The Equilibrium Flux Method for the calculation of flows with non-equilbrium chemical reactions

The Equilibrium Flux Method [1] is a kinetic theory based finite volume method for calculating the flow of a compressible ideal gas. It is shown here that, in effect, the method solves the Euler equations with added pseudo-dissipative terms and that it is a natural upwinding scheme. The method can be easily modified so that the flow of a chemically reacting gas mixture can be calculated. Results from the method for a one-dimensional non-equilibrium reacting flow are shown to agree well with a conventional continuum solution. Results are also presented for the calculation of a plane two-dimensional flow, at hypersonic speed, of a dissociating gas around a blunt-nosed body.

Dimensionless spray flux in wet granulation: Monte-Carlo simulations and experimental validation

Dimensionless spray flux Ψa is a dimensionless group that characterises the three most important variables in liquid dispersion: flowrate, drop size and powder flux through the spray zone. In this paper, the Poisson distribution was used to generate analytical solutions for the proportion of nuclei formed from single drops (fsingle) and the fraction of the powder surface covered by drops (fcovered) as a function of Ψa. Monte-Carlo simulations were performed to simulate the spray zone and investigate how Ψa, fsingle and fcovered are related. The Monte-Carlo data was an excellent match with analytical solutions of fcovered and fsingle as a function of Ψa. At low Ψa, the proportion of the surface covered by drops (fcovered) was equal to Ψa. As Ψa increases, drop overlap becomes more dominant and the powder surface coverage levels off. The proportion of nuclei formed from single drops (fsingle) falls exponentially with increasing Ψa. In the ranges covered, these results were independent of drop size, number of drops, drop size distribution (mono-sized, bimodal and trimodal distributions), and the uniformity of the spray. Experimental data of nuclei size distributions as a function of spray flux were fitted to the analytical solution for fsingle by defining a cutsize for single drop nuclei. The fitted cutsizes followed the spray drop sizes suggesting that the method is robust and that the cutsize does indicate the transition size between single drop and agglomerate nuclei. This demonstrates that the nuclei distribution is determined by the dimensionless spray flux and the fraction of drop controlled nuclei can be calculated analytically in advance.

High-Frequency Turbulence and Sediment Flux Measurements in an Upper Estuarine Zone

In natural estuaries, the predictions of scalar dispersion are rarely predicted accurately because of a lack of fundamental understanding of the turbulence structure in estuaries. Herein detailed turbulence field measurements were conducted continuously at high frequency for 50 hours in the upper zone of a small subtropical estuary with semi-diurnal tides. Acoustic Doppler velocimetry was deemed the most appropriate measurement technique for such shallow water depths (less than 0.4 m at low tides), and a thorough post-processing technique was applied. In addition, some experiments were conducted in laboratory under controlled conditions using water and soil samples collected in the estuary to test the relationship between acoustic backscatter strength and suspended sediment load. A striking feature of the field data set was the large fluctuations in all turbulence characteristics during the tidal cycle, including the suspended sediment flux. This feature was rarely documented.

High-Frequency Suspended Sediment Flux Measurements in a Small Estuary

In small estuaries, the predictions of scalar dispersion can rarely be predicted accurately because of a lack of fundamental understanding of the turbulence structure. Herein detailed turbulence measurements and suspended sediment concentrations were conducted simultaneously and continuously at high-frequency for 50 hours per investigation in a small subtropical estuary with semi-diurnal tides. The data analyses provided an unique characterisation of the turbulent mixing processes and suspended sediment fluxes. The turbulence was neither homogeneous nor isotropic, and it was not a Gaussian process. The integral time scales for turbulence and suspended sediment concentration were about equal during flood tides, but differed significantly during ebb tides. The field experiences showed that the turbulence measurements must be conducted at high-frequency to characterise the small eddies and the viscous dissipation process, while a continuous sampling was necessary to characterise the time-variations of the instantaneous velocity field, Reynolds stress tensor and suspended sediment flux during the tidal cycles.

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.

A mathematical model for estimating the extent of solute- and water-flux heterogeneity in multiple sample percolation experiments

Multiple sampling is widely used in vadose zone percolation experiments to investigate the extent in which soil structure heterogeneities influence the spatial and temporal distributions of water and solutes. In this note, a simple, robust, mathematical model, based on the beta-statistical distribution, is proposed as a method of quantifying the magnitude of heterogeneity in such experiments. The model relies on fitting two parameters, alpha and zeta to the cumulative elution curves generated in multiple-sample percolation experiments. The model does not require knowledge of the soil structure. A homogeneous or uniform distribution of a solute and/or soil-water is indicated by alpha = zeta = 1, Using these parameters, a heterogeneity index (HI) is defined as root 3 times the ratio of the standard deviation and mean. Uniform or homogeneous flow of water or solutes is indicated by HI = 1 and heterogeneity is indicated by HI > 1. A large value for this index may indicate preferential flow. The heterogeneity index relies only on knowledge of the elution curves generated from multiple sample percolation experiments and is, therefore, easily calculated. The index may also be used to describe and compare the differences in solute and soil-water percolation from different experiments. The use of this index is discussed for several different leaching experiments. (C) 1999 Elsevier Science B.V. All rights reserved.

Modeling of hepatic elimination and organ distribution kinetics with the extended convection-dispersion model

The conventional convection-dispersion (also called axial dispersion) model is widely used to interrelate hepatic availability (F) and clearance (Cl) with the morphology and physiology of the liver and to predict effects such as changes in liver blood flow on F and Cl. An extended form of the convection-dispersion model has been developed to adequately describe the outflow concentration-time profiles for vascular markers at both short and long times after bolus injections into perfused livers. The model, based on flux concentration and a convolution of catheters and large vessels, assumes that solute elimination in hepatocytes follows either fast distribution into or radial diffusion in hepatocytes. The model includes a secondary vascular compartment, postulated to be interconnecting sinusoids. Analysis of the mean hepatic transit time (MTT) and normalized variance (CV2) of solutes with extraction showed that the discrepancy between the predictions of MTT and CV2 for the extended and conventional models are essentially identical irrespective of the magnitude of rate constants representing permeability, volume, and clearance parameters, providing that there is significant hepatic extraction. In conclusion, the application of a newly developed extended convection-dispersion model has shown that the unweighted conventional convection-dispersion model can be used to describe the disposition of extracted solutes and, in particular, to estimate hepatic availability and clearance in booth experimental and clinical situations.

Wave-induced seepage flux into anisotropic seabeds

Considerable effort has been devoted to quantifying the wave-induced soil response in a porous seabed in the last few decades. Most previous investigations have focused on the analysis of pore pressure and effective stresses within isotropic sediments, despite strong evidence of anisotropic soil behaviour reported in the literature. Furthermore, the seepage flux, which is important in the context of contaminant transport, has not been examined. In this paper, we focus on water wave-driven seepage in anisotropic marine sediments of finite thickness. The numerical results predict that the effects of hydraulic anisotropy and anisotropic soil behaviour on the wave-driven seepage in marine sediment are significant. Copyright (C) 2001 John Wiley & Sons, Ltd.

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.

The sit-up: complex kinematics and muscle activity in voluntary axial movement

This paper describes the kinematics and muscle activity associated with the standard sit-up, as a first step in the investigation of complex motor coordination. Eight normal human subjects lay on a force table and performed at least 15 sit-ups, with the arms across the chest and the legs straight and unconstrained. Several subjects also performed sit-ups with an additional weight added to the head. Support surface forces were recorded to calculate the location of the center of pressure and center of gravity; conventional motion analysis was used to measure segmental positions; and surface EMG was recorded from eight muscles. While the sit-up consists of two serial components, 'trunk curling' and 'footward pelvic rotation', it can be further subdivided into five phases, based on the kinematics. Phases I and II comprise trunk curling. Phase I consists of neck and upper trunk flexion, and phase II consists of lumbar trunk lifting. Phase II corresponds to the point of peak muscle contraction and maximum postural instability, the 'critical point' of the sit-up. Phases III-V comprise footward pelvic rotation. Phase III begins with pelvic rotation towards the feet. phase W with leg lowering, and phase V with contact between the legs and the support surface. The overall pattern of muscle activity was complex with times of EMG onset, peak activity, offset, and duration differing for different muscles. This complex pattern changed qualitatively from one phase to the next, suggesting that the roles of different muscles and, as a consequence, the overall form of coordination, change during the sit-up. (C) 2003 Elsevier Science Ltd. All rights reserved.

Axial Young's modulus prediction of single-walled carbon nanotube arrays with diameters from nanometer to meter scales

Based on a self-similar array model, we systematically investigated the axial Young's modulus (Y-axis) of single-walled carbon nanotube (SWNT) arrays with diameters from nanometer to meter scales by an analytical approach. The results show that the Y-axis of SWNT arrays decreases dramatically with the increases of their hierarchy number (s) and is not sensitive to the specific size and constitution when s is the same, and the specific Young's modulus Y-axis(s) is independent of the packing configuration of SWNTs. Our calculations also show that the Y-axis of SWNT arrays with diameters of several micrometers is close to that of commercial high performance carbon fibers (CFs), but the Y-axis(s) of SWNT arrays is much better than that of high performance CFs. (C) 2005 American Institute of Physics.

Transport in bidisperse adsorbents: Significance of the macroscopic adsorbate flux

Transport in bidisperse adsorbents is investigated here, while incorporating a two-dimensional model for adsorbate diffusion in the microparticles. The latter treatment permits consideration of the macropore concentration variation around the microparticle surface, and thereby predicts an adsorbate through-flux on the macroscopic coordinate. Such a through-flux has earlier been postulated in the literature, but with unrealistic mechanistic justification. The new model therefore resolves the existing ambiguity in this regard, and covers the entire spectrum of behaviour between microparticle and macropore diffusion control. Computational results show that if the macroscopic adsorbate flux, ignored in the conventional analysis, has a significant contribution to the total flux under macropore control conditions then it is always important even when the microparticle diffusion resistance is not negligible. The effect of various parameters such as relative microparticle size and isotherm heterogeneity on the uptake is also studied and discussed. (C) 1997 Elsevier Science Ltd.

Percutaneous absorption of sunscreen agents from liquid paraffin: Self-association of octyl salicylate and effects on skin flux

This study provides an investigation of the availability of octyl salicylate (OS), a common sunscreen agent, from liquid paraffin and the effect of OS on skin permeability. A model membrane system to isolate the vehicle effect from membrane permeability has been developed. Partitioning of OS between liquid paraffin and aqueous receptor phases was conducted. Partition coefficients increased with increase in OS concentration. A range of OS concentrations in liquid paraffin was diffused across human epidermis and synthetic membranes into 4% bovine serum albumin in phosphate-buffered saline and 50% ethanol. Absorption profiles of OS obtained from silicone and low-density polyethylene (LDPE) membranes were similar to each other but higher than for the high-density polyethylene [HDPE (3 times)] membrane and human epidermis (15 times). The steady state fluxes and apparent permeability coefficients (K-p') obtained from the diffusion studies showed the same trends with all membranes, except for the HDPE membrane which showed greater increase in flux and K-p' at concentrations above 30%. IR spectra showed that several bands of OS were shifted with concentrations, and the molecular models further suggested that the main contribution to the self-association is from non-1,4 van der Waals interactions.

A flux ratio theorem for multicomponent linear diffusion equations

Ussing [1] considered the steady flux of a single chemical component diffusing through a membrane under the influence of chemical potentials and derived from his linear model, an expression for the ratio of this flux and that of the complementary experiment in which the boundary conditions were interchanged. Here, an extension of Ussing's flux ratio theorem is obtained for n chemically interacting components governed by a linear system of diffusion-migration equations that may also incorporate linear temporary trapping reactions. The determinants of the output flux matrices for complementary experiments are shown to satisfy an Ussing flux ratio formula for steady state conditions of the same form as for the well-known one-component case. (C) 2000 Elsevier Science Ltd. All rights reserved.