Gravity-driven fingering simulations for a thin liquid film flowing down the outside of a vertical cylinder

A numerical study is presented to examine the fingering instability of a gravity-driven thin liquid film flowing down the outer wall of a vertical cylinder. The lubrication approximation is employed to derive an evolution equation for the height of the film, which is dependent on a single parameter, the dimensionless cylinder radius. This equation is identified as a special case of that which describes thin film flow down an inclined plane. Fully three-dimensional simulations of the film depict a fingering pattern at the advancing contact line. We find the number of fingers observed in our simulations to be in excellent agreement with experimental observations and a linear stability analysis reported recently by Smolka & SeGall (Phys Fluids 23, 092103 (2011)). As the radius of the cylinder decreases, the modes of perturbation have an increased growth rate, thus increasing cylinder curvature partially acts to encourage the contact line instability. In direct competition with this behaviour, a decrease in cylinder radius means that fewer fingers are able to form around the circumference of the cylinder. Indeed, for a sufficiently small radius, a transition is observed, at which point the contact line is stable to transverse perturbations of all wavenumbers. In this regime, free surface instabilities lead to the development of wave patterns in the axial direction, and the flow features become perfectly analogous to the two-dimensional flow of a thin film down an inverted plane as studied by Lin & Kondic (Phys Fluids 22, 052105 (2010)). Finally, we simulate the flow of a single drop down the outside of the cylinder. Our results show that for drops with low volume, the cylinder curvature has the effect of increasing drop speed and hence promoting the phenomenon of pearling. On the other hand, drops with much larger volume evolve to form single long rivulets with a similar shape to a finger formed in the aforementioned simulations.

Ethanol sensitivity of thermally evaporated nanostructured WO3 thin films doped and implanted with Fe

Ethanol sensing performance of gas sensors made of Fe doped and Fe implanted nanostructured WO3 thin films prepared by a thermal evaporation technique was investigated. Three different types of nanostructured thin films, namely, pure WO3 thin films, iron-doped WO3 thin films by co-evaporation and Fe-implanted WO3 thin films have been synthesized. All the thin films have a film thickness of 300 nm. The physical, chemical and electronic properties of these films have been optimized by annealing heat treatment at 300ºC and 400ºC for 2 hours in air. Various analytical techniques were employed to characterize these films. Atomic Force Microscopy and Transmission Electron Microscopy revealed a very small grain size of the order 5-10 nm in as-deposited WO3 films, and annealing at 300ºC or 400ºC did not result in any significant change in grain size. This study has demonstrated enhanced sensing properties of WO3 thin film sensors towards ethanol at lower operating temperature, which was achieved by optimizing the physical, chemical and electronic properties of the WO3 film through Fe doping and annealing.

Cell migration and proliferation on homogeneous and non-homogeneous domains : modelling on the scale of individuals and populations

Cell migration is a behaviour critical to many key biological effects, including wound healing, cancerous cell invasion and morphogenesis, the development of an organism from an embryo. However, given that each of these situations is distinctly different and cells are extremely complicated biological objects, interest lies in more basic experiments which seek to remove conflating factors and present a less complex environment within which cell migration can be experimentally examined. These include in vitro studies like the scratch assay or circle migration assay, and ex vivo studies like the colonisation of the hindgut by neural crest cells. The reduced complexity of these experiments also makes them much more enticing as problems to mathematically model, like done here. The primary goal of the mathematical models used in this thesis is to shed light on which cellular behaviours work to generate the travelling waves of invasion observed in these experiments, and to explore how variations in these behaviours can potentially predict differences in this invasive pattern which are experimentally observed when cell types or chemical environment are changed. Relevant literature has already identified the difficulty of distinguishing between these behaviours when using traditional mathematical biology techniques operating on a macroscopic scale, and so here a sophisticated individual-cell-level model, an extension of the Cellular Potts Model (CPM), is been constructed and used to model a scratch assay experiment. This model includes a novel mechanism for dealing with cell proliferations that allowed for the differing properties of quiescent and proliferative cells to be implemented into their behaviour. This model is considered both for its predictive power and used to make comparisons with the travelling waves which result in more traditional macroscopic simulations. These comparisons demonstrate a surprising amount of agreement between the two modelling frameworks, and suggest further novel modifications to the CPM that would allow it to better model cell migration. Considerations of the model’s behaviour are used to argue that the dominant effect governing cell migration (random motility or signal-driven taxis) likely depends on the sort of invasion demonstrated by cells, as easily seen by microscopic photography. Additionally, a scratch assay simulated on a non-homogeneous domain consisting of a ’fast’ and ’slow’ region is also used to further differentiate between these different potential cell motility behaviours. A heterogeneous domain is a novel situation which has not been considered mathematically in this context, nor has it been constructed experimentally to the best of the candidate’s knowledge. Thus this problem serves as a thought experiment used to test the conclusions arising from the simulations on homogeneous domains, and to suggest what might be observed should this non-homogeneous assay situation be experimentally realised. Non-intuitive cell invasion patterns are predicted for diffusely-invading cells which respond to a cell-consumed signal or nutrient, contrasted with rather expected behaviour in the case of random-motility-driven invasion. The potential experimental observation of these behaviours is demonstrated by the individual-cell-level model used in this thesis, which does agree with the PDE model in predicting these unexpected invasion patterns. In the interest of examining such a case of a non-homogeneous domain experimentally, some brief suggestion is made as to how this could be achieved.

Fractional models for the migration of biological cells in complex spatial domains

Travelling wave phenomena are observed in many biological applications. Mathematical theory of standard reaction-diffusion problems shows that simple partial differential equations exhibit travelling wave solutions with constant wavespeed and such models are used to describe, for example, waves of chemical concentrations, electrical signals, cell migration, waves of epidemics and population dynamics. However, as in the study of cell motion in complex spatial geometries, experimental data are often not consistent with constant wavespeed. Non-local spatial models have successfully been used to model anomalous diffusion and spatial heterogeneity in different physical contexts. In this paper, we develop a fractional model based on the Fisher-Kolmogoroff equation and analyse it for its wavespeed properties, attempting to relate the numerical results obtained from our simulations to experimental data describing enteric neural crest-derived cells migrating along the intact gut of mouse embryos. The model proposed essentially combines fractional and standard diffusion in different regions of the spatial domain and qualitatively reproduces the behaviour of neural crest-derived cells observed in the caecum and the hindgut of mouse embryos during in vivo experiments.

Numerical solutions for thin film flow down the outside and inside of a vertical cylinder

We consider a model for thin film flow down the outside and inside of a vertical cylinder. Our focus is to study the effect that the curvature of the cylinder has on the gravity-driven instability of the advancing contact line and to simulate the resulting fingering patterns that form due to this instability. The governing partial differential equation is fourth order with a nonlinear degenerate diffusion term that represents the stabilising effect of surface tension. We present numerical solutions obtained by implementing an efficient alternating direction implicit scheme. When compared to the problem of flow down a vertical plane, we find that increasing substrate curvature tends to increase the fingering instability for flow down the outside of the cylinder, whereas flow down the inside of the cylinder substrate curvature has the opposite effect. Further, we demonstrate the existence of nontrivial travelling wave solutions which describe fingering patterns that propagate down the inside of a cylinder at constant speed without changing form. These solutions are perfectly analogous to those found previously for thin film flow down an inclined plane.

Development of an ultra-thin fibroin membrane for RPE cell transplantation

Purpose: One of the challenges associated with cell-based therapies for repairing the retina is the development of suitable materials on which to grow and transplant retinal cells. Using the ARPE-19 cell line, we have previously demonstrated the feasibility of growing RPE-derived cells on membranes prepared from the silk protein fibroin. The present study was aimed at developing a porous, ultra-thin fibroin membrane that might better support development of apical-basal polarity in culture, and to extend this work to primary cultures of human RPE cells. Methods: Ultra-thin fibroin membranes were prepared using a highly polished casting table coated with Topas® (a cyclic olefin copolymer) and a 1:0.03 aqueous solution of fibroin and PEO (Mv 900 000 g/mol). Following drying, the membranes were water annealed to make them water-stable, washed in water to remove PEO, sterilised by treatment with 95% ethanol, and washed extensively in saline. Primary cultures containing human RPE cells were established from donor posterior eye cups and maintained in DMEM/F12 medium supplemented with 10% fetal bovine serum and antibiotics. First passage cultures were seeded onto fibroin membranes pre-coated with vitronectin and grown for 6 weeks in medium supplemented with 1% serum. Comparative cultures were established on porous 1.0 µm pore PET membrane (Millipore) and using ARPE-19 cells. Results: The fibroin membranes displayed an average thickness of 3 µm and contained numerous dimples/pore-like structures of up to 3-5 µm in diameter. The primary cultures predominantly contained pigmented epithelial cells, but mesenchymal cells (presumed fibroblasts) were also often present. Passaged cultures appeared to attach equally well to either fibroin or PET membranes. Over time cells on either material adopted a more cobblestoned morphology. Conclusions: Progress has been made towards developing a porous ultra-thin fibroin membrane that supports cultivation of RPE cells. Further studies are required to determine the degree of membrane permeability and RPE polarity.

Modelling the failure of thin layered mortar joints in masonry

This paper deals with the failure of high adhesive, low compressive strength, thin layered polymer mortar joints in masonry through a contact modelling in finite element framework. Failure due to combined shear, tensile and compressive stresses are considered through a constitutive damaging contact model that incorporates traction–separation as a function of displacement discontinuity. The modelling method is verified using single and multiple contact analyses of thin mortar layered masonry specimens under shear, tensile and compressive stresses and their combinations. Using this verified method, the failure of thin mortar layered masonry under a range of shear to tension ratios and shear to compression ratios has been examined. Finally, this model is applied to thin bed masonry wallettes for their behaviour under biaxial tension–tension and compression–tension loadings perpendicular and parallel to the bed joints.

Flexural and shear bond characteristics of thin layer polymer cement mortared concrete masonry

This paper presents an experimental investigation of the flexural and shear bond characteristics of thin layer polymer cement mortared concrete masonry. It is well known that the bond characteristics of masonry depend upon the mortar type, the techniques of dispersion of mortar and the surface texture of concrete blocks; there exists an abundance of literature on the conventional 10 mm thick cement mortared masonry bond; however, 1-4 mm thick polymer cement mortared masonry bond is not yet well researched. This paper reports a study on the examination of the effect of mortar compositions, dispersion methods and unit surface textures to the flexural and shear bond characteristics of thin layer mortared concrete masonry. A non-contact digital image correlation method was adopted for the measurement of strains at the unit-mortar interface in this research. All mortar joints have been carefully prepared to ensure achievement of the desired thin layer mortar thickness on average. The results exhibit that the bond strength of thin mortar layered concrete masonry with polymer cement mortar is higher than that of the conventional masonry; moreover the unit surface texture and the mortar dispersion methods are found to have significant influence on the flexural and shear bond characteristics. From the experimental results, a correlation between the flexural and the shear bond strengths has been determined and is presented in this paper.

Elastic buckling analysis of ideal thin-walled structures under combined loading using a finite strip method

The details of an application of the finite strip method to the elastic buckling analysis of thin-walled structures with various boundary conditions and subjected to single or combined loadings of longitudinal compression, transverse compression, bending and shear are presented. The presence of shear loading is accounted for by modifying the displacement functions which are commonly used in cases when shear is absent. A program based on the finite strip method was used to obtain the elastic buckling stress, buckling plot and buckling mode of thin-walled structures and some of these results are presented.

Graphene-based thin film supercapacitor with graphene oxide as dielectric spacer

Thin film supercapacitors are produced by using electrochemically exfoliated graphene (G) and wet-chemically produced graphene oxide (GO). Either G/GO/G stacked film or sole GO film are sandwiched by two Au films to make devices, where GO is the dielectric spacer. The addition of graphene film for charge storage can increase the capacitance about two times, compared to the simple Au electrode. It is found that the GO film has very high dielectric constant, accounting for the high capacitance of these devices. AC measurements reveal that the relative permittivity of GO is in the order of 104 within the frequency range of 0.1–70 Hz.

YBCO thin films on Yttria stabilized Zirconia and LaAlO3-growth and properties

Laser deposition was used to deposit YBaCuO thin films on Yttria-stabilized Zirconia substrates, at substrate holder temperatures of 710-765 °C. We observed a transition from singlecrystalline to polycrystalline growth at a temperature of ∼750 °C. All films were highly c-axis oriented and had critical temperatures between 89.5 and 92 K. In the twinned singlecrystalline films, the lowest measured microwave surface resistance was 0.37 mΩ at 4.2 K and 21.5 GHz, and the highest critical current 5×106 A/cm2 at 77 K. The polycrystalline films had up to a factor of 50 higher surface resistance and a factor of 10 lower critical current. A meander line resonator made of a film on a LaAlO3 substrate, showed a microwave surface resistance of 5μΩ at 4.2 K and 2.5 GHz. © 1991.

Microstructure of an artificial grain boundary weak link in an YBa2Cu3O(7-δ) thin film grown on a (100)(110), [001]-tilt Y-ZrO2 bicrystal

The microstructure of an artificial grain boundary in an YBa2Cu3O7-δ (YBCO) thin film grown on a (100)(110), [001]-tilt yttria-stabilized-zirconia (YSZ) bicrystal substrate has been studied using transmission electron microscopy (TEM). The orientation relationship between the YBCO film and the YSZ substrate was [001]YBCO∥[001]YSZ and [110]YBCO∥[100]YSZ for each half of the bicrystal film. However, the exact boundary geometry of the bicrystal substrate was not transferred to the film. The substrate boundary was straight while the film boundary was wavy. In several cases there was bending of the lattice confined within a distance of a few basal-plane lattice spacings from the boundary plane and microfaceting. No intergranular secondary phase was observed but about 25% of the boundary was covered by c-axis-tilted YBCO grains and a-axis-oriented grains, both of which were typically adjacent to CuO grains or surrounded by a thin Cu-rich amorphous layer.

Microstructure and properties of artificial grain boundaries in epitaxial YBA2Cu3O7-δ thin films grown on [001] tilt YZrO2 bicrystals

The microstructure of artificial grain boundaries in YBa2Cu3O7-δ (YBCO) thin films grown on [001] tilt YZrO2 (YSZ) bicrystal substrates has been characterized using transmission electron microscopy and atomic force microscopy. Despite a relatively straight morphology of the substrate boundaries, the film boundaries were wavy. The waviness was a result of the combined effects of grooving at the substrate boundaries prior to the film deposition and an island-growth mechanism for YBCO on YSZ substrates. The dihedral angle of the groove walls varied with the misorientation angle and depended on the symmetry of the substrate boundary. The amplitudes of the film boundary waviness compared well with the widths of the grooves. In addition, the grooves induced local bending of the YBCO lattice planes and additional tilt components perpendicular to the c-axis close to the film boundaries. © 1995.

Observation of exsolution textures within Ba-Cu-O-rich solidified melts of Y-Ba-Cu-O materials and their relationship to Y123 nucleation and texturing

Layers (about 60-100 μm thick) of almost pure BaCuO2 (BC1), as determined using X-ray diffractometry (XRD) and scanning electron microscopy (SEM), coat the surfaces of YBa2Cu3O7-x (Y123) samples partial melt processed using a single-zone vertical furnace. The actual Cu/Ba ratio of the BC1 phase is 1.2-1.3 as determined using energy dispersive X-ray spectrometry (EDS). The nominally BC1 phase displays an exsolution of BC1.5 or BC2 in the form of thin plates (about 50-100 nm thick) along {100}-type cleavage planes or facets. The exsolved phase also fills cracks within the BC1 layer that require it to be in a molten state at some stage of processing. The samples were influenced by Pt contamination from the supporting wire, which may have stabilised the BC1.5 phase. Many of the Y123 grains have the same morphology as the exsolution domains, and run nearly parallel to the thin plates of the exsolved phases, strongly indicating that Y123 nucleation took place at the interface between the BC1 and the BC1.5 or BC2 exsolved phases. The network of nearly parallel exsolved 'channels' provides a matrix and a mechanism through which a high degree of local texture can be initiated in the material.

A nanometre-scale non-periodic structural variation in high temperature superconducting ceramics and the implications for properties

Non-periodic structural variation has been found in the high Tc cuprates, YBa2Cu3O7-x and Hg0.67Pb0.33Ba2Ca2Cu 3O8+δ, by image analysis of high resolution transmission electron microscope (HRTEM) images. We use two methods for analysis of the HRTEM images. The first method is a means for measuring the bending of lattice fringes at twin planes. The second method is a low-pass filter technique which enhances information contained by diffuse-scattered electrons and reveals what appears to be an interference effect between domains of differing lattice parameter in the top and bottom of the thin foil. We believe that these methods of image analysis could be usefully applied to the many thousands of HRTEM images that have been collected by other workers in the high temperature superconductor field. This work provides direct structural evidence for phase separation in high Tc cuprates, and gives support to recent stripes models that have been proposed to explain various angle resolved photoelectron spectroscopy and nuclear magnetic resonance data. We believe that the structural variation is a response to an opening of an electronic solubility gap where holes are not uniformly distributed in the material but are confined to metallic stripes. Optimum doping may occur as a consequence of the diffuse boundaries between stripes which arise from spinodal decomposition. Theoretical ideas about the high Tc cuprates which treat the cuprates as homogeneous may need to be modified in order to take account of this type of structural variation.