Bose-Einstein condensate in a quartic potential:static and dynamic properties

In this paper, we present a theoretical study of a Bose-Einstein condensate of interacting bosons in a quartic trap in one, two, and three dimensions. Using Thomas-Fermi approximation, suitably complemented by numerical solutions of the Gross-Pitaevskii equation, we study the ground sate condensate density profiles, the chemical potential, the effects of cross-terms in the quartic potential, temporal evolution of various energy components of the condensate, and width oscillations of the condensate. Results obtained are compared with corresponding results for a bose condensate in a harmonic confinement.

Gold nanoparticles decorated with oligo(ethylene glycol) thiols:enhanced Hofmeister effects in colloid−protein mixtures

Oligo(ethylene glycol) (OEG) thiol self-assembled monolayer (SAM) decorated gold nanoparticles (AuNPs) have potential applications in bionanotechnology due to their unique property of preventing the nonspecific absorption of protein on the colloidal surface. For colloid-protein mixtures, a previous study (Zhang et al. J. Phys. Chem. A 2007, 111, 12229) has shown that the OEG SAM-coated AuNPs become unstable upon addition of proteins (BSA) above a critical concentration, c*. This has been explained as a depletion effect in the two-component system. Adding salt (NaCl) can reduce the value of c*; that is, reduce the stability of the mixture. In the present work, we study the influence of the nature of the added salt on the stability of this two-component colloid-protein system. It is shown that the addition of various salts does not change the stability of either protein or colloid in solution in the experimental conditions of this work, except that sodium sulfate can destabilize the colloidal solutions. In the binary mixtures, however, the stability of colloid-protein mixtures shows significant dependence on the nature of the salt: chaotropic salts (NaSCN, NaClO4, NaNO3, MgCl2) stabilize the system with increasing salt concentration, while kosmotropic salts (NaCl, Na2SO4, NH4Cl) lead to the aggregation of colloids with increasing salt concentration. These observations indicate that the Hofmeister effect can be enhanced in two-component systems; that is, the modification of the colloidal interface by ions changes significantly the effective depletive interaction via proteins. Real time SAXS measurements confirm in all cases that the aggregates are in an amorphous state.

Mixtures of probabilistic principal component analysers

Principal component analysis (PCA) is one of the most popular techniques for processing, compressing and visualising data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a combination of local linear PCA projections. However, conventional PCA does not correspond to a probability density, and so there is no unique way to combine PCA models. Previous attempts to formulate mixture models for PCA have therefore to some extent been ad hoc. In this paper, PCA is formulated within a maximum-likelihood framework, based on a specific form of Gaussian latent variable model. This leads to a well-defined mixture model for probabilistic principal component analysers, whose parameters can be determined using an EM algorithm. We discuss the advantages of this model in the context of clustering, density modelling and local dimensionality reduction, and we demonstrate its application to image compression and handwritten digit recognition.

The development of a modified dissolution method suitable for investigating powder mixtures

A novel dissolution method was developed, suitable for powder mixtures, based on the USP basket apparatus. The baskets were modified such that the powder mixtures were retained within the baskets and not dispersed, a potential difficulty that may arise when using conventional USP basket and paddle apparatus. The advantages of this method were that the components of the mixtures were maintained in close proximity, maximizing any drug:excipient interaction and leading to more linear dissolution profiles. Two weakly acidic model drugs, ibuprofen and acetaminophen, and a selection of pharmaceutical excipients, including potential dissolution-enhancing alkalizing agents, were chosen for investigation. Dissolution profiles were obtained for simple physical mixtures. The f1 fit factor values, calculated using pure drug as the reference material, demonstrated a trend in line with expectations, with several dissolution enhancers apparent for both drugs. Also, the dissolution rates were linear over substantial parts of the profiles. For both drugs, a rank order comparison between the f1 fit factor and calculated dissolution rate, obtained from the linear section of the dissolution profile, demonstrated a correlation using a significance level of P=0.05. The method was proven to be suitable for discriminating between the effects of excipients on the dissolution of the model drugs. The method design produced dissolution profiles where the dissolution rate was linear for a substantial time, allowing determination of the dissolution rate without mathematical transformation of the data. This method may be suitable as a preliminary excipient-screening tool in the drug formulation development process.

Mass transfer characteristics of two-aqueous-phase liquid-liquid mixtures

Mass transfer rates were studied using the falling drop method. Cibacron Blue 3 GA dye was the transferring solute from the salt phase to the PEG phase. Measurements were undertaken for several concentrations of the dye and the phase-forming solutes and with a range of different drop sizes, e.g. 2.8, 3.0 and 3.7 mm. The dye was observed to be present in the salt phase as finely dispersed solids but a model confirmed that the mass transfer process could still be described by an equation based upon the Whitman two-film model. The overall mass transfer coefficient increased with increasing concentration of the dye. The apparent mass transfer coefficient ranged from 1 x 10-5 to 2 x 10 -4 m/s. Further experiments suggested that mass transfer was enhanced at high concentration by several mechanisms. The dye was found to change the equilibrium composition of the two phases, leading to transfer of salt between the drop and continuous phases. It also lowered the interfacial tension (i.e. from 1.43 x 10-4 N/m for 0.01% w/w dye concentration to 1.07 x 10-4 N/m for 0.2% w/w dye concentration) between the two phases, which could have caused interfacial instabilities (Marangoni effects). The largest drops were deformable, which resulted in a significant increase in the mass transfer rate. Drop size distribution and Sauter mean drop diameter were studied on-line in a 1 litre agitated vessel using a laser diffraction technique. The effects of phase concentration, dispersed phase hold-up and impeller speed were investigated for the salt-PEG system. An increase in agitation speed in the range 300 rpm to 1000 rpm caused a decrease in mean drop diameter, e.g. from 50 m to 15 m. A characteristic bimodal drop size distribution was established within a very short time. An increase in agitation rate caused a shift of the larger drop size peak to a smaller size.

Continous annular chromatography for the separation of carbohydrate mixtures

The continuous separation of beet molasses resulting in a sucrose rich product and a non-sugar waste product was carried out using a rotating annular chromatograph. The annulus was 12 mm wide and 1.4 m long and was packed with a sodium charged 5.5% cross-linked polystyrene ion exchange resin. Separation was achieved by the simultaneous mechanisms of ion exclusion, size exclusion and partition chromatography. The entire packed bed was slowly rotated while beet molasses was fed continuously through a stationary feed nozzle to the top of the bed. Each molasses constituent having a different relative affinity for the packing and the deionised water mobile phase describes a characteristic helical path as it progresses from the stationary feed point to the bottom of the rotating bed. Each solute then elutes from the annulus at a different angular distance from the feed and separation of the multicomponent mixture is thereby achieved. When a 35% w/w sucrose beet molasses feed was used the throughput achievable was 45.1 kg sucrose m~3 resin h"1. In addition to beet molasses separation other carbohydrate mixtures were separated. In particular the separation of glucose and fructose by Ligand exchange chromatography on a calcium charged ion exchange bed was carried out. The effects of flowrates, concentration, rotation rate, temperature and particle size on resolution and dilution of constituents in the mixtures to be separated were studied. A small test rig was designed and built to determine the cause of liquid maldistribution around the annulus. The problem was caused by the porous bed support media becoming clogged with fines being introduced by eluent flows and off the resin. An outer ring was constructed to house the bed support which could be quickly replaced with the onset of maldistribution. The computer simulation of the operation of the rotating annular chromatograph has been carried out successfully.

Biosynthesis and separation of dextran fructose mixtures in a chromatographic reactor

A literature review of work carried out on batch and continuous chromatographic biochemical reactor-separators has been made. The major part of this work has involved the development of a batch chromatographic reactor-separator for the production of dextran and fructose by the enzymatic action of the enzyme dextransucrase on sucrose. In this reactor, simultaneous reaction and separation occurs thus reducing downstream processing and isolation of products as compared to the existing industrial process. The chromatographic reactor consisted of a glass column packed with a stationary phase consisting of cross linked polysytrene resin in the calcium form. The mobile phase consisted of diluted dextransucrase in deionised water. Initial experiments were carried out on a reactor separtor which had an internal diameter of 0.97cm and length of 1.5m. To study the effect of scale up the reactor diameter was doubled to 1.94cm and length increased to 1.75m. The results have shown that the chromatographic reactor uses more enzyme than a conventional batch reactor for a given conversion of sucrose and that an increase in void volume results in higher conversions of sucrose. A comparison of the molecular weight distribution of dextran produced by the chromatographic reactor was made with that from a conventional batch reactor. The results have shown that the chromatographic reactor produces 30% more dextran of molecular weight greater than 150,000 daltons at 20% w/v sucrose concentration than conventional reactors. This is because some of the fructose molecules are prevented as acting as acceptors in the chromatographic reactor due to their removal from the reaction zone. In the conventional reactor this is not possible and therefore a greater proportion of low molecular weight dextran is produced which does not have much clinical use. A theoretical model was developed to describe the behaviour of the reactor separator and this model was simulated using a computer. The simulation predictions showed good agreement with experimental results at high eluent flowrates and low conversions.

The chromatographic separation of carbohydrate mixtures

The separation performance of a semicontinuous counter-current chromatographic refiner (SCCR7), consisting of twelve 5.4 cm id x 75cm long columns packed with calcium charged cross-linked polysytrene resin (KORELA VO7C), was optimised. An industrial barley syrup was used containing 42% fructose, 52% glucose and 6% maltose and oligosaccharides. The effects of temperature, flow rates and concentration on the distribution coefficients were evaluated and quantified by deriving general relationships. The effects of flow rates, feed composition and concentration on the separation performance of the SCCR7 were identified and general relationships between them and the switch time, which was found to be the controlling parameter, were developed. Fructose rich (FRP) and glucose rich (GRP) product purities of 99.9% were obtained at 18.6% w/v feed concentrations. When a 66% w/v feed concentration was used and product splitting technique was employed, the throughput was 32.1 kg sugar solids/m3 resin/hr. The GRP contained less than 4.5% fructose, the FRP was over 95% pure, and the respective concentrations were 22.56 and 11.29% w/v. Over 94% of the glucose and 95.78% of the fructose in the feed were recovered in the GRP and FRP respectively. By recycling the dilute product split fractions, the GRP and FRP concentrations were increased to 25.4 and 12.96% w/v; the FRP was 90.2% pure and the GRP contained 6.69% w/v fructose. A theoretical link between batch and semicontinuous chromatographic equipments has been determined. A computer simulation was developed predicting successfully the purging concentration profiles at `pseudo-equilibrium', and also certain system design parameters. An important further aspect of the work has been to study the behaviour of chromatographic bioreactor-separators. Such batch systems of 5.4cm id and lengths varying between 30 and 230cm, were used to investigate the effect of scaling up on the conversion of sucrose into dextran and fructose in the presence of the dextransucrase enzyme. Conversions of over 80% were achieved at 4 hr sucrose residence times. The crude dextransucrase was purified using centrifugation, ultrafiltration and cross-flow microfiltration techniques. Better enzyme stability was obtained by first separating the non-solid impurities using cross-flow microfiltration, and then removing the cells from the enzyme immediately before use by continuous centrifugation.

The adsorptive separation of aromatic hydrocarbon mixtures

A detailed study has been made of the feasibility of adsorptive purification of slack waxes from traces of aromatic compounds using type 13X molecular sieves to achieve 0.01% aromatics in the product. The limited literature relating to the adsorption of high molecular weight aromatic compounds by zeolites was reviewed. Equilibrium isotherms were determined for typical individual aromatic compounds. Lower molecular weight, or more compact, molecules were preferentially adsorbed and the number of molecules captured by one unit cell decreased with increasing molecular weight of the adsorbate. An increase in adsorption temperature resulted in a decrease in the adsorption value. The isosteric heat of adsorption of differnt types of aromatic compounds was determined from pairs of isotherms at 303 K to 343 K at specific coverages. The lowest heats of adsorption were for dodecylbenzene and phenanthrene. Kinetics of adsorption were studied for different aromatic compounds. The diffusivity decreased significantly when a long alkyl chain was attached to the benzene ring e.g. in dodecylbenzene; molecules with small cross-sectional diameter e.g. cumene were adsorbed most rapidly. The sorption rate increased with temperature. Apparent activation energies increased with increasing polarity. In a study of the dynamic adsorption of selected aromatic compounds from binary solutions in isooctane or n-alkanes, naphthalene exhibited the best dynamic properties followed by dibenzothiophene and finally dodecylbenzene. The dynamic adsorption of naphthalene from different n-alkane solvents increased with a decrease in solvent molecular weight. A tentative mathematical approach is proposed for the prediction of dynamic breakthrough curves from equilibrium isotherms and kinetic data. The dynamic properties of liquid phase adsorption of aromatics from slack waxes were studied at different temperatures and concentrations. The optimum operating temperature was 543 K. The best dynamic performance was achieved with feeds of low aromatic content. The studies with individual aromatic compounds demonstrated the affinity of type NaX molecular sieves to adsorb aromatics in the concentration range 3% - 5% . Wax purification by adsorption was considered promising and extension of the experimental programme was recommended.