PHASE-SPACE DIFFUSION EQUATIONS FOR SINGLE BROWNIAN PARTICLE MOTION NEAR SURFACES

In numerous physical processes involving the motion of micron and submicron sized particles near surfaces, such as the filtration of hydrosols and aerosols, the particle motion is the net result of the combined effects of fluid convection, external forces, particle inertia, Brownian particle motion, and particle-surface fluid dynamic interactions. The most general method of describing particle motion under the combined action of these effects is through the so-called Fokker-Planck equation. In the absence of particle-surface fluid dynamic interactions, the Fokker-Planck equation is well-known, and it has been applied in a general way to problems involving the adsorption or deposition of Brownian particles onto surfaces through a solution technique known as the Brownian dynamics simulation method.

In this study, the Fokker-Planck equation for Brownian particle motion near surfaces is generalized to include particle-surface fluid dynamic interactions. The Fokker-Planck equation is shown to follow from the Liouville equation for the Brownian particle and n-fluid molecules present in the system, thus, establishing a firm theoretical foundation for the Fokker-Planck equation and the various other phase-space diffusion equations that follow from it.

Based on diagonalization of the Fokker-Planck equation, its short-time behavior is also derived here which enables a generalization of the Brownian dynamics method for the study of particle motion near surfaces including fluid dynamic interactions. Additionally, a perturbation solution of the Fokker-Planck equation under the conditions of small, but finite particle Stokes number is also derived. These solutions are shown to agree with previously given representations of the Smoluchowski or convective-diffusion equation for Brownian particle motion near surfaces, as well as with inertial corrections to the Smoluchowski equation available in the literature. This latter equation is also generalized here to include particle-surface fluid dynamic interactions.     

Control policies for an industrial acetylene hydrogenation reactor

This paper addresses the problem of finding optimal operational policies for an acetylene reactor for day to day operation. A lumped parameter model based on four main reactions is developed and used to examine the effects of the reactor manipulated variables on key reaction parameters. An optimal and a sub-optimal operational policy which minimize the ethylene loss over time are formulated and the solution techniques are presented. The results indicate that the reactor model is in good agreement with industrial plant data. The performance of the optimal control policy is very similar to the performance of the sub-optimal control policy. However, the sub-optimal formulation, while retaining the dominant features of the optimal response, reduces the computational requirements. Finally, some issues concerning the real-time implementation of an advanced acetylene reactor control scheme are presented. These include the estimation of the optimum regeneration cycle, a recursive model update algorithm, the process optimizer and their overall coordination. A preliminary analysis of the benefits associated with the advanced control scheme suggests a considerable reduction in the yearly ethylene loss.     

Mass determination of the fatty acids released from tannin-stimulated rabbit alveolar macrophages

Previous studies with macrophages that had been prelabeled with [¹⁴C]arachidonic acid (20∶4) have shown that condensed tannin is a potent agonist for the release of arachidonic acid. However, it has not been demonstrated that the percentage release of [¹⁴C]20∶4 accurately reflects the metabolic activity of the endogenous 20∶4 pool. In order to measure the 20∶4 mass release relative to the total cellular 20∶4 pool, the free fatty acids of freshly isolated alveolar macrophages were derivatized with a fluorescent reagent, and then separated and quantified by high-performance liquid chromatography. The amounts of esterified fatty acids were measured by gas chromatography of the methyl esters. Free fatty acid levels were compared to those of the total esterified plus unesterified fatty acids to determine the actual percentage released of each fatty acid. Tannin-stimulated release of 20∶4 mass reflected that previously reported for the release of [¹⁴C]20∶4 label but at a slower rate and at a much lower percentage indicating that [¹⁴C]20∶4 had been incorporated into part of a more reactive pool. The specificity of the fatty acid release induced by tannin and β-1,3-glucan, a known agonist for 20∶4 release, was also examined. Both agonists promoted an increase in the levels of free 20∶4 and of other fatty acids. A comparison of the absolute increases of each of the fatty acids indicated that tannin caused a preferential increase in the mass of free 20∶4, whereas β-1,3-glucan evoked a selective increase in the mass of 16∶0. Deceased.     

An analysis of thermal warpage in injection molded flat parts due to unbalanced cooling

To illustrate the potential effect of unbalanced cooling on warpage of flat parts, a simplified two-part analysis is presented. First a computational model for amorphous polymers cooling in an injection molding cavity is presented. The simulation is a finite difference solution of the one-dimensional, transient heat conduction equation with constant material properties. Plastic and mold temperature profiles are calculated through the cooling cycle and the transients from cycle to cycle are included. Temperatures are predicted for both sides of the mold allowing asymmetrical cooling to be analyzed. The model is verified analytically and is in agreement with published data. Secondly, a simplified method of predicting the thermal warpage of a fiat part from calculated temperature profiles is discussed and illustrated. The relative effects on calculated part warpage of asymmetric mold geometry and cooling fluid temperature are predicted with this analysis method. The sensitivity of warpage to these design factors is illustrated for an example part.     

Activated gas plasma surface treatment of polymers for adhesive bonding

Polyethylene, polypropylene, poly(vinyl fluoride) (Tedlar), polystyrene, nylon 6, poly(ethylene terephthalate) (Mylar), polycarbonate, cellulose acetate butyrate, and a poly(oxymethylene) copolymer were treated with activated helium and with activated oxygen. Mechanical strengths of adhesive-bonded specimens prepared from treated and from untreated coupons were compared. Polyethylene (PE) and polypropylene (PP) showed the greatest increases in bond strength. Oxygen and helium were both effective with polyethylene, but polypropylene showed no improvement when treated with activated helium. The results with excited helium parallel the effects of ionizing radiation on these two polymers, as does the appearance of unsaturation bands in the infrared (965 cm^?1 in PE, and 887 and 910 cm^?1 in PP). Active nitrogen produced excellent bond strength with polyethylene but not with polypropylene. Of the remaining polymers examined, Tedlar, polystyrene, and nylon 6 showed the greatest improvement in bondability after treatment, and Mylar showed moderate improvement. Polycarbonate, cellulose acetate butyrate, and the poly(oxymethylene) copolymer gave approximately two-fold increases in lap-shear bond strength. In several cases, significant differences in response to time of treatment and type of excited gas were found.     

The synthesis and characterization of calcium aluminate monoiodide

The hydrated calcium aluminate AFt and AFm phases are known hosts for a wide variety of chemical species. This characteristic is beneficial to those using portland cement to solidify/encapsulate radioactive waste which more often than not contains a wide variety of elements. In order to investigate the potential of the calcium aluminate hydrates as host phases for selected ions, the following experiments were carried out. Bottle hydration studies (water/solid > 1) were used to investigate the suitability of the AFt and AFm phases as hosts for iodine, one of the more mobile radioactive waste elements. Trial compositions along the AFt and AFm joins in the systems 3CaO·Al₂O₃---CaSO₄---CaI₂---H₂O were investigated. No stable iodine end-member AFt phase was formed at room temperature. The end-member AFm phase, 3CaO·Al₂O₃·CaI₂·12H₂O, was synthesized and was designated monoiodide. Characterization was carried out using chemical analysis, scanning electron microscopy, x-ray diffraction (conventional and high temperature), thermogravimetric analysis and differential thermal analysis. Monoiodide was indexed as hexagonal and thus isostructural with previously described AFm phases. Monoiodide is stable to about 85°C. A loss of approximately four molecules of water occurs between 71° and 101°C. The lower hydrate, tentatively identified as 3CaO·Al₂O₃·CaI₂·8H₂O, is stable to approximately 300°C. The latter hydrate was observed to revert to the original hydrate on exposure to the relative humidity in the laboratory.     

A predicted three-dimensional structure of human cytochrome P450: implications for substrate specificity

A three-dimensional structure for human cytochrome P450IA1 waspredicted based on the crystal coordinates of cytochrome P450camfrom Pseudomonas putida. As there was only 15% residue identitybetween the two enzymes, additional information was used toestablish an accurate sequence alignment that is a prerequisitefor model building. Twelve representative eukaryotic sequenceswere aligned and a net prediction of secondary structure wasmatched against the known -helices and ß-sheets ofP450cam. The cam secondary structure provided a fixed main-chainframework onto which loops of appropriate length from the humanP450IA1 structure were added. The model-built structure of thehuman cytochrome conformed to the requirements for the segregationof polar and nonpolar residues between the core and the surface.The first 44 residues of human cytochrome P450 could not bebuilt into the model and sequence analysis suggested that residues1–26 formed a single membrane-spanning segment. Examinationof the sequences of cytochrome P450s from distinct gene familiessuggested specific residues that could account for the differencesin substrate specificity. A major substrate for P450IA1, 3-methyl-cholanthrene,was fitted into the proposed active site and this planar aromaticmolecule could be accommodated into the available cavity. Residuesthat are likely to interact with the haem were identified. Thesequence similarity between 59 eukaryotic enzymes was representedas a dendrogram that in general clustered according to genefamily. Until a crystallographic structure is available, thismodel-building study identifies potential residues in cytochromeP450s important in the function of these enzymes and these residuesare candidates for site-directed mutagenesis.     

Isosteric heat of sorption of CO2 in poly(ethylene terephthalate)

Sorption isotherms for carbon dioxide in poly(ethylene terephthalate) have been measured at 35–55°C. The isotherms were measured gravimetrically on a Mettler Thermoanalyzer-1 from vacuum to 1 atmosphere. The sorption data were used to generate sorption isotherms from which the isosteric heat of sorption of CO₂ in PET was determined. At 45°C the isosteric heat of sorption increases from −10 kcal/mole at a concentration of 0.5 cm³ (STP)/cm³ (polymer) to −8 kcal mole⁻¹ at a concentration of 1.5 cm³ (STP)/cm³ (polymer). It has been reported in the literature that the isosteric heat of sorption for this system decreased through a minimum before increasing with increasing concentration. Our measurement of the low-pressure sorption isotherms shows that this is not the case.     

NN-based Prediction Interval for Nonlinear Processes Controller

Neural networks (NNs) are extensively used in modelling, optimization, and control of nonlinear plants. NN-based inverse type point prediction models are commonly used for nonlinear process control. However, prediction errors (root mean square error (RMSE), mean absolute percentage error (MAPE) etc.) significantly increase in the presence of disturbances and uncertainties. In contrast to point forecast, prediction interval (PI)-based forecast bears extra information such as the prediction accuracy. The PI provides tighter upper and lower bounds with considering uncertainties due to the model mismatch and time dependent or time independent noises for a given confidence level. The use of PIs in the NN controller (NNC) as additional inputs can improve the controller performance. In the present work, the PIs are utilized in control applications, in particular PIs are integrated in the NN internal model-based control framework. A PI-based model that developed using lower upper bound estimation method (LUBE) is used as an online estimator of PIs for the proposed PI-based controller (PIC). PIs along with other inputs for a traditional NN are used to train the PIC to predict the control signal. The proposed controller is tested for two case studies. These include, a chemical reactor, which is a continuous stirred tank reactor (case 1) and a numerical nonlinear plant model (case 2). Simulation results reveal that the tracking performance of the proposed controller is superior to the traditional NNC in terms of setpoint tracking and disturbance rejections. More precisely, 36% and 15% improvements can be achieved using the proposed PIC over the NNC in terms of IAE for case 1 and case 2, respectively for setpoint tracking with step changes.