Bubble extinction in Hele-Shaw flow with surface tension and kinetic undercooling regularisation

We perform an analytic and numerical study of an inviscid contracting bubble in a two-dimensional Hele-Shaw cell, where the effects of both surface tension and kinetic undercooling on the moving bubble boundary are not neglected. In contrast to expanding bubbles, in which both boundary effects regularise the ill-posedness arising from the viscous (Saffman-Taylor) instability, we show that in contracting bubbles the two boundary effects are in competition, with surface tension stabilising the boundary, and kinetic undercooling destabilising it. This competition leads to interesting bifurcation behaviour in the asymptotic shape of the bubble in the limit it approaches extinction. In this limit, the boundary may tend to become either circular, or approach a line or "slit" of zero thickness, depending on the initial condition and the value of a nondimensional surface tension parameter. We show that over a critical range of surface tension values, both these asymptotic shapes are stable. In this regime there exists a third, unstable branch of limiting self-similar bubble shapes, with an asymptotic aspect ratio (dependent on the surface tension) between zero and one. We support our asymptotic analysis with a numerical scheme that utilises the applicability of complex variable theory to Hele-Shaw flow.

Measurement of anisotropies of the kinetic energy and anharmonicity in pyrolytic graphite by neutron Compton scattering

Neutron Compton scattering (NCS) measurements of the anisotropy of the momentum distribution and the mean Laplacian of the interatomic potential ∇2V have been performed using electron volt neutrons, with wave vector transfers between 24 Å−1 and 98 Å−1. The measured momentum distribution of the atoms displays significantly more anisotropy than a calculation using a model density of states. We have observed anisotropies in ∇2V for the first time. The results suggest that the atomic potential is harmonic within the graphite planes, but anharmonic for vibrations perpendicular to the planes.

Kinetic energy of He atoms in liquid He-4-He-3 mixtures

Deep inelastic neutron scattering measurements on liquid 3He-4He mixtures in the normal phase have been performed on the VESUVIO spectrometer at the ISIS pulsed neutron source at exchanged wave vectors of about q≃120.0Å-1. The neutron Compton profiles J(y) of the mixtures were measured along the T=1.96K isotherm for 3He concentrations, x, ranging from 0.1 to 1.0 at saturated vapor pressures. Values of kinetic energies 〈T〉 of 3He and 4He atoms as a function of x, 〈T〉(x), were extracted from the second moment of J(y). The present determinations of 〈T〉(x) confirm previous experimental findings for both isotopes and, in the case of 3He, a substantial disagreement with theory is found. In particular 〈T〉(x) for the 3He atoms is found to be independent of concentration yielding a value 〈T〉3(x=0.1)≃12K, much lower than the value suggested by the most recent theoretical estimates of approximately 19 K.

The effect of surface tension and kinetic undercooling on a radially-symmetric melting problem

The addition of surface tension to the classical Stefan problem for melting a sphere causes the solution to blow up at a finite time before complete melting takes place. This singular behaviour is characterised by the speed of the solid-melt interface and the flux of heat at the interface both becoming unbounded in the blow-up limit. In this paper, we use numerical simulation for a particular energy-conserving one-phase version of the problem to show that kinetic undercooling regularises this blow-up, so that the model with both surface tension and kinetic undercooling has solutions that are regular right up to complete melting. By examining the regime in which the dimensionless kinetic undercooling parameter is small, our results demonstrate how physically realistic solutions to this Stefan problem are consistent with observations of abrupt melting of nanoscaled particles.

Reliability of spatiotemporal and kinetic gait parameters determined by a new instrumented treadmill system

Background Despite the emerging use of treadmills integrated with pressure platforms as outcome tools in both clinical and research settings, published evidence regarding the measurement properties of these new systems is limited. This study evaluated the within– and between–day repeatability of spatial, temporal and vertical ground reaction forces measured by a treadmill system instrumented with a capacitance–based pressure platform. Methods Thirty three healthy adults (mean age, 21.5 ± 2.8 years; height, 168.4 ± 9.9 cm; and mass, 67.8 ± 18.6 kg), walked barefoot on a treadmill system (FDM–THM–S, Zebris Medical GmbH) on three separate occasions. For each testing session, participants set their preferred pace but were blinded to treadmill speed. Spatial (foot rotation, step width, stride and step length), temporal (stride and step times, duration of stance, swing and single and double support) and peak vertical ground reaction force variables were collected over a 30–second capture period, equating to an average of 52 ± 5 steps of steady–state walking. Testing was repeated one week following the initial trial and again, for a third time, 20 minutes later. Repeated measures ANOVAs within a generalized linear modelling framework were used to assess between–session differences in gait parameters. Agreement between gait parameters measured within the same day (session 2 and 3) and between days (session 1 and 2; 1 and 3) were evaluated using the 95% repeatability coefficient. Results There were statistically significant differences in the majority (14/16) of temporal, spatial and kinetic gait parameters over the three test sessions (P < .01). The minimum change that could be detected with 95% confidence ranged between 3% and 17% for temporal parameters, 14% and 33% for spatial parameters, and 4% and 20% for kinetic parameters between days. Within–day repeatability was similar to that observed between days. Temporal and kinetic gait parameters were typically more consistent than spatial parameters. The 95% repeatability coefficient for vertical force peaks ranged between ± 53 and ± 63 N. Conclusions The limits of agreement in spatial parameters and ground reaction forces for the treadmill system encompass previously reported changes with neuromuscular pathology and footwear interventions. These findings provide clinicians and researchers with an indication of the repeatability and sensitivity of the Zebris treadmill system to detect changes in common spatiotemporal gait parameters and vertical ground reaction forces.

An Artificial Neutral Network (ANN) model for predicting biodiesel kinetic viscosity as a function of temperature and chemical compositions

An Artificial Neural Network (ANN) is a computational modeling tool which has found extensive acceptance in many disciplines for modeling complex real world problems. An ANN can model problems through learning by example, rather than by fully understanding the detailed characteristics and physics of the system. In the present study, the accuracy and predictive power of an ANN was evaluated in predicting kinetic viscosity of biodiesels over a wide range of temperatures typically encountered in diesel engine operation. In this model, temperature and chemical composition of biodiesel were used as input variables. In order to obtain the necessary data for model development, the chemical composition and temperature dependent fuel properties of ten different types of biodiesels were measured experimentally using laboratory standard testing equipments following internationally recognized testing procedures. The Neural Networks Toolbox of MatLab R2012a software was used to train, validate and simulate the ANN model on a personal computer. The network architecture was optimised following a trial and error method to obtain the best prediction of the kinematic viscosity. The predictive performance of the model was determined by calculating the absolute fraction of variance (R2), root mean squared (RMS) and maximum average error percentage (MAEP) between predicted and experimental results. This study found that ANN is highly accurate in predicting the viscosity of biodiesel and demonstrates the ability of the ANN model to find a meaningful relationship between biodiesel chemical composition and fuel properties at different temperature levels. Therefore the model developed in this study can be a useful tool in accurately predict biodiesel fuel properties instead of undertaking costly and time consuming experimental tests.

Identification, functional expression and kinetic analysis of two primary amine oxidases from Rhodococcus opacus

Two native copper-containing amine oxidases (EC 1.4.3.21) have been isolated from Rhodococcus opacus and reveal phenotypic plasticity and catalytic activity with respect to structurally diverse natural and synthetic amines. Altering the amine growth substrate has enabled tailored and targeted oxidase upreg-ulation, which with subsequent treatment by precipitation, ion exchange and gel filtration, achieved a 90–150 fold purification. MALDI-TOF mass spectrometric and genomic analysis has indicated multiple gene activation with complex biodegradation pathways and regulatory mechanisms. Additional post-purification characterisation has drawn on the use of carbonyl reagent and chelating agent inhibitors. Michaelis–Menten kinetics for common aliphatic and aromatic amine substrates and several structural analogues demonstrated a broad specificity and high affinity with Michaelis constants (K M) ranging from 0.1 to 0.9 mM for C 1 –C 5 aliphatic mono-amines and <0.2 mM for a range of aromatic amines. Potential exploitation of the enzymatic versatility of the two isolated oxidases in biosensing and bioprocessing is discussed.

The salt dependence of DNA recognition by NF-kappaB p50 : a detailed kinetic analysis of the effects on affinityand specificity

The binding kinetics of NF-kappaB p50 to the Ig-kappaB site and to a DNA duplex with no specific binding site were determined under varying conditions of potassium chloride concentration using a surface plasmonresonance biosensor. Association and dissociation rate constants were measured enabling calculation of the dissociation constants. Under previously established high affinity buffer conditions, the k a for both sequences was in the order of 10(7) M-1s-1whilst the k d values varied 600-fold in a sequence-dependent manner between 10(-1) and 10(-4 )s-1, suggesting that the selectivity of p50 for different sequences is mediated primarily through sequence-dependent dissociation rates. The calculated K D value for the Ig-kappaB sequence was 16 pM, whilst the K D for the non-specific sequence was 9.9 nM. As the ionic strength increased to levels which are closer to that of the cellular environment, the binding of p50 to the non-specific sequence was abolished whilst the specific affinity dropped to nanomolar levels. From these results, a mechanism is proposed in which p50 binds specific sequences with high affinity whilst binding non-specific sequences weakly enough to allow efficient searching of the DNA.

Thermodynamical and plasma-driven kinetic growth of high-aspect-ratio nanostructures : effect of hydrogen termination

The results of studies on the growth of high-aspect nanostructures in low-temperature non-equilibrium plasmas of reactive gas mixtures with or without hydrogen are presented. The results suggest that the hydrogen in the reactive plasma strongly affects the length of the nanostructures. This phenomenon is explained in terms of selective hydrogen passivation of the lateral and top surfaces of the surface-supported nanostructures. The theoretical model describes the effect of the atomic hydrogen passivation on the nanostructure shape and predicts the critical hydrogen coverage of the lateral surfaces necessary to achieve the nanostructure growth with the pre-determined shape. Our results demonstrate that the use of a strongly non-equilibrium plasma is very effective in significantly improving the shape control of quasi-one-dimensional single-crystalline nanostructures.

A kinetic model for an argon plasma containing dust grains

A complex low-pressure argon discharge plasma containing dust grains is studied using a Boltzmann equation for the electrons and fluid equations for the ions. Local effects, such as the spatial distribution of the dust density and external electric field, are included, and their effect on the electron energy distribution, the electron and ion number densities, the electron temperature, and the dust charge are investigated. It is found that dust particles can strongly affect the plasma parameters by modifying the electron energy distribution, the electron temperature, the creation and loss of plasma particles, as well as the spatial distributions of the electrons and ions. In particular, for sufficiently high grain density and/or size, in a low-pressure argon glow discharge, the Druyvesteyn-like electron distribution in pristine plasmas can become nearly Maxwellian. Electron collection by the dust grains is the main cause for the change in the electron distribution function.

Corner and finger formation in Hele-Shaw flow with kinetic undercooling regularisation

We examine the effect of a kinetic undercooling condition on the evolution of a free boundary in Hele--Shaw flow, in both bubble and channel geometries. We present analytical and numerical evidence that the bubble boundary is unstable and may develop one or more corners in finite time, for both expansion and contraction cases. This loss of regularity is interesting because it occurs regardless of whether the less viscous fluid is displacing the more viscous fluid, or vice versa. We show that small contracting bubbles are described to leading order by a well-studied geometric flow rule. Exact solutions to this asymptotic problem continue past the corner formation until the bubble contracts to a point as a slit in the limit. Lastly, we consider the evolving boundary with kinetic undercooling in a Saffman--Taylor channel geometry. The boundary may either form corners in finite time, or evolve to a single long finger travelling at constant speed, depending on the strength of kinetic undercooling. We demonstrate these two different behaviours numerically. For the travelling finger, we present results of a numerical solution method similar to that used to demonstrate the selection of discrete fingers by surface tension. With kinetic undercooling, a continuum of corner-free travelling fingers exists for any finger width above a critical value, which goes to zero as the kinetic undercooling vanishes. We have not been able to compute the discrete family of analytic solutions, predicted by previous asymptotic analysis, because the numerical scheme cannot distinguish between solutions characterised by analytic fingers and those which are corner-free but non-analytic.