictions of both reliability and hazard rate. In addition, a comparison of the continuum and the microstructural kinetic equations highlights a strong resemblance in the two approaches

Reliability analysis of structural ceramic components using a three-parameter Weibull distribution

Described here are nonlinear regression estimators for the three-Weibull distribution. Issues relating to the bias and invariance associated with these estimators are examined numerically using Monte Carlo simulation methods. The estimators were used to extract parameters from sintered silicon nitride failure data. A reliability analysis was performed on a turbopump blade utilizing the three-parameter Weibull distribution and the estimates from the sintered silicon nitride data