A dynamical instability due to fluid–wall coupling lowers the transition Reynolds number in the flow through a flexible tube

A flow-induced instability in a tube with flexible walls is studied experimentally. Tubes of diameter 0.8 and 1.2 mm are cast in polydimethylsiloxane (PDMS) polymer gels, and the catalyst concentration in these gels is varied to obtain shear modulus in the range 17–550 kPa. A pressure drop between the inlet and outlet of the tube is used to drive fluid flow, and the friction factor $f$ is measured as a function of the Reynolds number $Re$. From these measurements, it is found that the laminar flow becomes unstable, and there is a transition to a more complicated flow profile, for Reynolds numbers as low as 500 for the softest gels used here. The nature of the $f$–$Re$ curves is also qualitatively different from that in the flow past rigid tubes; in contrast to the discontinuous increase in the friction factor at transition in a rigid tube, it is found that there is a continuous increase in the friction factor from the laminar value of $16\ensuremath{/} Re$ in a flexible tube. The onset of transition is also detected by a dye-stream method, where a stream of dye is injected into the centre of the tube. It is found that there is a continuous increase of the amplitude of perturbations at the onset of transition in a flexible tube, in contrast to the abrupt disruption of the dye stream at transition in a rigid tube. There are oscillations in the wall of the tube at the onset of transition, which is detected from the laser scattering off the walls of the tube. This indicates that the coupling between the fluid stresses and the elastic stresses in the wall results in an instability of the laminar flow.

Stability of the flow of a fluid through a flexible tube at high Reynolds number

The stability of the Hagen-Poiseuille flow of a Newtonian fluid in a tube of radius R surrounded by an incompressible viscoelastic medium of radius R < r < HR is analysed in the high Reynolds number regime. The dimensionless numbers that affect the fluid flow are the Reynolds number Re = (ρVR / η), the ratio of the viscosities of the wall and fluid ηr = (ηs/η), the ratio of radii H and the dimensionless velocity Γ = (ρV2/G)1/2. Here ρ is the density of the fluid, G is the coefficient of elasticity of the wall and Vis the maximum fluid velocity at the centre of the tube. In the high Reynolds number regime, an asymptotic expansion in the small parameter ε = (1/Re) is employed. In the leading approximation, the viscous effects are neglected and there is a balance between the inertial stresses in the fluid and the elastic stresses in the medium. There are multiple solutions for the leading-order growth rate do), all of which are imaginary, indicating that the fluctuations are neutrally stable, since there is no viscous dissipation of energy or transfer of energy from the mean flow to the fluctruations due to the Reynolds strees. There is an O(ε1/2) correction to the growth rate, s(1), due to the presence of a wall layer of thickness ε1/2R where the viscous stresses are O(ε1/2) smaller than the inertial stresses. An energy balance analysis indicates that the transfer of energy from the mean flow to the fluctuations due to the Reynolds stress in the wall layer is exactly cancelled by an opposite transfer of equal magnitude due to the deformation work done at the interface, and there is no net transfer from the mean flow to the fluctuations. Consequently, the fluctuations are stabilized by the viscous dissipation in the wall layer, and the real part of s(1) is negative. However, there are certain values of Γ and wavenumber k where s(l) = 0. At these points, the wail layer amplitude becomes zero because the tangential velocity boundary condition is identically satisfied by the inviscid flow solution. The real part of the O(ε) correction to the growth rate s(2) turns out to be negative at these points, indicating a small stabilizing effect due to the dissipation in the bulk of the fluid and the wall material. It is found that the minimum value of s(2) increases [is proportional to] (H − 1)−2 for (H − 1) [double less-than sign] 1 (thickness of wall much less than the tube radius), and decreases [is proportional to] (H−4 for H [dbl greater-than sign] 1. The damping rate for the inviscid modes is smaller than that for the viscous wall and centre modes in a rigid tube, which have been determined previously using a singular perturbation analysis. Therefore, these are the most unstable modes in the flow through a flexible tube.

Constitutive Response of Passivated Copper Films: Experiments and Analyses

The constitutive behavior of passivated copper films is studied. Stresses in copper films of thickness ranging from 1000 nm to 40 nm, passivated with silicon oxide on a quartz or silicon substrate, were measured using the curvature method. The thermal cycling spans a temperature range from - 196 to 600°C. It is seen that the strong relaxation at high temperatures normally found in unpassivated films is nonexistent for passivated films. The copper film did not show any rate-dependent effect over a range of heating/cooling rate from 5 to 25°C/min. Further analyses showed that significant strain hardening exists during the course of thermal loading. In particular, the measured stress- temperature response can only be fitted with a kinematic hardening model, if a simple constitutive law within the continuum plasticity framework is to be used. The analytic procedures for extracting the film properties are presented. Implications to stress modeling of copper interconnects in actual devices are discussed.

Crack formation due to annealing of Al2O3 films grown on Si(100) by MOCVD

We report crack formation in alumina films grown on Si(100), caused by annealing in a controlled oxidizing ambient. The films were grown in a low-pressure CVD reactor, using aluminium acetylacetonate as precursor. High purity argon and nitrous oxide were employed as carrier and oxidizing gas, respectively. The films were characterized by optical microscopy and SEM/EDAX. The proportion and chemical nature of the heteroatoms, namely C and H, incorporated into the films from the precursor, were characterized by XPS, and FTIR. As-deposited films do not exhibit any cracks, while post-deposition annealing results in cracks. Apart from the delamination of the films, annealing in nitrous oxide ambient leads to an unusual crack geometry, which we term the “railway-track”. These twin cracks are very straight and run parallel to each other for as much as several millimeters. Often, two such linear tracks meet at exactly 90°. Between some of these tracks lie bullet-like structures with very sharp tips, oriented in a specific direction. As cracks are generally activated by residual stress, both thermal and intrinsic, the origins of the stresses that generate these linear cracks are discussed. The redistribution of stress, arising from the removal of C and H during annealing, will also be discussed. An attempt has been made to correlate the formation of cracks with the crystal structure of the film.

Axially homogeneous, zero mean flow buoyancy-driven turbulence in a vertical pipe

We report an experimental study of a new type of turbulent flow that is driven purely by buoyancy. The flow is due to an unstable density difference, created using brine and water, across the ends of a long (length/diameter=9) vertical pipe. The Schmidt number Sc is 670, and the Rayleigh number (Ra) based on the density gradient and diameter is about 108. Under these conditions the convection is turbulent, and the time-averaged velocity at any point is ‘zero’. The Reynolds number based on the Taylor microscale, Reλ, is about 65. The pipe is long enough for there to be an axially homogeneous region, with a linear density gradient, about 6–7 diameters long in the midlength of the pipe. In the absence of a mean flow and, therefore, mean shear, turbulence is sustained just by buoyancy. The flow can be thus considered to be an axially homogeneous turbulent natural convection driven by a constant (unstable) density gradient. We characterize the flow using flow visualization and particle image velocimetry (PIV). Measurements show that the mean velocities and the Reynolds shear stresses are zero across the cross-section; the root mean squared (r.m.s.) of the vertical velocity is larger than those of the lateral velocities (by about one and half times at the pipe axis). We identify some features of the turbulent flow using velocity correlation maps and the probability density functions of velocities and velocity differences. The flow away from the wall, affected mainly by buoyancy, consists of vertically moving fluid masses continually colliding and interacting, while the flow near the wall appears similar to that in wall-bound shear-free turbulence. The turbulence is anisotropic, with the anisotropy increasing to large values as the wall is approached. A mixing length model with the diameter of the pipe as the length scale predicts well the scalings for velocity fluctuations and the flux. This model implies that the Nusselt number would scale as Ra1/2Sc1/2, and the Reynolds number would scale as Ra1/2Sc−1/2. The velocity and the flux measurements appear to be consistent with the Ra1/2 scaling, although it must be pointed out that the Rayleigh number range was less than 10. The Schmidt number was not varied to check the Sc scaling. The fluxes and the Reynolds numbers obtained in the present configuration are much higher compared to what would be obtained in Rayleigh–Bénard (R–B) convection for similar density differences.

Studies on thin film materials on acrylics for optical applications

Deposition of durable thin film coatings by vacuum evaporation on acrylic substrates for optical applications is a challenging job. Films crack upon deposition due to internal stresses and leads to performance degradation. In this investigation, we report the preparation and characterization of single and multi-layer films of TiO2, CeO2, Substance2 (E Merck, Germany), Al2O3, SiO2 and MgF2 by electron beam evaporation on both glass and PMMA substrates. Optical micrographs taken on single layer films deposited on PMMA substrates did not reveal any cracks. Cracks in films were observed on PMMA substrates when the substrate temperature exceeded 80degreesC. Antireflection coatings of 3 and 4 layers have been deposited and characterized. Antireflection coatings made on PMMA substrate using Substance2 (H2) and SiO2 combination showed very fine cracks when observed under microscope. Optical performance of the coatings has been explained with the help of optical micrographs.

Turbulent flow computations using upwind RANS technique for a flat plate and an airfoil

Reynolds Averaged Navier Stokes (RANS) equations are solved using third order upwind biased Roe's scheme for the inviscid fluxes and second order central difference scheme for the viscous fluxes. The Baldwin & Lomax turbulence model is employed for Reynolds stresses. The governing equations are solved using finite-volume implicit scheme in body fitted curvilinear coordinate O-grid system. Computations axe reported for a flat plate apart from RAE 2822 and NACA 0012 airfoils. Results for the flat plate at M = 0.3, R-c = 4.0 x 10(6) compare favourably with the analytical solution. Results for the two airfoils are compared with experiment. There is a good agreement in C-p distribution between experiment and computation for both the airfoils. Comparison of C-f distribution with experiment for RAE 2822 airfoil is reasonable.

Unsteady MUD rotating flow over a rotating sphere near the equator

The unsteady rotating flow of a laminar incompressible viscous electrically conducting fluid over a rotating sphere in the vicinity of the equator has been studied. The fluid and the body rotate either in the same direction or in opposite directions. The effects of surface suction and magnetic field have been included in the analysis. There is an initial steady state that is perturbed by a sudden change in the rotational velocity of the sphere, and this causes unsteadiness in the flow field. The nonlinear coupled parabolic partial differential equations governing the boundary-layer flow have been solved numerically by using an implicit finite-difference scheme. For large suction or magnetic field, analytical solutions have also been obtained. The magnitude of the radial, meridional and rotational velocity components is found to be higher when the fluid and the body rotate in opposite directions than when they rotate in the same direction. The surface shear stresses in the meridional and rotational directions change sign when the ratio of the angular velocities of the sphere and the fluid lambda greater than or equal to lambda(0). The final (new) steady state is reached rather quickly which implies that the spin-up time is small. The magnetic field and surface suction reduce the meridional shear stress, but increase the surface shear stress in the rotational direction.

Shear banding in a yield stress bearing Langmuir monolayer

We examine the shear-thinning behaviour of a two dimensional yield stress bearing monolayer of sorbitan tristearate at air/water interface. The flow curve consists of a linear region at low shear stresses/shear rates, followed by a stress plateau at higher values. The velocity profile obtained from particle imaging velocimetry indicates that shear banding occurs, showing coexistence of the fluidized region near the rotor and solid region with vanishing shear-rate away from the rotor. In the fluidized region, the velocity profile, which is linear at low shear rates, becomes exponential at the onset of shear-thinning, followed by a time varying velocity profile in the plateau region. At low values of constant applied shear rates, the viscosity of the film increases with time, thus showing aging behaviour like in soft glassy three-dimensional (3D) systems. Further, at the low values of the applied stress in the yield stress regime, the shear-rate fluctuations in time show both positive and negative values, similar to that observed in sheared 3D jammed systems. By carrying out a statistical analysis of these shear-rate fluctuations, we estimate the effective temperature of the soft glassy monolayer using the Galavatti-Cohen steady state fluctuation relation.

Modeling Indian Ocean circulation: Bay of Bengal fresh water plume and the Arabian Sea Mini Warm Pool

The Indian subcontinent divides the north Indian Ocean into two tropical basins, namely the Arabian Sea and the Bay of Bengal. The Arabian Sea has high salinity whereas the salinity of the Bay of Bengal is much lower due to the contrast in freshwater forcing of the two basins. The freshwater received by the Bay in large amounts during the summer monsoon through river discharge is flushed out annually by ocean circulation. After the withdrawal of the summer monsoon, the Ganga – Brahmaputra river plume flows first along the Indian coast and then around Sri Lanka into the Arabian Sea creating a low salinity pool in the southeastern Arabian Sea (SEAS). In the same region, during the pre-monsoon months of February – April, a warm pool, known as the Arabian Sea Mini Warm Pool (ASMWP), which is distinctly warmer than the rest of the Indian Ocean, takes shape. In fact, this is the warmest region in the world oceans during this period. Simulation of the river plume and its movement as well as its implications to thermodynamics has been a challenging problem for models of Indian Ocean. Here we address these issues using an ocean general circulation model – first we show that the model is capable of reproducing fresh plumes in the Bay of Bengal as well as its movement and then we use the model to determine the processes that lead to formation of the ASMWP. Hydrographic observations from the western Bay of Bengal have shown the presence of a fresh plume along the northern part of the Indian coast during summer monsoon. The Indian Ocean model when forced by realistic winds and climatological river discharge reproduces the fresh plume with reasonable accuracy. The fresh plume does not advect along the Indian coast until the end of summer monsoon. The North Bay Monsoon Current, which flows eastward in the northern Bay, separates the low salinity water from the more saline southern parts of the bay and thus plays an important role in the fresh water budget of the Bay of Bengal. The model also reproduces the surge of the fresh-plume along the Indian coast, into the Arabian Sea during northeast monsoon. Mechanisms that lead to the formation of the Arabian Sea Mini Warm Pool are investigated using several numerical experiments. Contrary to the existing theories, we find that salinity effects are not necessary for the formation of the ASMWP. The orographic effects of the Sahyadris (Western Ghats) and resulting reduction in wind speed leads to the formation of the ASMWP. During November – April, the SEAS behave as a low-wind heatdominated regime where the evolution of sea surface temperature is solely determined by atmospheric forcing. In such regions the evolution of surface layer temperature is not dependent on the characteristics of the subsurface ocean such as the barrier layer and temperature inversion.

The selection of a sugar for transport and storage of carbon in plants

Sugars perform two vital functions in plants: as compatible solutes protecting the cell against osmotic stress and as mobile source of immediate and long-term energy requirement for growth and development. The two sugars that occur commonly in nature are sucrose and trehalose. Sucrose comprises one glucose and one fructose molecule; trehalose comprises two glucose molecules. Trehalose occurs in significant amounts in insects and fungi which greatly outnumber the plants. Surprisingly, in plants trehalose has been found in barely detectable amounts, if at all, raising the question `why did nature select sucrose instead of trehalose as the mobile energy source and as storage sugar for the plants'? Modelling revealed that when attached to the ribbon-shaped beta-1,4 glucan a trehalose molecule is shaped like a hook. This suggests that the beta-1,4 glucan chains with attached trehalose will fail to align to form inter-chain hydrogen bonds and coalesce into a cellulose microfibril, as a result of which in trehalose-accumulating plant cells, the cell wall will tend to become leaky. Thus in plants an evolutionary selection was made in favour of sucrose as the mobile energy source. Genetic engineering of plant cells for combating abiotic stresses through microbial trehalose-producing genes is fraught with risk of damage to plant cell walls.

The Behaviour of Two-Phase Flow of DNAPL and Water through a Fractured Rock under Confining Pressure

This study presents the characterization of DNAPL and water flow in a fracture under confining pressure. A comprehensive mathematical model and the conditions under which DNAPL will enter an initially water-saturated deforming rock fracture are discussed. A numerical model with which to predict the quantity of each phase in terms of their saturations in deforming rock joint is developed. The effect of varying confining stresses on the traverse time of DNAPL across a fractured aquitard is studied. The sensitivity analysis for physical and hydraulic properties like initial fracture apertures, fracture dips, equivalent fracture aperture and confining pressures are performed and discussed.

Geometrically Nonlinear Dynamics of Composite Four-Bar Mechanisms

This work intends to demonstrate the importance of geometrically nonlinear crosssectional analysis of certain composite beam-based four-bar mechanisms in predicting system dynamic characteristics. All component bars of the mechanism are made of fiber reinforced laminates and have thin rectangular cross-sections. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. We restrict ourselves to linear materials with small strains within each elastic body (beam). Each component of the mechanism is modeled as a beam based on geometrically nonlinear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and nonlinear 1-D analyses along the four beam reference curves. For thin rectangular cross-sections considered here, the 2-D cross-sectional nonlinearity is overwhelming. This can be perceived from the fact that such sections constitute a limiting case between thin-walled open and closed sections, thus inviting the nonlinear phenomena observed in both. The strong elastic couplings of anisotropic composite laminates complicate the model further. However, a powerful mathematical tool called the Variational Asymptotic Method (VAM) not only enables such a dimensional reduction, but also provides asymptotically correct analytical solutions to the nonlinear cross-sectional analysis. Such closed-form solutions are used here in conjunction with numerical techniques for the rest of the problem to predict multi-body dynamic responses, more quickly and accurately than would otherwise be possible. The analysis methodology can be viewed as a three-step procedure: First, the cross-sectional properties of each bar of the mechanism is determined analytically based on an asymptotic procedure, starting from Classical Laminated Shell Theory (CLST) and taking advantage of its thin strip geometry. Second, the dynamic response of the nonlinear, flexible fourbar mechanism is simulated by treating each bar as a 1-D beam, discretized using finite elements, and employing energy-preserving and -decaying time integration schemes for unconditional stability. Finally, local 3-D deformations and stresses in the entire system are recovered, based on the 1-D responses predicted in the previous step. With the model, tools and procedure in place, we shall attempt to identify and investigate a few problems where the cross-sectional nonlinearities are significant. This will be carried out by varying stacking sequences and material properties, and speculating on the dominating diagonal and coupling terms in the closed-form nonlinear beam stiffness matrix. Numerical examples will be presented and results from this analysis will be compared with those available in the literature, for linear cross-sectional analysis and isotropic materials as special cases.

Biomonitoring of Lotic habitats through Diatoms

Freshwater ecosystems vary in size and composition and contain a wide range of organisms which interact with each other and with the environment. These interactions are between organisms and the environment as nutrient cycling, biomass formation and transfer, maintenance of internal environment and interactions with the external environment. The range of organisms present in aquatic communities decides the generation and transfer function of biomass, which defines and characterises the system. These organisms have distinct roles as they occupy particular trophic levels, forming an interconnected system in a food chain. Availability of resources and competition would primarily determine the balance of individual species within the food web, which in turn influences the variety and proportions of the different organisms, with important implications for the overall functioning of the system. This dynamic and diverse relationship decides the physical, chemical and biological elements across spatial and temporal scales in the aquatic ecosystem, which can be recorded by regular inventorying and monitoring to maintain the integrity and conserve the ecosystem. Regular environmental monitoring, particularly water quality monitoring allows us to detect, assess and manage the overall impacts on the rivers. The appreciation of water quality is in constant flux. Water quality assessments derived through the biotic indices, i.e. assessments based on observations of the resident floral and faunal communities has gained importance in recent years. Biological evaluations provide a description of the water quality that is often not achievable from elemental analyses alone. A biological indicator (or bioindicator) is a taxon or taxa selected based on its sensitivity to a particular attribute, and then assessed to make inferences about that attribute. In other words, they are a substitute for directly measuring abiotic features or other biota. Bioindicators are evaluated through presence or absence, condition, relative abundance, reproductive success, community structure (i.e. composition and diversity), community function (i.e. trophic structure), or any combination thereof.Biological communities reflect the overall ecological integrity by integrating various stresses, thus providing a broad measure of their synergistic impacts. Aquatic communities, both plants and animals, integrate and reflect the effects of chemical and physical disturbances that occur over extended periods of time. Monitoring procedures based on the biota measure the health of a river and the ability of aquatic ecosystems to support life as opposed to simply characterising the chemical and physical components of a particular system. This is the central purpose of assessing the biological condition of aquatic communities of a river.Diatoms (Bacillariophyceae), blue green algae (Cyanophyceae), green algae (Chlorophyceae), and red algae (Rhodphyceae) are the main groups of algae in flowing water. These organisms are widely used as biological indicators of environmental health in the aquatic ecosystem because algae occupy the most basic level in the transfer of energy through natural aquatic systems. The distribution of algae in an aquatic ecosystem is directly related to the fundamental factors such as physical, chemical and biological constituents. Soft algae (all the algal groups except diatoms) have also been used as indicators of biological integrity, but they may have less efficiency than diatoms in this respect due to their highly variable morphology. The diatoms (Bacillariophyceae) comprise a ubiquitous, highly successful and distinctive group of unicellular algae with the most obvious distinguishing characteristic feature being siliceous cell walls (frustules). The photosynthetic organisms living within its photic zone are responsible for about one-half of global primary productivity. The most successful organisms are thought to be photosynthetic prokaryotes (cyanobacteria and prochlorophytes) and a class of eukaryotic unicellular algae known as diatoms. Diatoms are likely to have arisen around 240 million years ago following an endosymbiotic event between a red eukaryotic alga and a heterotrophic flagellate related to the Oomycetes.The importance of algae to riverine ecology is easily appreciated when one considers that they are primary producers that convert inorganic nutrients into biologically active organic compounds while providing physical habitat for other organisms. As primary producers, algae transform solar energy into food from which many invertebrates obtain their energy. Algae also transform inorganic nutrients, such as atmospheric nitrogen into organic forms such as ammonia and amino acids that can be used by other organisms. Algae stabilises the substrate and creates mats that form structural habitats for fish and invertebrates. Algae are a source of organic matter and provide habitat for other organisms such as non-photosynthetic bacteria, protists, invertebrates, and fish. Algae's crucial role in stream ecosystems and their excellent indicator properties make them an important component of environmental studies to assess the effects of human activities on stream health. Diatoms are used as biological indicators for a number of reasons: 1. They occur in all types of aquatic ecosystems. 2. They collectively show a broad range of tolerance along a gradient of aquatic productivity, individual species have specific water chemistry requirements. 3. They have one of the shortest generation times of all biological indicators (~2 weeks). They reproduce and respond rapidly to environmental change and provide early measures of both pollution impacts and habitat restoration. 4. It takes two to three weeks before changes are reflected to a measurable extent in the assemblage composition.

Size and temperature dependent stability and phase transformation in single-crystal zirconium nanowire

A novel size dependent FCC (face-centered-cubic) -> HCP (hexagonally-closed-pack) phase transformation and stability of an initial FCC zirconium nanowire are studied. FCC zirconium nanowires with cross-sectional dimensions < 20 are found unstable in nature, and they undergo a FCC -> HCP phase transformation, which is driven by tensile surface stress induced high internal compressive stresses. FCC nanowire with cross-sectional dimensions > 20 , in which surface stresses are not enough to drive the phase transformation, show meta-stability. In such a case, an external kinetic energy in the form of thermal heating is required to overcome the energy barrier and achieve FCC -> HCP phase transformation. The FCC-HCP transition pathway is also studied using Nudged Elastic Band (NEB) method, to further confirm the size dependent stability/metastability of Zr nanowires. We also show size dependent critical temperature, which is required for complete phase transformation of a metastable-FCC nanowire.