Pendant drop formation of shear-thinning and yield stress fluids

A volume-of-fluid numerical method is used to predict the dynamics of shear-thinning liquid drop formation in air from a circular orifice. The validity of the numerical calculation is confirmed for a Newtonian liquid by comparison with experimental measurements. For particular values of Weber number and Froude number, predictions show a more rapid pinch-off, and a reduced number of secondary droplets, with increasing shear-thinning. Also a minimum in the limiting drop length occurs for the smallest Weber number as the zero-shear viscosity is varied. At the highest viscosity, the drop length is reduced due to shear-thinning, whereas at lower viscosities there is little effect of shear-thinning. The evolution of predicted drop shape, drop thickness and length, and the configuration at pinch-off are discussed for shear-thinning drops. The evolution of a drop of Bingham yield stress liquid is also considered as a limiting case. In contrast to the shear-thinning cases, it exhibits a plug flow prior to necking, an almost step-change approach to pinch-off of a torpedo shaped drop following the onset of necking, and a much smaller neck length; no secondary drops are formed. The results demonstrate the potential of the numerical model as a design tool in tailoring the fluid rheology for controlling drop formation behaviour. (c) 2006 Elsevier Inc. All rights reserved.

Simulation of a complete reflected shock tunnel showing a vortex mechanism for flow contamination

Simulations of a complete reflected shock tunnel facility have been performed with the aim of providing a better understanding of the flow through these facilities. In particular, the analysis is focused on the premature contamination of the test flow with the driver gas. The axisymmetric simulations model the full geometry of the shock tunnel and incorporate an iris-based model of the primary diaphragm rupture mechanics, an ideal secondary diaphragm and account for turbulence in the shock tube boundary layer with the Baldwin-Lomax eddy viscosity model. Two operating conditions were examined: one resulting in an over-tailored mode of operation and the other resulting in approximately tailored operation. The accuracy of the simulations is assessed through comparison with experimental measurements of static pressure, pitot pressure and stagnation temperature. It is shown that the widely-accepted driver gas contamination mechanism in which driver gas 'jets' along the walls through action of the bifurcated foot of the reflected shock, does not directly transport the driver gas to the nozzle at these conditions. Instead, driver gas laden vortices are generated by the bifurcated reflected shock. These vortices prevent jetting of the driver gas along the walls and convect driver gas away from the shock tube wall and downstream into the nozzle. Additional vorticity generated by the interaction of the reflected shock and the contact surface enhances the process in the over-tailored case. However, the basic mechanism appears to operate in a similar way for both the over-tailored and the approximately tailored conditions.

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.

Metabolite mean transit times in the liver as predicted by various models of hepatic elimination

Predicted area under curve (AUC), mean transit time (MTT) and normalized variance (CV2) data have been compared for parent compound and generated metabolite following an impulse input into the liver, Models studied were the well-stirred (tank) model, tube model, a distributed tube model, dispersion model (Danckwerts and mixed boundary conditions) and tanks-in-series model. It is well known that discrimination between models for a parent solute is greatest when the parent solute is highly extracted by the liver. With the metabolite, greatest model differences for MTT and CV2 occur when parent solute is poorly extracted. In all cases the predictions of the distributed tube, dispersion, and tasks-in-series models are between the predictions of the rank and tube models. The dispersion model with mixed boundary conditions yields identical predictions to those for the distributed tube model (assuming an inverse gaussian distribution of tube transit times). The dispersion model with Danckwerts boundary conditions and the tanks-in series models give similar predictions to the dispersion (mixed boundary conditions) and the distributed tube. The normalized variance for parent compound is dependent upon hepatocyte permeability only within a distinct range of permeability values. This range is similar for each model but the order of magnitude predicted for normalized variance is model dependent. Only for a one-compartment system is the MIT for generated metabolite equal to the sum of MTTs for the parent compound and preformed metabolite administered as parent.

Kinetic analysis of vascular marker distribution in perfused rat livers after regeneration following partial hepatectomy

Background/Aims: Liver clearance models are based on information (or assumptions) on solute distribution kinetics within the microvasculatory system, The aim was to study albumin distribution kinetics in regenerated livers and in livers of normal adult rats, Methods: A novel mathematical model was used to evaluate the distribution space and the transit time dispersion of albumin in livers following regeneration after a two-thirds hepatectomy compared to livers of normal adult rats. Outflow curves of albumin measured after bolus injection in single-pass perfused rat livers were analyzed by correcting for the influence of catheters and fitting a long-tailed function to the data. Results: The curves were well described by the proposed model. The distribution volume and the transit time dispersion of albumin observed in the partial hepatectomy group were not significantly different from livers of normal adult rats. Conclusions: These findings suggest that the distribution space and the transit time dispersion of albumin (CV2) is relatively constant irrespective of the presence of rapid and extensive repair. This invariance of CV2 implies, as a first approximation, a similar degree of intrasinusoidal mixing, The finding that a sum of two (instead of one) inverse Gaussian densities is an appropriate empirical function to describe the outflow curve of vascular indicators has consequences for an improved prediction of hepatic solute extraction.

Solute transport by surface runoff from low-angle slopes: theory and application

The removal of chemicals in solution by overland how from agricultural land has the potential to be a significant source of chemical loss where chemicals are applied to the soil surface, as in zero tillage and surface-mulched farming systems. Currently, we lack detailed understanding of the transfer mechanism between the soil solution and overland flow, particularly under field conditions. A model of solute transfer from soil solution to overland flow was developed. The model is based on the hypothesis that a solute is initially distributed uniformly throughout the soil pore space in a thin layer at the soil surface. A fundamental assumption of the model is that at the time runoff commences, any solute at the soil surface that could be transported into the soil with the infiltrating water will already have been convected away from the area of potential exchange. Solute remaining at the soil surface is therefore not subject to further infiltration and may be approximated as a layer of tracer on a plane impermeable surface. The model fitted experimental data very well in all but one trial. The model in its present form focuses on the exchange of solute between the soil solution and surface water after the commencement of runoff. Future model development requires the relationship between the mass transfer parameters of the model and the time to runoff: to be defined. This would enable the model to be used for extrapolation beyond the specific experimental results of this study. The close agreement between experimental results and model simulations shows that the simple transfer equation proposed in this study has promise for estimating solute loss to surface runoff. Copyright (C) 2000 John Wiley & Sons, Ltd.

A model for adsorption of condensable vapors on nonporous materials

A new isotherm is proposed here for adsorption of condensable vapors and gases on nonporous materials having type II isotherms according to the Brunauer-Deming-Deming-Teller (BDDH) classification. The isotherm combines the recent molecular-continuum model in the multilayer region, with other widely used models for sub-monolayer coverage, some of which satisfy the requirement of a Henry's law asymptote. The model is successfully tested using isotherm data for nitrogen adsorption on nonporous silica, carbon and alumina, as well as benzene and hexane adsorption on nonporous carbon. Based on the data fits, out of several different alternative choices of model for the monolayer region, the Freundlich and the Unilan models are found to be the most successful when combined with the multilayer model to predict the whole isotherm. The hybrid model is consequently applicable over a wide pressure range. (C) 2000 Elsevier Science B.V. All rights reserved.

Scope for further analytical solutions for constant flux infiltration into a semi-infinite soil profile or redistribution in a finite soil profile

[1] We attempt to generate new solutions for the moisture content form of the one-dimensional Richards' [1931] equation using the Lisle [1992] equivalence mapping. This mapping is used as no more general set of transformations exists for mapping the one-dimensional Richards' equation into itself. Starting from a given solution, the mapping has the potential to generate an infinite number of new solutions for a series of nonlinear diffusivity and hydraulic conductivity functions. We first seek new analytical solutions satisfying Richards' equation subject to a constant flux surface boundary condition for a semi-infinite dry soil, starting with the Burgers model. The first iteration produces an existing solution, while subsequent iterations are shown to endlessly reproduce this same solution. Next, we briefly consider the problem of redistribution in a finite-length soil. In this case, Lisle's equivalence mapping is generalized to account for arbitrary initial conditions. As was the case for infiltration, however, it is found that new analytical solutions are not generated using the equivalence mapping, although existing solutions are recovered.

Modification-related porosity formation in hypoeutectic aluminum-silicon alloys

A series of aluminum-10 wt pet silicon castings were produced in sand molds to investigate the effect of modification on porosity formation. Modification with individual additions of either strontium or sodium resulted in a statistically significant increase in the level of porosity compared to unmodified castings. The increase in porosity with modification is due to the presence of numerous dispersed pores, which were absent in the unmodified casting. It is proposed that these pores form as a result of differences in size of the aluminum-silicon eutectic grains between unmodified and modified alloys. A geometric model is developed to show how the size of eutectic grains can influence the amount and distribution of porosity. Unlike traditional feeding-based models, which incorporate the effect: of microstructure on permeability, this model considers what happens when liquid is isolated from the riser and can no longer flow. This simple isolation model complements rather than contradicts existing theories on modification-related porosity formation and should be considered in the development of future comprehensive models.

Discrete and continuous models for dry masonry columns

The dynamic response of dry masonry columns can be approximated with finite-difference equations. Continuum models follow by replacing the difference quotients of the discrete model by corresponding differential expressions. The mathematically simplest of these models is a one-dimensional Cosserat theory. Within the presented homogenization context, the Cosserat theory is obtained by making ad hoc assumptions regarding the relative importance of certain terms in the differential expansions. The quality of approximation of the various theories is tested by comparison of the dispersion relations for bending waves with the dispersion relation of the discrete theory. All theories coincide with differences of less than 1% for wave-length-block-height (L/h) ratios bigger than 2 pi. The theory based on systematic differential approximation remains accurate up to L/h = 3 and then diverges rapidly. The Cosserat model becomes increasingly inaccurate for L/h < 2 pi. However, in contrast to the systematic approximation, the wave speed remains finite. In conclusion, considering its relative simplicity, the Cosserat model appears to be the natural starting point for the development of continuum models for blocky structures.

Structure-hepatic disposition relationships for cationic drugs in isolated perfused rat livers: Transmembrane exchange and cytoplasmic binding process

This work studied the structure-hepatic disposition relationships for cationic drugs of varying lipophilicity using a single-pass, in situ rat liver preparation. The lipophilicity among the cationic drugs studied in this work is in the following order: diltiazem. propranolol. labetalol. prazosin. antipyrine. atenolol. Parameters characterizing the hepatic distribution and elimination kinetics of the drugs were estimated using the multiple indicator dilution method. The kinetic model used to describe drug transport (the two-phase stochastic model) integrated cytoplasmic binding kinetics and belongs to the class of barrier-limited and space-distributed liver models. Hepatic extraction ratio (E) (0.30-0.92) increased with lipophilicity. The intracellular binding rate constant (k(on)) and the equilibrium amount ratios characterizing the slowly and rapidly equilibrating binding sites (K-S and K-R) increase with the lipophilicity of drug (k(on) : 0.05-0.35 s(-1); K-S : 0.61-16.67; K-R : 0.36-0.95), whereas the intracellular unbinding rate constant (k(off)) decreases with the lipophilicity of drug (0.081-0.021 s(-1)). The partition ratio of influx (k(in)) and efflux rate constant (k(out)), k(in)/k(out), increases with increasing pK(a) value of the drug [from 1.72 for antipyrine (pK(a) = 1.45) to 9.76 for propranolol (pK(a) = 9.45)], the differences in k(in/kout) for the different drugs mainly arising from ion trapping in the mitochondria and lysosomes. The value of intrinsic elimination clearance (CLint), permeation clearance (CLpT), and permeability-surface area product (PS) all increase with the lipophilicity of drug [CLint (ml . min(-1) . g(-1) of liver): 10.08-67.41; CLpT (ml . min(-1) . g(-1) of liver): 10.80-5.35; PS (ml . min(-1) . g(-1) of liver): 14.59-90.54]. It is concluded that cationic drug kinetics in the liver can be modeled using models that integrate the presence of cytoplasmic binding, a hepatocyte barrier, and a vascular transit density function.

A small disturbance in the strong vortex flow

A small disturbance in the axisymmetric, bathtub-like flow with strong vorticity is considered and the asymptotic representation of the solution is found. It is shown that if the disturbance is smaller than a certain critical scale, the conventional strong vortex approximation cannot describe the field generated by the disturbance not only in the vicinity of the disturbance but also at the distances much larger than the critical scale. (C) 2001 American Institute of Physics.

Surface diffusion and adsorption of hydrocarbons in activated carbon

Adsorption and diffusion in a porous media were studied theoretically and experimentally with a differential transient permeation method. The porous medium is allowed to equilibrate at some specified loading, and then the time trajectory of the permeation process is followed after a small difference between the pressures at the end faces of the porous medium is introduced at time t = 0 +. Such a trajectory us. time would contain adsorption and diffusion characteristics of the system. By studying this for various surface loadings, pore and surface diffusions can be fully characterized. Mathematical modeling of transient permeation is detailed for pure gases or vapors diffusion and adsorption in porous media. Effects of nonlinearity of adsorption isotherm, pressure, temperature and heat effects were considered in the model. Experimental data of diffusion and adsorption of propane, n-butane and n-hexane in activated carbon at different temperatures and loadings show the potential of this method as a useful tool to study adsorption kinetics in porous media. Validity of the model is best tested against the transient data where the kinetics curves exhibit sigmoidal shape, which is a result of the diffusion and adsorption rate during the initial stage of permeation.

Breeding dynamics of koalas in open woodlands

The spatial and breeding dynamics of koalas in sub-tropical woodlands at Blair Athol in central Queensland were intensively monitored between 1993 and 1998. Genetic relationships among koalas at this locality were studied to determine the breeding dynamics of males, including whether 'resident' or 'transient' males dominate as sires. Males and females were radio-collared and tracked periodically throughout each year of the study. Genotypes from hypervariable microsatellite loci identified uniquely all individuals and were used to analyse parentage as well as to determine population genetic parameters when compared with other regional localities. Koalas at Blair Athol comprise a population in genetic equilibrium. Gene diversity estimates show the population to be similar to other populations found in similar habitat in the region, and estimates of genetic differentiation among four regional populations showed that gene flow conforms to a model of isolation by distance. Analysis of parentage found that both resident and transient males sired about equal numbers of offspring. Familial DNA analysis revealed multiple paternities of successive young in this population. The conclusion from this study is that 'resident' status among males does not confer any advantage for parentage.