Numerical solution to the Saffman-Taylor finger problem with kinetic undercooling regularisation

The Saffman-Taylor finger problem is to predict the shape and,in particular, width of a finger of fluid travelling in a Hele-Shaw cell filled with a different, more viscous fluid. In experiments the width is dependent on the speed of propagation of the finger, tending to half the total cell width as the speed increases. To predict this result mathematically, nonlinear effects on the fluid interface must be considered; usually surface tension is included for this purpose. This makes the mathematical problem suffciently diffcult that asymptotic or numerical methods must be used. In this paper we adapt numerical methods used to solve the Saffman-Taylor finger problem with surface tension to instead include the effect of kinetic undercooling, a regularisation effect important in Stefan melting-freezing problems, for which Hele-Shaw flow serves as a leading order approximation when the specific heat of a substance is much smaller than its latent heat. We find the existence of a solution branch where the finger width tends to zero as the propagation speed increases, disagreeing with some aspects of the asymptotic analysis of the same problem. We also find a second solution branch, supporting the idea of a countably infinite number of branches as with the surface tension problem.

Vibration of L-shaped plates under a deterministic force or moment excitation : a case of statistical energy analysis application

Analytical and closed form solutions are presented in this paper for the vibration response of an L-shaped plate under a point force or a moment excitation. Inter-relationships between wave components of the source and the receiving plates are clearly defined. Explicit expressions are given for the quadratic quantities such as input power, energy flow and kinetic energy distributions of the L-shaped plate. Applications of statistical energy analysis (SEA) formulation in the prediction of the vibration response of finite coupled plate structures under a single deterministic forcing are examined and quantified. It is found that the SEA method can be employed to predict the frequency averaged vibration response and energy flow of coupled plate structures under a deterministic force or moment excitation when the structural system satisfies the following conditions: (1) the coupling loss factors of the coupled subsystems are known; (2) the source location is more than a quarter of the plate bending wavelength away from the source plate edges in the point force excitation case, or is more than a quarter wavelength away from the pair of source plate edges perpendicular to the moment axis in the moment excitation case due to the directional characteristic of moment excitations. SEA overestimates the response of the L-shaped plate when the source location is less than a quarter bending wavelength away from the respective plate edges owing to wave coherence effect at the plate boundary

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.

Locked nucleic acid (LNA) single nucleotide polymorphism (SNP) genotype analysis and validation using real-time PCR

With an increased emphasis on genotyping of single nucleotide polymorphisms (SNPs) in disease association studies, the genotyping platform of choice is constantly evolving. In addition, the development of more specific SNP assays and appropriate genotype validation applications is becoming increasingly critical to elucidate ambiguous genotypes. In this study, we have used SNP specific Locked Nucleic Acid (LNA) hybridization probes on a real-time PCR platform to genotype an association cohort and propose three criteria to address ambiguous genotypes. Based on the kinetic properties of PCR amplification, the three criteria address PCR amplification efficiency, the net fluorescent difference between maximal and minimal fluorescent signals and the beginning of the exponential growth phase of the reaction. Initially observed SNP allelic discrimination curves were confirmed by DNA sequencing (n = 50) and application of our three genotype criteria corroborated both sequencing and observed real-time PCR results. In addition, the tested Caucasian association cohort was in Hardy-Weinberg equilibrium and observed allele frequencies were very similar to two independently tested Caucasian association cohorts for the same tested SNP. We present here a novel approach to effectively determine ambiguous genotypes generated from a real-time PCR platform. Application of our three novel criteria provides an easy to use semi-automated genotype confirmation protocol.

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 investigation of goethite-seeded Al(OH)3 precipitation using in situ X-ray diffraction and Rietveld-based quantitative phase analysis

An in situ X-ray diffraction investigation of goethite-seeded Al(OH)3 precipitation from synthetic Bayer liquor at 343 K has been performed. The presence of iron oxides and oxyhydroxides in the Bayer process has implications for alumina reversion, which causes significant process losses through unwanted gibbsite precipitation, and is also relevant for the nucleation and growth of scale on mild steel process equipment. The gibbsite, bayerite and nordstrandite polymorphs of Al(OH)3 precipitated from the liquor; gibbsite appeared to precipitate first, with subsequent formation of bayerite and nordstrandite. A Rietveld-based approach to quantitative phase analysis was implemented for the determination of absolute phase abundances as a function of time, from which kinetic information for the formation of the Al(OH)3 phases was determined.

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.

Spectrophotometric analysis of phenols, which involves a hemin-graphene hybrid nanoparticles with peroxidase-like activity

Phenols are well known noxious compounds, which are often found in various water sources. A novel analytical method has been researched and developed based on the properties of hemin–graphene hybrid nanosheets (H–GNs). These nanosheets were synthesized using a wet-chemical method, and they have peroxidase-like activity. Also, in the presence of H2O2, the nanosheets are efficient catalysts for the oxidation of the substrate, 4-aminoantipine (4-AP), and the phenols. The products of such an oxidation reaction are the colored quinone-imines (benzodiazepines). Importantly, these products enabled the differentiation of the three common phenols – pyrocatechol, resorcin and hydroquinone, with the use of a novel, spectroscopic method, which was developed for the simultaneous determination of the above three analytes. This spectroscopic method produced linear calibrations for the pyrocatechol (0.4–4.0 mg L−1), resorcin (0.2–2.0 mg L−1) and hydroquinone (0.8–8.0 mg L−1) analytes. In addition, kinetic and spectral data, obtained from the formation of the colored benzodiazepines, were used to establish multi-variate calibrations for the prediction of the three phenol analytes found in various kinds of water; partial least squares (PLS), principal component regression (PCR) and artificial neural network (ANN) models were used and the PLS model performed best.

Simultaneous kinetic spectrometric determination of three flavonoid antioxidants in fruit with the aid of chemometrics

A simple, inexpensive and sensitive kinetic spectrophotometric method was developed for the simultaneous determination of three anti-carcinogenic flavonoids: catechin, quercetin and naringenin, in fruit samples. A yellow chelate product was produced in the presence neocuproine and Cu(I) – a reduction product of the reaction between the flavonoids with Cu(II), and this enabled the quantitative measurements with UV–vis spectrophotometry. The overlapping spectra obtained, were resolved with chemometrics calibration models, and the best performing method was the fast independent component analysis (fast-ICA/PCR (Principal component regression)); the limits of detection were 0.075, 0.057 and 0.063 mg L−1 for catechin, quercetin and naringenin, respectively. The novel method was found to outperform significantly the common HPLC procedure.

Thermochemical and kinetic studies on the effects of cobalt salicylate on the oxidative degradation of polystyrene

The effect of cobalt salicylate on the oxidative degradation and ignition of polystyrene has been studied. It was found that cobalt salicylate sensitizes both the degradation and ignition of polystyrene by facilitating electron-transfer processes in the propagation step. From thermochemical and kinetic studies it was found that the cobalt ion, owing to its ability to exist in variable valence states, promotes electron transfer in the propagation step of polymer degradation, increasing the rate of propagation and consequently the overall rate. Using solid-phase thermal ignition theory, an attempt has been made to explain the sensitization of ignition by the cobalt ion.

Flux balance analysis of biological systems: applications and challenges

Systems level modelling and simulations of biological processes are proving to be invaluable in obtaining a quantitative and dynamic perspective of various aspects of cellular function. In particular, constraint-based analyses of metabolic networks have gained considerable popularity for simulating cellular metabolism, of which flux balance analysis (FBA), is most widely used. Unlike mechanistic simulations that depend on accurate kinetic data, which are scarcely available, FBA is based on the principle of conservation of mass in a network, which utilizes the stoichiometric matrix and a biologically relevant objective function to identify optimal reaction flux distributions. FBA has been used to analyse genome-scale reconstructions of several organisms; it has also been used to analyse the effect of perturbations, such as gene deletions or drug inhibitions in silico. This article reviews the usefulness of FBA as a tool for gaining biological insights, advances in methodology enabling integration of regulatory information and thermodynamic constraints, and finally addresses the challenges that lie ahead. Various use scenarios and biological insights obtained from FBA, and applications in fields such metabolic engineering and drug target identification, are also discussed. Genome-scale constraint-based models have an immense potential for building and testing hypotheses, as well as to guide experimentation.

Blood pressure lowering effects of Lactobacillus helveticus fermented milk containing bioactive peptides Ile-Pro-Pro and Val-Pro-Pro; mechanistic, kinetic and clinical studies

The purpose of the present study was to evaluate the effects of Lactobacillus helveticus fermented milk (peptide milk) containing the casein-derived tripeptides Isoleucyl-prolyl-proline (Ile-Pro-Pro) and Valyl-prolyl-proline (Val-Pro-Pro) on blood pressure and vascular function in hypertensive subjects. The peptide milk lowered systolic and diastolic blood pressure in long-term use in hypertensive subjects when blood pressure was measured by using 24-hour ambulatory blood pressure measurement (ABPM). The blood pressure lowering effect was seen with the dose of 50 mg of tripeptides, and a tendency for lowering blood pressure was also observed when the dose was 5 mg. No adverse effects compared to the placebo group were reported or detected in laboratory analysis. The effect of the peptide milk on arterial stiffness was shown using two different methods, the ambulatory arterial stiffness index (AASI) and pulse wave analysis (PWA). According to the AASI, arterial stiffness was significantly reduced in the peptide milk group compared to the baseline level, but the difference was not significant compared to the placebo group. PWA showed that the peptide milk reduced arterial stiffness significantly compared to the placebo group. Endothelium-independent relaxation (nitroglycerin) and endothelium-dependent relaxation (salbutamol) did not differ between the groups. The blood pressure lowering mechanisms of the tripeptides and the kinetics of Ile-Pro-Pro were investigated using spontaneously hypertensive rats (SHR) and Sprague-Dawley rats. Previous studies have suggested that the blood pressure lowering effect of the tripeptides Ile-Pro-Pro and Val-Pro-Pro is based on angiotensin-converting enzyme inhibition, but the present findings did not agree with these previous studies. It was shown in SHR that calcium, potassium and magnesium may also have an important role in attenuating the development of hypertension as part of the peptide milk effect. In addition, the present study suggests indirectly that improved endothelial nitric oxide release capacity is not the mechanism by which peptide milk mediates its favourable circulatory effects. The kinetics of Ile-Pro-Pro were studied using adult Sprague-Dawley rats. The results showed that orally administered Ile-Pro-Pro is absorbed at least partly intact from the gastrointestinal tract. Radiolabelled Ile-Pro-Pro was distributed in different tissues and considerable radioactivity levels were found in tissues related to the renin-angiotensin system (RAS), adrenals, aorta and kidneys. Ile-Pro-Pro does not bind to plasma proteins, and therefore it is possible that its blood pressure lowering effect is mediated by free Ile-Pro-Pro. In conclusion, consumption of the peptide milk lowers blood pressure and reduces arterial stiffness in hypertensive subjects. Ile-Pro-Pro can be absorbed partly intact from the gastrointestinal tract and might accumulate in tissues related to the RAS. The precise blood pressure lowering mechanism of peptide milk remains to be studied.

Kinetic studies on thermal decomposition of polystyrene peroxide

Polystyrene peroxide has been synthesized and its decomposition has been studied by thermogravimetry and differential thermal analysis. Polystyrene peroxide has been found to decompose exothermically at about 110°C. The activation energy for the decomposition was estimated to be 30 kcal/mole both by the Jacobs and Kureishy method and by fitting the α versus time curves to the first-order kinetic equation. This suggests that the rate-controlling step in the decomposition of polystyrene peroxide is cleavage of the O---O bond.

A Comparative Study of Electrochemical Kinetic Parameters by the Potential Step Method. Electrode Reactions of CyDTA and EDTA Complexes of Cu(II) at DME

By using the same current-time (I-t) curves, electrochemical kinetic parameters are determined by two methods, (a) using the ratio of current at a given potential to the diffusion-controlled limiting current and (b) curve fitting method, for the reduction of Cu(II)–CyDTA complex. The analysis by the method (a) shows that the rate determining step involves only one electron although the overall reduction of the complex involves two electrons suggesting thereby the stepwise reduction of the complex. The nature of I-t curves suggests the adsorption of intermediate species at the electrode surface. Under these circumstances more reliable kinetic parameters can be obtained by the method (a) compared to that of (b). Similar observations are found in the case of reduction of Cu(II)–EDTA complex.

Factors influencing kinetic and equilibrium behaviour of sodium ion exchange with strong acid cation resin

This study reports an investigation of the ion exchange treatment of sodium chloride solutions in relation to use of resin technology for applications such as desalination of brackish water. In particular, a strong acid cation (SAC) resin (DOW Marathon C) was studied to determine its capacity for sodium uptake and to evaluate the fundamentals of the ion exchange process involved. Key questions to answer included: impact of resin identity; best models to simulate the kinetics and equilibrium exchange behaviour of sodium ions; difference between using linear least squares (LLS) and non-linear least squares (NLLS) methods for data interpretation; and, effect of changing the type of anion in solution which accompanied the sodium species. Kinetic studies suggested that the exchange process was best described by a pseudo first order rate expression based upon non-linear least squares analysis of the test data. Application of the Langmuir Vageler isotherm model was recommended as it allowed confirmation that experimental conditions were sufficient for maximum loading of sodium ions to occur. The Freundlich expression best fitted the equilibrium data when analysing the information by a NLLS approach. In contrast, LLS methods suggested that the Langmuir model was optimal for describing the equilibrium process. The Competitive Langmuir model which considered the stoichiometric nature of ion exchange process, estimated the maximum loading of sodium ions to be 64.7 g Na/kg resin. This latter value was comparable to sodium ion capacities for SAC resin published previously. Inherent discrepancies involved when using linearized versions of kinetic and isotherm equations were illustrated, and despite their widespread use, the value of this latter approach was questionable. The equilibrium behaviour of sodium ions form sodium fluoride solution revealed that the sodium ions were now more preferred by the resin compared to the situation with sodium chloride. The solution chemistry of hydrofluoric acid was suggested as promoting the affinity of the sodium ions to the resin.