Precipitation In Small Systems--II. Mean Field Equations More Effective Than Population Balance

Part I (Manjunath et al., 1994, Chem. Engng Sci. 49, 1451-1463) of this paper showed that the random particle numbers and size distributions in precipitation processes in very small drops obtained by stochastic simulation techniques deviate substantially from the predictions of conventional population balance. The foregoing problem is considered in this paper in terms of a mean field approximation obtained by applying a first-order closure to an unclosed set of mean field equations presented in Part I. The mean field approximation consists of two mutually coupled partial differential equations featuring (i) the probability distribution for residual supersaturation and (ii) the mean number density of particles for each size and supersaturation from which all average properties and fluctuations can be calculated. The mean field equations have been solved by finite difference methods for (i) crystallization and (ii) precipitation of a metal hydroxide both occurring in a single drop of specified initial supersaturation. The results for the average number of particles, average residual supersaturation, the average size distribution, and fluctuations about the average values have been compared with those obtained by stochastic simulation techniques and by population balance. This comparison shows that the mean field predictions are substantially superior to those of population balance as judged by the close proximity of results from the former to those from stochastic simulations. The agreement is excellent for broad initial supersaturations at short times but deteriorates progressively at larger times. For steep initial supersaturation distributions, predictions of the mean field theory are not satisfactory thus calling for higher-order approximations. The merit of the mean field approximation over stochastic simulation lies in its potential to reduce expensive computation times involved in simulation. More effective computational techniques could not only enhance this advantage of the mean field approximation but also make it possible to use higher-order approximations eliminating the constraints under which the stochastic dynamics of the process can be predicted accurately.

Insurance contract disclosure – an uncertain balance

This article canvasses recent case law adjudicating the uneasy disclosure balance between the interests of the insurer and the insured in the process of transacting an insurance contract. It examines also the consequences of non-disclosure and misrepresentation and whether the avowed legislative intent — that the liability of the insurer in respect of a claim is to be reduced to the amount that would place the insurer in the position it would have been had the non-disclosure or misrepresentation not occurred — is being achieved in practice. As there is no doubt as to who bears the onus of proof as to non-disclosure or misrepresentation it is surprising that insurers continue to flounder in this regard in relation to underwriting guidelines and adherence to them. The article reviews recent case law in this context and stresses that an insurer wishing to preserve its capacity to avoid liability on the basis that it would not have entered into a contract at all had the true situation been known to it must maintain detailed underwriting guidelines supported by consistent adherence to those guidelines. Recent case law also emphasises that the insurer must provide clear and cogent admissible evidence from appropriate personnel and officers of the company to discharge its onus.

Vertical structure and horizontal gradients of aerosol extinction coefficients over coastal India inferred from airborne lidar measurements during the Integrated Campaign for Aerosol, Gases and Radiation Budget (ICARB) field campaign

Quantitative estimates of the vertical structure and the spatial gradients of aerosol extinction coefficients have been made from airborne lidar measurements across the coastline into offshore oceanic regions along the east and west coasts of India. The vertical structure revealed the presence of strong, elevated aerosol layers in the altitude region of similar to 2-4 km, well above the atmospheric boundary layer (ABL). Horizontal gradients also showed a vertical structure, being sharp with the e(-1) scaling distance (D-0H) as small as similar to 150 km in the well-mixed regions mostly under the influence of local source effects. Above the ABL, where local effects are subdued, the gradients were much shallower (similar to 600-800 km); nevertheless, they were steep compared to the value of similar to 1500-2500 km reported for columnar AOD during winter. The gradients of these elevated layers were steeper over the east coast of India than over the west coast. Near-simultaneous radio sonde (Vaisala, Inc., Finland) ascents made over the northern Bay of Bengal showed the presence of convectively unstable regions, first from surface to similar to 750-1000 m and the other extending from 1750 to 3000 m separated by a stable region in between. These can act as a conduit for the advection of aerosols and favor the transport of continental aerosols in the higher levels (> 2 km) into the oceans without entering the marine boundary layer below. Large spatial gradient in aerosol optical and hence radiative impacts between the coastal landmass and the adjacent oceans within a short distance of < 300 km (even at an altitude of 3 km) during summer and the premonsoon is of significance to the regional climate.

Axially homogeneous, zero mean flow buoyancy-driven turbulence in a vertical pipe

We report an experimental study of a new type of turbulent flow that is driven purely by buoyancy. The flow is due to an unstable density difference, created using brine and water, across the ends of a long (length/diameter = 9) vertical pipe. The Schmidt number Sc is 670, and the Rayleigh number (Ra) based on the density gradient and diameter is about 10(8). Under these conditions the convection is turbulent, and the time-averaged velocity at any point is `zero'. The Reynolds number based on the Taylor microscale, Re-lambda, is about 65. The pipe is long enough for there to be an axially homogeneous region, with a linear density gradient, about 6-7 diameters long in the midlength of the pipe. In the absence of a mean flow and, therefore, mean shear, turbulence is sustained just by buoyancy. The flow can be thus considered to be an axially homogeneous turbulent natural convection driven by a constant (unstable) density gradient. We characterize the flow using flow visualization and particle image velocimetry (PIV). Measurements show that the mean velocities and the Reynolds shear stresses are zero across the cross-section; the root mean squared (r.m.s.) of the vertical velocity is larger than those of the lateral velocities (by about one and half times at the pipe axis). We identify some features of the turbulent flow using velocity correlation maps and the probability density functions of velocities and velocity differences. The flow away from the wall, affected mainly by buoyancy, consists of vertically moving fluid masses continually colliding and interacting, while the flow near the wall appears similar to that in wall-bound shear-free turbulence. The turbulence is anisotropic, with the anisotropy increasing to large values as the wall is approached. A mixing length model with the diameter of the pipe as the length scale predicts well the scalings for velocity fluctuations and the flux. This model implies that the Nusselt number would scale as (RaSc1/2)-Sc-1/2, and the Reynolds number would scale as (RaSc-1/2)-Sc-1/2. The velocity and the flux measurements appear to be consistent with the Ra-1/2 scaling, although it must be pointed out that the Rayleigh number range was less than 10. The Schmidt number was not varied to check the Sc scaling. The fluxes and the Reynolds numbers obtained in the present configuration are Much higher compared to what would be obtained in Rayleigh-Benard (R-B) convection for similar density differences.

Critical Cation Balance In B-]Z Transition - Role Of Li+

The sodium salt of poly(dG-dC) is known to exhibit a B + Z transition in the presence of various cations and 60% alcohol. We here show that the lithium salt of poly(dG-dC) does not undergo B 4 Z transition in the presence of 60% alcohol since Li’ with its large hydration shell cannot stabilize the Z-form. On the other hand, high concentrations of Mg2* or micromolar concentrations of the cobalt hexamine complex which are known to stabilize the Z-form can compete with Li+ for charge neutraIization and hence bring about a B--t Z transition in the same polymer. From the model building studies the mode of action of the cobalt-hexamine complex in stabilizing the Z-form is postulated.

An overview of land application of pig effluent-P using soil P chemistry and mass balance calculations.

Attention is directed at land application of piggery effluent (containing urine, faeces, water, and wasted feed) as a potential source of water resource contamination with phosphorus (P). This paper summarises P-related properties of soil from 0-0.05 m depth at 11 piggery effluent application sites, in order to explore the impact that effluent application has had on the potential for run-off transport of P. The sites investigated were situated on Alfisol, Mollisol, Vertisol, and Spodosol soils in areas that received effluent for 1.5-30 years (estimated effluent-P applications of 100-310000 kg P/ha in total). Total (PT), bicarbonate extractable (PB), and soluble P forms were determined for the soil (0-0.05 m) at paired effluent and no-effluent sites, as well as texture, oxalate-extractable Fe and Al, organic carbon, and pH. All forms of soil P at 0-0.05 m depth increased with effluent application (PB at effluent sites was 1.7-15 times that at no-effluent sites) at 10 of the 11 sites. Increases in PB were strongly related to net P applications (regression analysis of log values for 7 sites with complete data sets: 82.6 % of variance accounted for, p <0.01). Effluent irrigation tended to increase the proportion of soil PT in dilute CaCl2-extractable forms (PTC: effluent average 2.0 %; no-effluent average 0.6%). The proportion of PTC in non-molybdate reactive forms (centrifuged supernatant) decreased (no-effluent average, 46.4 %; effluent average, 13.7 %). Anaerobic lagoon effluent did not reliably acidify soil, since no consistent relationship was observed for pH with effluent application. Soil organic carbon was increased in most of the effluent areas relative to the no-effluent areas. The four effluent areas where organic carbon was reduced had undergone intensive cultivation and cropping. Current effluent management at many of the piggeries failed to maximise the potential for waste P recapture. Ten of the case-study effluent application areas have received effluent-P in excess of crop uptake. While this may not represent a significant risk of leaching where sorption retains P, it has increased the risk of transport of P by run-off. Where such sites are close to surface water, run-off P loads should be managed.

Natural convection from a vertical cone in a porous medium due to the combined effects of heat and mass diffusion with non-uniform wall temperature/concentration or heat/mass flux and suction/injection

An analysis has been carried out to study the non-Darcy natural convention flow of Newtonian fluids on a vertical cone embedded in a saturated porous medium with power-law variation of the wall temperature/concentration or heat/mass flux and suction/injection with the streamwise distance x. Both non-similar and self-similar solutions have been obtained. The effects of non-Darcy parameter, ratio of the buoyancy forces due to mass and heat diffusion, variation of wall temperature/concentration or heat/mass flux and suction/injection on the Nusselt and Sherwood numbers have been studied.

Analysis of an internally mountable accelerometer balance system for use with non-isotropic models in shock tunnels

Knowledge of drag force is an important design parameter in aerodynamics. Measurement of aerodynamic forces at hypersonic speed is a challenge and usually ground test facilities like shock tunnels are used to carry out such tests. Accelerometer based force balances are commonly employed for measuring aerodynamic drag around bodies in hypersonic shock tunnels. In this study, we present an analysis of the effect of model material on the performance of an accelerometer balance used for measurement of drag in impulse facilities. From the experimental studies performed on models constructed out of Bakelite HYLEM and Aluminum, it is clear that the rigid body assumption does not hold good during the short testing duration available in shock tunnels. This is notwithstanding the fact that the rubber bush used for supporting the model allows unconstrained motion of the model during the short testing time available in the shock tunnel. The vibrations induced in the model on impact loading in the shock tunnel are damped out in metallic model, resulting in a smooth acceleration signal, while the signal become noisy and non-linear when we use non-isotropic materials like Bakelite HYLEM. This also implies that careful analysis and proper data reduction methodologies are necessary for measuring aerodynamic drag for non-metallic models in shock tunnels. The results from the drag measurements carried out using a 60 degrees half angle blunt cone is given in the present analysis.

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.

CFD Analysis of conjugate natural convection in a vertical annulus

Conjugate natural convection in a vertical annulus with a centrally located vertical heat generating rod is studied numerically. The governing equations are discretized on a staggered mesh and are solved using a pressure-correction algorithm. A parametric study is performed by varying the Grashof number, aspect ratio, and the solid-to-fluid thermal conductivity ratio over wide ranges with the Prandtl number fixed at 0.7. Results are presented for the variation of several quantities of interest such as the local Nusselt numbers on the inner and outer boundaries, the axial variation of the centerline and interface temperatures, maximum solid, average solid and average interface temperature variations with Grashof number, and the average Nusselt number variation for the inner and outer boundaries with Grashof number. The average Nusselt number from the conjugate analysis is found to be between the Nusselt numbers of the isothermal and the isoflux cases. The average Nusselt numbers on the inner and outer boundaries show an increasing trend with the Grashof number. Correlations are presented for the Nusselt number and the dimensionless temperatures of interest in terms of the parameters of the problem.

Vertical uplift capacity of two interfering horizontal anchors in sand using an upper bound limit analysis

The vertical uplift resistance of two interfering rigid rough strip anchors embedded horizontally in sand at shallow depths has been examined. The analysis is performed by using an upper bound theorem o limit analysis in combination with finite elements and linear programming. It is specified that both the anchors are loaded to failure simultaneously at the same magnitude of the failure load. For different clear spacing (S) between the anchors, the magnitude of the efficiency factor (xi(gamma)) is determined. On account of interference, the magnitude of xi(gamma) is found to reduce continuously with a decrease in the spacing between the anchors. The results from the numerical analysis were found to compare reasonably well with the available theoretical data from the literature.

Axial heat conduction effects in natural convection along a vertical cylinder

MANY TRANSPORprTo cesses occur in nature and in industrial applications in which the transfer of heat is governed by the process of natural convection. Natural convection arises in fluids when the temperature changes cause density variations leading to buoyancy forces. An excellent review of natural convection flows has been given by Ede [I]. Recently, Minkowycz and Sparrow [2, 31, Cebeci [4], and Aziz and Na [S] have studied the steady, laminar, incompressible, natural convection flow over a vertical cylinder using a local nonsimilarity method, a finite-difference scheme, and an improved perturbation method, respectively. However, they did not take into account the effect ofaxial heat conduction for small Prandtl number. It is known that the axial heat conductioneffect becomesimportant for low-Prandtl-number fluids such as a liquid metal.

Managing the grass-legume balance in Stylosanthes scabra cv. Seca pastures in central Queensland

The impacts of 4 grazing strategies (year-long grazing, summer grazing, winter grazing and winter grazing plus spring burning) on the grass:legume balance were studied between 2000 and 2006 in a pasture oversown with Stylosanthes scabra cv. Seca (Seca stylo) in central Queensland. Seasonal rainfall throughout the study was generally below average. Total pasture yields in autumn were higher in the 2 winter grazing than the 2 summer grazing treatments, largely reflecting the sampling time relative to when grazing occurred. There were few differences in Seca composition in autumn, although there was a clear trend for Seca composition to be reduced by winter grazing plus burning. Both the frequency of occurrence and plant density of Seca were higher under the 2 summer grazing treatments and there was also a trend for the density of juvenile plants (<5 cm height) to be higher in the 2 summer grazing treatments. Seca soil seed banks were generally low and were reduced in the winter grazing plus burning treatment in spring 2002. The frequency of the palatable perennial grass Pennisetum ciliaris (Biloela buffel grass) was reduced while that of the 'increaser' species Bothriochloa pertusa (Indian couch grass) and Stachytarpheta jamaicensis (snake weed) increased in the 2 summer grazing treatments compared with the 2 winter grazing treatments. Burning in spring increased soil loss in treatments grazed in winter. Differences in Seca frequency and density but not composition were explained by the 2 summer grazing treatments promoting 'gaps' in the pasture which were then colonised by Seca plants and other 'increaser' species. It was reasoned that, with time, mature Seca plants in the 2 winter grazing treatments would die so that Seca composition would eventually become higher under summer grazing regimes than under winter grazing. It was concluded that limiting grazing to particular seasons can alter legume:grass balance and that a time-frame of 5-8 years with average to good rainfall would be necessary to achieve large shifts in composition.