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.

A unified approach to bubble and drop formation

An approach, starting with the bubble formation model of Khurana and Khumar, has been presented, which is found to be reasonably applicable to the formation of both bubbles and drops from single submerged nozzles. The model treats both the phenomena jointly as the formation of a dispersed phase entity resulting from injection, whose size depends upon operating parameters and physical properties.

Drop formation in non-newtonian liquids under pulsed conditions

Drop formation from single nozzles under pulsed flow conditions in non-Newtonian fluids following the power law model has been studied. An existing model has been modified to explain the experimental data. The flow conditions employed correspond to the mixer—settler type of operation in pulsed sieve-plate extraction columns. The modified model predicts the drop sizes satisfactorily. It has been found that consideration of non-Newtonian behaviour is important at low pulse intensities and its significance decreases with increasing intensity of pulsation. Further, the proposed model for single orifices has been tested to predict the sizes of drops formed from a sieve-plate distributor having four holes, and has been found to predict the sizes fairly well in the absence of coalescence.

Secondary breakup of a drop at moderate Weber numbers

We present volume of fluid based numerical simulations of secondary breakup of a drop with high density ratio (approx. 1000) and also perform experiments by injecting monodisperse water droplets in a continuous jet of air and capture the breakup regimes, namely, bag formation, bag-stamen, multibag and shear breakup, observed in the moderate Weber number range (20-120). We observe an interesting transition regime between bag and shear breakup for We = 80, in both simulations as well as experiments, where the formation of multiple lobes, is observed, instead of a single bag, which are connected to each other via thicker rim-like threads that hold them. We show that the transition from bag to shear breakup occurs owing to the rim dynamics which shows retraction under capillary forces at We = 80, whereas the rim is sheared away with flow at We = 120 thus resulting in a backward facing bag. The drop characteristics and timescales obtained in simulations are in good agreement with experiments. The drop size distribution after the breakup shows bimodal nature for the single-bag breakup mode and a unimodal nature following lognormal distribution for higher Weber numbers.

Spatial B-jump at sudden channel enlargements with abrupt drop

An analytical and experimental study of the hydraulic jump in stilling basins with abrupt drop and sudden enlargement, called the spatial B-jump here, is carried out for finding the sequent depth ratio and resulting energy dissipation. The spatial B-jump studied has its toe downstream of the expansion section, and the stream lines at the toe are characterized by downward curvature. An expression is obtained for the sequent depth ratio based on the momentum equation with suitable assumptions for the extra pressure force term because of the abrupt drop in the bed and sudden enlargement in the basin width. Predictions compare favorably with experiments. It is shown that the spatial B-jump needs less tailwater depth, thereby enhancing the stability of the jump when compared either with spatial jump, which forms in sudden expanding channels, or with B-jump, which forms in a channel with an abrupt drop in bed. It is also shown that there is a significant increase in relative energy loss for the spatial B-jump compared to either the spatial jump or B-jump alone.

Vortex dynamics at rf frequencies in Bi2Sr2CaCu2O8 single crystals

We have studied the low magnetic field high temperature region of the H-T phase diagram of Bi2Sr2CaCu2O8 single crystals using the technique of non-resonant rf response at a frequency of 20 MHz. With H(rf)parallel to a, H parallel to c, the isothermal magnetic field scans below T-c show that the frequency f(H) of the tank circuit decreases continuously with increase in H before saturating at H similar to H-D(T). Such a decrease in f(H) reflects increasing rf penetration into the weakly screened region between CuO bilayers. The saturation of f(H) at its lowest value for H similar to H-D(T) indicates complete rf penetration land hence the disappearance of field dependence) due to the vanishing of the screening rf currents I-rf(c) in those regions or equivalently when the phase coherence between adjacent superconducting layers vanishes. Therefore H,(T) represents the decoupling of the adjacent superconducting bilayers, and hence also a 3D to 2D decoupling transition of the vortex structure. Simultaneous monitoring of the field dependent rf power dissipation P(H) shows a maximum in dP/dH at H-D(T). The observed H-D(T) line in many crystals is in excellent agreement with the (l/t-1) behavior proposed for decoupling.

Fluctuations in protein synthesis from a single RNA template: Stochastic kinetics of ribosomes

Proteins are polymerized by cyclic machines called ribosomes, which use their messenger RNA (mRNA) track also as the corresponding template, and the process is called translation. We explore, in depth and detail, the stochastic nature of the translation. We compute various distributions associated with the translation process; one of them-namely, the dwell time distribution-has been measured in recent single-ribosome experiments. The form of the distribution, which fits best with our simulation data, is consistent with that extracted from the experimental data. For our computations, we use a model that captures both the mechanochemistry of each individual ribosome and their steric interactions. We also demonstrate the effects of the sequence inhomogeneities of real genes on the fluctuations and noise in translation. Finally, inspired by recent advances in the experimental techniques of manipulating single ribosomes, we make theoretical predictions on the force-velocity relation for individual ribosomes. In principle, all our predictions can be tested by carrying out in vitro experiments.

Phase transitions and rare-earth magnetism in hexagonal and orthorhombic $DyMnO_{3}$ single crystals

The floating-zone method with different growth ambiences has been used to selectively obtain hexagonal or orthorhombic DyMnO3 single crystals. The crystals were characterized by x-ray powder diffraction of ground specimens and a structure refinement as well as electron diffraction. We report magnetic susceptibility, magnetization and specific heat studies of this multiferroic compound in both the hexagonal and the orthorhombic structure. The hexagonal DyMnO3 shows magnetic ordering of Mn3+ (S = 2) spins on a triangular Mn lattice at T-N(Mn) = 57 K characterized by a cusp in the specific heat. This transition is not apparent in the magnetic susceptibility due to the frustration on the Mn triangular lattice and the dominating paramagnetic susceptibility of the Dy3+ (S = 9/2) spins. At T-N(Dy) = 3 K, a partial antiferromagnetic order of Dy moments has been observed. In comparison, the magnetic data for orthorhombic DyMnO3 display three transitions. The data broadly agree with results from earlier neutron diffraction experiments, which allows for the following assignment: a transition from an incommensurate antiferromagnetic ordering of Mn3+ spins at T-N(Mn) = 39 K, a lock-in transition at Tlock-in = 16 K and a second antiferromagnetic transition at T-N(Dy) = 5 K due to the ordering of Dy moments. Both the hexagonal and the orthorhombic crystals show magnetic anisotropy and complex magnetic properties due to 4f-4f and 4f-3d couplings.

Growth and characterization of pure and doped single crystals of $CuGeO_{3}$

Good quality single crystals of copper metagermanite, CuGeO3, are grown by flux technique. Growth is carried out at relatively low temperatures by using Bi2O3 along with CuO in an optimal flux ratio. Besides rendering the procedure simple, lower growth temperature reduces growth defect concentration. Single crystals of Cu1 - xCoxGeO3 and CuGe1 - yGayO3 are grown by the same method for different values of x and y to investigate the influence of in-chain and off-chain doping on spin-Peierls (SP) transition. Change in color, morphology and surface features as a result of doping are briefly discussed. Spin-Peierls transition of these crystals is studied by susceptibility measurements on a commercial SQUID magnetometer. Cationic substitution resulted in reduction of spin-Peierls transition temperature (T-SP) of CuGeO3. Substitution of magnetic impurity cobalt in-chain site caused more pronounced effects such as suppression of SP phase.

Orchestration of Haemophilus influenzae RecJ Exonuclease by Interaction with Single-Stranded DNA-Binding Protein

RecJ exonuclease plays crucial roles in several DNA repair and recombination pathways, and its ubiquity in bacterial species points to its ancient origin and vital cellular function. RecJ exonuclease from Haemophilus influenzae is a 575-amino-acid protein that harbors the characteristic motifs conserved among RecJ homologs. The purified protein exhibits a process 5'-3' single-stranded-DNA-specific exonuclease activity. The exonuclease activity of H. influenzae RecJ (HiRecJ) was supported by Mg2+ or Mn2+ and inhibited by Cd2+ suggesting a different mode of metal binding in HiRecJ as compared to Escherichia coli RecJ (EcoRecJ). Site-directed mutagenesis of highly conserved residues in HiRecJ abolished enzymatic activity. Interestingly, substitution of alanine for aspartate 77 resulted in a catalytically inactive enzyme that bound to DNA with a significantly higher affinity as compared to the wild-type enzyme. Noticeably, steady-state kinetic studies showed that H. influenzae single-stranded DNA-binding protein (HiSSB) increased the affinity of HiRecJ for single-stranded DNA and stimulated its exonuclease activity. HiSSB, whose C-terminal tail had been deleted, failed to enhance RecJ exonuclease activity. More importantly, HiRecJ was found to directly associate with its cognate single-stranded DNA-binding protein (SSB), as demonstrated by various in vitro assays, Interaction studies carried out with the truncated variants of HiRecJ and HiSSB revealed that the two proteins interact via the C-terminus of SSB protein and the core-catalytic domain of RecJ. Taken together, these results emphasize direct interactio between RecJ and SSB, which confers functional cooperativity to these two proteins. In addition, these results implicate SSB as being involved in the recruitment of RecJ to DNA and provide insights into the interplay between these proteins in repair and recombination pathways.

Influence of cobalt doping on superconducting transition in as-grown YBCO single crystals

The role of a charge buffer layer in the superconductivity of high-T-c materials is best studied by cationic substitutions. In this work, the chain copper in YBCO single crystals is substituted by Co3+ ion and consequent effect on superconducting transition temperature (T-c) studied. The T-c is measured using non-resonant Microwave Absorption technique, which is a highly sensitive and contactless method. It is seen that T-c of as-grown crystals is considerably enhanced by cobalt doping in low concentration regime. In contrast, higher T-c is achieved in undoped crystals only after extended oxygen anneal. When dopant concentration increases beyond an optimal value, T-c decreases and the system does not show superconductivity when cobalt content is high (x > 0.5 in YBa2Cu3-xCOxO7+/-delta). This behaviour consequent to cobalt substitution is discussed with reference to the apical oxygen model. Optimal cobalt doping can be thought of as an alternative to extended oxygen anneal in as-grown crystals of YBCO.

Families of asymptotic tensile crack tip stress fields in elastic-perfectly plastic single crystals

In this work, two families of asymptotic near-tip stress fields are constructed in an elastic-ideally plastic FCC single crystal under mode I plane strain conditions. A crack is taken to lie on the (010) plane and its front is aligned along the [(1) over bar 01] direction. Finite element analysis is first used to systematically examine the stress distributions corresponding to different constraint levels. The general framework developed by Rice (Mech Mater 6:317-335, 1987) and Drugan (J Mech Phys Solids 49:2155-2176, 2001) is then adopted to generate low triaxiality solutions by introducing an elastic sector near the crack tip. The two families of stress fields are parameterized by the normalized opening stress (tau(A)(22)/tau(o)) prevailing in the plastic sector in front of the tip and by the coordinates of a point where elastic unloading commences in stress space. It is found that the angular stress variations obtained from the analytical solutions show good agreement with finite element analysis.

Analysis Of The Energy Quantization Effects On Single Electron Inverter Performance Through Noise Margin Modeling

Possible integration of Single Electron Transistor (SET) with CMOS technology is making the study of semiconductor SET more important than the metallic SET and consequently, the study of energy quantization effects on semiconductor SET devices and circuits is gaining significance. In this paper, for the first time, the effects of energy quantization on SET inverter performance are examined through analytical modeling and Monte Carlo simulations. It is observed that the primary effect of energy quantization is to change the Coulomb Blockade region and drain current of SET devices and as a result affects the noise margin, power dissipation, and the propagation delay of SET inverter. A new model for the noise margin of SET inverter is proposed which includes the energy quantization effects. Using the noise margin as a metric, the robustness of SET inverter is studied against the effects of energy quantization. It is shown that SET inverter designed with CT : CG = 1/3 (where CT and CG are tunnel junction and gate capacitances respectively) offers maximum robustness against energy quantization.

Synthesis and characterisation of heterometallic molecular triangles using ambidentate linker: self-selection of a single linkage isomer

The coordination driven self-assembly of discrete molecular triangles from a non-symmetric ambidentate linker 5-pyrimidinecarboxylate (5-pmc) and Pd(II)/Pt(II) based 90◦ acceptors is presented. Despite the possibility of formation of a mixture of isomeric macrocycles (linkage isomers) due to different connectivity of the ambidentate linker, formation of a single and symmetrical linkage somer in both the cases is an interesting observation. Moreover, the reported macrocycles represent the first example of discrete metallamacrocycles of bridging 5-pmc. While solution composition in both the cases was characterised by multinuclear NMR study and electrospray ionization mass spectrometry (ESI-MS), the identity of the assemblies in the solid state was established by X-ray single crystals structure analysis. Variable temperature NMR study clearly ruled out the formation of any other macrocycles by [4 + 4] or [2 + 2] self-assembly of the reacting components.

Syntheses and characterization of trans-[NiL2(NCS)2][L = 2-(aminomethyl) pyridine], trans-[NiL02(NSC)2][L0 = 2-(2-aminoethyl)pyridine] and trans-[NiL00 2(NSC)2] [L00 = 2-(2-methylaminoethyl)pyridine] complexes: X-ray single crystal structure of trans-[NiL02(NSC)2] [L0 = 2-(2-aminoethyl)pyridine]

[NiL2(NCS)2] (1) [L = 2-(aminomethyl)pyridine], [NiL02(NCS)2] (2) [(L0) = 2-(2-aminoethyl)pyridine and [NiL00 2(NCS)2] (3) [L00 = 2-(2-methylaminoethyl)pyridine] have been synthesized from solution. All the complexes possess trans geometry as is evident from solid state UV–Vis spectral study and X-ray single crystal structure analysis of complex 2 unambiguously proves trans geometry of the species.