Dissolution of a solid sphere in an unbounded, stagnant liquid

An exact analytical solution is obtained for the transient dissolution of solid spheres in a diffusion-controlled environment. This result provides a useful reference point for drug testing in humans. The dimensionless solution is expressed in terms of a single parameter, which accounts for solubility, bulk flow, and stagnant fluid composition. A simple, explicit and exact expression was found to predict time-to-complete dissolution (TCD). An approximate solution was also found which tracks the exact case for low solubility conditions.

Entanglement in a simple quantum phase transition

What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems that can be solved. An example of such a system is the one-dimensional infinite-lattice anisotropic XY model. This model is exactly solvable using the Jordan-Wigner transform, and it is possible to calculate the two-site reduced density matrix for all pairs of sites. Using the two-site density matrix, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. We also study the entanglement in the transverse Ising model, a special case of the XY model, which exhibits a quantum phase transition. It is found that the next-nearest-neighbor entanglement (though not the nearest-neighbor entanglement) is a maximum at the critical point. Furthermore, we show that the critical point in the transverse Ising model corresponds to a transition in the behavior of the entanglement between a single site and the remainder of the lattice.

Comparison of experimental and numerical studies of ionizing flow over a cylinder

Comparisons are made between experimental measurements and numerical simulations of ionizing flows generated in a superorbital facility. Nitrogen, with a freestream velocity of around 10 km/s, was passed over a cylindrical model, and images were recorded using two-wavelength holographic interferometry. The resulting density, electron concentration, and temperature maps were compared with numerical simulations from the Langley Research Center aerothermodynamic upwind relaxation algorithm. The results showed generally good agreement in shock location and density distributions. Some discrepancies were observed for the electron concentration, possibly, because simulations were of a two-dimensional flow, whereas the experiments were likely to have small three-dimensional effects.

Enhanced flow visualisation using near-resonant holographic interferometry

Holographic interferometry measurements have been performed on high-speed, high-temperature gas flows with a laser output tuned near a resonant sodium transition. The technique allows the detection and quantification of the sodium concentration in the flow. By controlling the laser detuning and seeded sodium concentration, we performed flow visualization in low-density flows that are not normally detectable with standard interferometry. The technique was also successfully used to estimate the temperature in the boundary layer of the flow over a flat plate.

Turbulence in Small Sub-Tropical Estuary with Semi-Diurnal Tides

In natural estuaries, contaminant transport is driven by the turbulent momentum mixing. The predictions of scalar dispersion can rarely be predicted accurately because of a lack of fundamental understanding of the turbulence structure in estuaries. Herein detailed turbulence field measurements were conducted at high frequency and continuously for up to 50 hours per investigation in a small subtropical estuary with semi-diurnal tides. Acoustic Doppler velocimetry was deemed the most appropriate measurement technique for such small estuarine systems with shallow water depths (less than 0.5 m at low tides), and a thorough post-processing technique was applied. The estuarine flow is always a fluctuating process. The bulk flow parameters fluctuated with periods comparable to tidal cycles and other large-scale processes. But turbulence properties depended upon the instantaneous local flow properties. They were little affected by the flow history, but their structure and temporal variability were influenced by a variety of mechanisms. This resulted in behaviour which deviated from that for equilibrium turbulent boundary layer induced by velocity shear only. A striking feature of the data sets is the large fluctuations in all turbulence characteristics during the tidal cycle. This feature was rarely documented, but an important difference between the data sets used in this study from earlier reported measurements is that the present data were collected continuously at high frequency during relatively long periods. The findings bring new lights in the fluctuating nature of momentum exchange coefficients and integral time and length scales. These turbulent properties should not be assumed constant.

Turbulence in Hydraulic Jumps: Experimental Measurements

A hydraulic jump is the transition from a supercritical open channel flow to a subcritical regime. It is characterised by a highly turbulent flow with macro-scale vortices, some kinetic energy dissipation and a bubbly two-phase flow structure. New air-water flow measurements were performed in hydraulic jump flows for a range of inflow Froude numbers. The experiments were conducted in a large-size facility using two types of phase-detection intrusive probes: i.e., single-tip and double-tip conductivity probes. These were complemented by some measurements of free-surface fluctuations using ultrasonic displacement meters. The present study was focused on the turbulence characteristics of hydraulic jumps with partially-developed inflow conditions. The void fraction measurements showed the presence of an advective diffusion shear layer in which the void fractions profiles matched closely an analytical solution of the advective diffusion equation for air bubbles. The present results highlighted some influence of the inflow Froude number onto the air bubble entrainment process. At the largest Froude numbers, the advected air bubbles were more thoroughly dispersed vertically, and larger amount of air bubbles were detected in the turbulent shear layer. In the air-water mixing layer, the maximum void fraction and bubble count rate data showed some longitudinal decay function in the flow direction. Such trends were previously reported in the literature. The measurements of interfacial velocity and turbulence level distributions provided new information on the turbulent velocity field in the highly-aerated shear region. The present data suggested some longitudinal decay of the turbulence intensity. The velocity profiles tended to follow a wall jet flow pattern. The air–water turbulent time and length scales were deduced from some auto- and cross-correlation analyses based upon the method of CHANSON (2006,2007). The results provided the integral turbulent time and length scales of the eddy structures advecting the air bubbles in the developing shear layer. The experimental data showed that the auto-correlation time scale Txx was larger than the transverse cross-correlation time scale Txz. The integral turbulence length scale Lxz was a function of the inflow conditions, of the streamwise position (x-x1)/d1 and vertical elevation y/d1. Herein the dimensionless integral turbulent length scale Lxz/d1 was closely related to the inflow depth: i.e., Lxz/d1 = 0.2 to 0.8, with Lxz increasing towards the free-surface. The free-surface fluctuations measurements showed large turbulent fluctuations that reflected the dynamic, unsteady structure of the hydraulic jumps. A linear relationship was found between the normalized maximum free-surface fluctuation and the inflow Froude number.

Surface Waves and Roughness in Self-Aerated Supercritical Flow

In high-velocity open channel flows, free-surface aeration is commonly observed. The effects of surface waves on the air-water flow properties are tested herein. The study simulates the air-water flow past a fixed-location phase-detection probe by introducing random fluctuations of the flow depth. The present model yields results that are close to experimental observations in terms of void fraction, bubble count rate and bubble/droplet chord size distributions. The results show that the surface waves have relatively little impact on the void fraction profiles, but that the bubble count rate profiles and the distributions of bubble and chord sizes are affected by the presence of surface waves.

Non-Equilibrium Reaction Rates in the Macroscopic Chemistry Method for DSMC Calculations

The Direct Simulation Monte Carlo (DSMC) method is used to simulate the flow of rarefied gases. In the Macroscopic Chemistry Method (MCM) for DSMC, chemical reaction rates calculated from local macroscopic flow properties are enforced in each cell. Unlike the standard total collision energy (TCE) chemistry model for DSMC, the new method is not restricted to an Arrhenius form of the reaction rate coefficient, nor is it restricted to a collision cross-section which yields a simple power-law viscosity. For reaction rates of interest in aerospace applications, chemically reacting collisions are generally infrequent events and, as such, local equilibrium conditions are established before a significant number of chemical reactions occur. Hence, the reaction rates which have been used in MCM have been calculated from the reaction rate data which are expected to be correct only for conditions of thermal equilibrium. Here we consider artificially high reaction rates so that the fraction of reacting collisions is not small and propose a simple method of estimating the rates of chemical reactions which can be used in the Macroscopic Chemistry Method in both equilibrium and non-equilibrium conditions. Two tests are presented: (1) The dissociation rates under conditions of thermal non-equilibrium are determined from a zero-dimensional Monte-Carlo sampling procedure which simulates ‘intra-modal’ non-equilibrium; that is, equilibrium distributions in each of the translational, rotational and vibrational modes but with different temperatures for each mode; (2) The 2-D hypersonic flow of molecular oxygen over a vertical plate at Mach 30 is calculated. In both cases the new method produces results in close agreement with those given by the standard TCE model in the same highly nonequilibrium conditions. We conclude that the general method of estimating the non-equilibrium reaction rate is a simple means by which information contained within non-equilibrium distribution functions predicted by the DSMC method can be included in the Macroscopic Chemistry Method.

Satellite protection and drag reduction using a purging gas flow

We have used the DSMC method to determine contamination (impingement of atmospheric molecules) and the aerodynamic forces on a cold satellite when a protective “purge gas” is ejected from a sting protruding ahead of the satellite. Forward ejection of the purge gas provides the greatest protection for a given mass of purge gas and the aerodynamic drag can be significantly reduced, thus compensating for the backward reaction from the forward ejection. If the purge gas is ejected backward from the sting (towards the satellite) the ejection provides thrust and the net retarding force can be reduced to zero. Contamination can be reduced and the mass of purging gas is less than the mass of conventional rocket propellant required to maintain the orbit of an unprotected satellite.

Flow and axial dispersion simulation for traveling axisymmetric Taylor vortices

Numerical experiments using a finite difference method were carried out to determine the motion of axisymmetric Taylor vortices for narrow-gap Taylor vortex flow. When a pressure gradient is imposed on the flow the vortices are observed to move with an axial speed of 1.16 +/- 0.005 times the mean axial flow velocity. The method of Brenner was used to calculate the long-time axial spread of material in the flow. For flows where there is no pressure gradient, the axial dispersion scales with the square root of the molecular diffusion, in agreement with the results of Rosen-bluth et al. for high Peclet number dispersion in spatially periodic flows with a roll structure. When a pressure gradient is imposed the dispersion increases by an amount approximately equal to 6.5 x 10(-4) (W) over bar(2)d(2)/D-m, where (W) over bar is the average axial velocity in the annulus, analogous to Taylor dispersion for laminar flow in an empty tube.

Concordance between dispersal and mitochondrial gene flow: isolation by distance in a tropical teleost, Lates calcarifer (Australian barramundi)

Patterns of population subdivision and the relationship between gene flow and geographical distance in the tropical estuarine fish Lares calcarifer (Centropomidae) were investigated using mtDNA control region sequences. Sixty-three putative haplotypes were resolved from a total of 270 individuals from nine localities within three geographical regions spanning the north Australian coastline. Despite a continuous estuarine distribution throughout the sampled range, no haplotypes were shared among regions. However, within regions, common haplotypes were often shared among localities. Both sequence-based (average Phi(ST)=0.328) and haplotype-based (average Phi(ST)=0.182) population subdivision analyses indicated strong geographical structuring. Depending on the method of calculation, geographical distance explained either 79 per cent (sequence-based) or 23 per cent (haplotype-based) of the variation in mitochondrial gene flow. Such relationships suggest that genetic differentiation of L. calcarifer has been generated via isolation-by-distance, possibly in a stepping-stone fashion. This pattern of genetic structure is concordant with expectations based on the life history of L. calcarifer and direct studies of its dispersal patterns. Mitochondrial DNA variation, although generally in agreement with patterns of allozyme variation, detected population subdivision at smaller spatial scales. Our analysis of mtDNA variation in L. calcarifer confirms that population genetic models can detect population structure of not only evolutionary significance but also of demographic significance. Further, it demonstrates the power of inferring such structure from hypervariable markers, which correspond to small effective population sizes.