In this communication we are reporting, for the first time, results of peeling experiments carried out on spherical glass beads coated with an (approximately) micron-sized thin layer of copper. The glass beads, after a due process of... more
In this communication we are reporting, for the first time, results of peeling experiments carried out on spherical glass beads coated with an (approximately) micron-sized thin layer of copper. The glass beads, after a due process of pretreatment, sensitization and activation, are coated with copper via an electroless deposition method from a standard electroless bath. In each experiment, a copper coated bead is suspended in an agar gel medium and subjected to electrolysis using electrolyte solution containing copper sulphate. As the electrolysis proceeds, the coating starts peeling at the hemisphere facing the cathode, and the extent of peeling is measured by measuring the progress of the critical angle with time. The factors influencing the progress of the critical angle, namely, the applied voltage, electrolyte concentration, and bead size are varied and the resulting profiles are presented and discussed.
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In this article, we present a mathematical model that answers a classical question concerning how much force, which is generally called static friction force, will it require to initiate the motion of a soft solid block such as gel,... more
In this article, we present a mathematical model that answers a classical question concerning how much force, which is generally called static friction force, will it require to initiate the motion of a soft solid block such as gel, rubber or elastomer on a hard surface for instance glass surface. The model uses population balance of the bonds between the polymer chains of the soft solid and the hard surface to estimate rate and aging time dependent static friction. The model predicts that under certain range of the pulling velocity, the friction stress at the onset of sliding (static friction stress) varies as the logarithm of the pulling velocity, as well as the logarithm of the aging time. These predictions are consistent with the experimental observations.
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The technique presented here for the measurement of electrical conductivity is based on the principle that the current converges on a small disk electrode. Most of the ohmic resistance therefore lies within a narrow region surrounding the... more
The technique presented here for the measurement of electrical conductivity is based on the principle that the current converges on a small disk electrode. Most of the ohmic resistance therefore lies within a narrow region surrounding the disk. If the reference electrode is kept outside this zone, the potential difference between the working and the reference electrode includes practically all ohmic potential drops occurring in the solution. Moreover, this ohmic drop can be related to the conductivity of the solution by an analytical expression derived by Newman. At sufficiently high overpotentials, the rate of charge transfer is limited by the conduction of current from the bulk solution to the electrode. In this regime, the current varies linearly with the electrode potential and the conductivity of the solution can be estimated from the slope of the voltammogram using Newman's expression. The electrochemical reaction used for measuring conductivity of solutions of salts is th...
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Nitration reactions are generally conducted using mixed acid. These are extremely exothermic, and tend to run away. Our study show that the reaction is more complex than it is generally believed. We have provided some preliminary evidence... more
Nitration reactions are generally conducted using mixed acid. These are extremely exothermic, and tend to run away. Our study show that the reaction is more complex than it is generally believed. We have provided some preliminary evidence to show that nitrobenzene, above a critical concentration of sulfuric acid exists forms microemulsion at ambient temperatures. This hypothesis is consent with anomalous solubility of nitro-aromatics in concentrated sulfuric acid. There is also formation of Winsor III-phases. In this work we have studied kinetics of nitration of nitrobenzene (NB) (below solubility limits) in concentrated sulfuric acid ( > 82% w/w) and found that although the reaction follows second order kinetics, the rate constant show a discontinuous decrease after a critical loading of the organic phase. Reaction is also inhibited by addition of dinitrobenzene (DNB). We have provided the explanation for this finding based on the hypothesis that the reaction between nitrobenzen...
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ABSTRACT
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Sorption behavior of phosphoric acid on the weak base resins Amberlite IRA-93 and Dowex WGR-2 is reported. Studies on sorption equilibria and dynamics reveal anomalous sorption behavior as compared to sorption of strong and weak monobasic... more
Sorption behavior of phosphoric acid on the weak base resins Amberlite IRA-93 and Dowex WGR-2 is reported. Studies on sorption equilibria and dynamics reveal anomalous sorption behavior as compared to sorption of strong and weak monobasic acids. A mathematical treatment is developed to correlate the experimental data on sorption dynamics. An alternative type of mechanism is also proposed based on
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ABSTRACT A cell model has been proposed to predict the enhancement of gas absorption rates into slurries containing catalyst particles which are smaller than liquid diffusion flim thickness. The model accounts for interparticle and... more
ABSTRACT A cell model has been proposed to predict the enhancement of gas absorption rates into slurries containing catalyst particles which are smaller than liquid diffusion flim thickness. The model accounts for interparticle and particle—film interactions. The finite-element technique has been used to solve the model equations. Simulations have been carried out to study the effect of catalyst loading, particle diameter, and homogeneous reaction rate constant on enhancements of the rate of gas absorption. The experimental data available in the literature have been used to verify the model. The agreement has been found to be fair, keeping in view the limitations of the experimental data. An analytical model has also been proposed to predict the upper limit of the enhancement factor.
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Abstract Catalyst particles, smaller than the diffusion film thickness, in slurry reactors, can enhance the specific rate of absorption substantially over that in the presence of coarser particles, even when the reaction is sufficiently... more
Abstract Catalyst particles, smaller than the diffusion film thickness, in slurry reactors, can enhance the specific rate of absorption substantially over that in the presence of coarser particles, even when the reaction is sufficiently fast to occur in the film in the absence of catalyst particles. This is illustrated with a study of the kinetics of absorption of oxygen in aqueous solutions of sodium sulphide. This study was carried out in stirred contactors with plane interface of 14.5 and 7.5 cm i.d. at temperatures of 80° to 150°C and a total pressure of 1.5 to 9.5 atm, with or without fine activated carbon particles (average particle size 1.7 and 4.33 microns; 0.01 to 2.0% w/w loading) as a catalyst. Some experiments were also conducted with coarse carbon particles (average particle size 85 microns and particle size > 20 μm). Under certain conditions, in the absence of activated carbon, the absorption is accompanied by fast pseudo first order reaction in the film. In a number of cases with fine carbon particles, the specific rate of absorption increased by a factor of 2 to 11 and in some cases this factor was as high as 14. A simple theory has been developed which indicates that, under certain conditions, at higher catalyst loading, the specific rate of absorption will be inversely proportional to the particle size.
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ABSTRACT
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Oxidation of nitric oxide is an important step in NOx absorption. Recent advances namely catalytic oxidation and the use of slrong oxidizing agents have been reviewed. The refinements which have been made in the kinetics of NO oxidation... more
Oxidation of nitric oxide is an important step in NOx absorption. Recent advances namely catalytic oxidation and the use of slrong oxidizing agents have been reviewed. The refinements which have been made in the kinetics of NO oxidation have been discussed. Several liquid phase absorbents have been suggested for the NO removal, particularly for the purpose of pollution abatement. Different
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Experiments were conducted on batch nitration of nitrobenzene in a mechanically agitated reactor using a mixed acid. It was observed that with an increase in the intensity of agitation, the extent of formation of o- and p-dinitrobenzene... more
Experiments were conducted on batch nitration of nitrobenzene in a mechanically agitated reactor using a mixed acid. It was observed that with an increase in the intensity of agitation, the extent of formation of o- and p-dinitrobenzene increase at the expense of m-dinitrobenzene. An attempt has been made to explain the reason for this shift in selectivity based on the mechanism of interfacial nitration.
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ABSTRACT The conventional two-bubble-class model for bubble column reactors has been modified to account for interactions between the two bubble classes. It is shown that the modified model is more consistent with the observed residence... more
ABSTRACT The conventional two-bubble-class model for bubble column reactors has been modified to account for interactions between the two bubble classes. It is shown that the modified model is more consistent with the observed residence time distribution in the gas phase than the conventional model. The results indicate that there is an intensive cross-mixing between the bubble phases. This study also reveals that the modified two-bubble-class model cannot be distinguished from the single-bubble-class model solely on the basis of the residence time distribution.
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Higher rates of uptake of dibasic acids by weak base anion exchange resins, in comparison to those of monobasic acids, have been satisfactorily explained on the basis of dual site adsorption of divalent anion on the protonated resin... more
Higher rates of uptake of dibasic acids by weak base anion exchange resins, in comparison to those of monobasic acids, have been satisfactorily explained on the basis of dual site adsorption of divalent anion on the protonated resin sites. Due to dual site sorption, ...
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Suspension of solids in stirred reactor is widely used for catalytic reactions, dissolution, etc. Quality of solid suspension is an important parameter required for the reliable design, optimum performance, and scale up of the system.... more
Suspension of solids in stirred reactor is widely used for catalytic reactions, dissolution, etc. Quality of solid suspension is an important parameter required for the reliable design, optimum performance, and scale up of the system. Quality of suspension depends on ...
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We formulate a coarse-grained mean-field approach to study the dynamics of the flexible ring polymer in any given obstacle (gel or melt) environment. The similarity of the static structure of the ring polymer with that of the ideal... more
We formulate a coarse-grained mean-field approach to study the dynamics of the flexible ring polymer in any given obstacle (gel or melt) environment. The similarity of the static structure of the ring polymer with that of the ideal randomly branched polymer is exploited in formulating the dynamical model using aspects of the pom-pom model for branched polymers. The topological constraints are handled via the tube model framework. Based on our formulation we obtain expressions for diffusion coefficient D, relaxation times tau, and dynamic structure factor g(k,t). Further, based on the framework we develop a molecular theory of linear viscoelasticity for ring polymers in a given obstacle environment and derive the expression for the relaxation modulus G(t). The predictions of the theoretical model are in agreement with previously proposed scaling arguments and in qualitative agreement with the available experimental results for the melt of rings.
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This article develops a model for kinetics of ion exchange accompanied by chemical reaction with reference to the following irreversible reaction: R-COOH + Na + + OH - → R-COONa + H 2 O where R is a fixed site of the weak acid resin. The... more
This article develops a model for kinetics of ion exchange accompanied by chemical reaction with reference to the following irreversible reaction: R-COOH + Na + + OH - → R-COONa + H 2 O where R is a fixed site of the weak acid resin. The model uses the concept of shell-core mechanism.
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Solid suspension in stirred tank reactor is widely used in process industries for catalytic reactions, dissolution of solids, crystallization, and so on. Suspension quality is a key issue in design and operation of stirred reactor and its... more
Solid suspension in stirred tank reactor is widely used in process industries for catalytic reactions, dissolution of solids, crystallization, and so on. Suspension quality is a key issue in design and operation of stirred reactor and its determination is not straight forward. Cloud height measurements of solid suspension provide a relatively simple way to quantify quality of suspension. In this work, experiments were carried out to quantify variation of cloud heights with impeller speed and particle characteristics. These measurements were carried out using visual observations, image analysis, and ultrasound velocity profiler techniques. The obtained data demonstrated the existence of hysteresis in cloud heights with respect to impeller speed. Apart from possible applications in reducing power required for achieving desired solid suspension quality, the existence of hysteresis also provides a new way to evaluate computational fluid dynamics (CFD) simulations of solid–liquid flows in stirred vessels. An attempt was made to capture observed hysteresis in cloud heights in CFD simulations. The simulated results were compared with the experimental data. The presented models and results (experimental and computational) will be useful for simulating complex solid–liquid flows in stirred reactors. © 2010 American Institute of Chemical Engineers AIChE J, 2010
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Sodium polystyrene sulfonate (NaPSS) is synthesized by two different methods: one using free radical polymerization of sodium styrene sulfonate and another through post-sulfonation of polystyrene. Both the solution and interfacial... more
Sodium polystyrene sulfonate (NaPSS) is synthesized by two different methods: one using free radical polymerization of sodium styrene sulfonate and another through post-sulfonation of polystyrene. Both the solution and interfacial properties of the two polymers obtained from these two methods are different. The osmotic coefficient of free radically polymerized NaPSS is 20% higher than that of the NaPSS obtained from the post-sulfonation method. Further, the free radically polymerized NaPSS has negligible interfacial activity at both air–water and toluene–water interfaces, as compared to post-sulfonated NaPSS. The former type of NaPSS also adsorbs to a comparatively lesser extent at a solid–liquid interface. The enhanced hydrophobic character of post-sulfonated NaPSS is explained on the basis of its intrinsically lower configurational entropy that results from the formation of intramolecular sulfone linkages, whereas the free radical method gives only a linear structure. Also, the intramolecular sulfone linkage will enhance the counter-ion condensation and consequently decrease the osmotic coefficient of the post-sulfonated sample. However, it is generally difficult to predict the exact degree of intramolecular sulfone linkage that may occur, as it depends on several factors. An attempt has been made to interpret some of the experimental data in the existing literature on NaPSS, which has mostly been prepared using the post-sulfonation route. Copyright © 2006 Society of Chemical Industry
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A new approach to cation-exchange kinetics views ion-exchange resin as an aggregate of uniform cylindrical pores. Ion exchange occurs at the pore surface. The counterions dissociate only partially from the fixed sites, and the charge... more
A new approach to cation-exchange kinetics views ion-exchange resin as an aggregate of uniform cylindrical pores. Ion exchange occurs at the pore surface. The counterions dissociate only partially from the fixed sites, and the charge created on the pore surface is balanced by the counterions in the electrical double layer. Thus, any cross section of a pore consists of an annular double-layer region and a central core region. Electroneutrality prevails in the core region through an influx of coions. Diffusion of ions through both regions is considered. The complete model incorporating these ideas for kinetics of monovalent cation exchange was tested with our experimental data as well as with the reported data. The pore diffusion coefficients used in the model are free ionic diffusion coefficients corrected for the tortuosity factor of the pores. Unknown parameters of the model are the degree of dissociation of counterions from the fixed sites of the pore (fσ), and the film thickness (δ). Both parameters are insensitive to the type of counterions, solution concentration, and the direction of exchange. Further, fσ appears to be a characteristic property of resin alone. Superiority of the developed model over the previous models is established.
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Abstract A modified shrinking core model is proposed to correlate dynamics of acid sorption on weak base ion-exchange resins in free base form. The model considers reversibility of the sorption process which is ignored in the conventional... more
Abstract A modified shrinking core model is proposed to correlate dynamics of acid sorption on weak base ion-exchange resins in free base form. The model considers reversibility of the sorption process which is ignored in the conventional shrinking core model. The ...
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In a topologically constraining environment the size of a flexible nonconcatenated ring polymer (macrocycles) and its dynamics are known to differ from that of linear polymers. Hence, the diffusion coefficient of ring polymers can be... more
In a topologically constraining environment the size of a flexible nonconcatenated ring polymer (macrocycles) and its dynamics are known to differ from that of linear polymers. Hence, the diffusion coefficient of ring polymers can be expected to be different from linear chains. We present here scaling arguments for the concentration and molecular weight dependence of self-diffusion coefficient of ring polymers in semidilute solutions, and show that contrary to expectations these scaling relations are identical to what is known for linear polymers. At higher concentrations excluded volume interactions arising from possibilities of segmental overlap can become effective for large ring polymers. In this regime the diffusion coefficient of large ring polymers shows a relatively weaker dependence on concentration and molecular weight. ©2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2370–2379, 2008
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The dynamical behavior of cyclic macromolecules in a fixed obstacle (FO) environment is very different than the behavior of linear chains in the same topological environment; while the latter relax by a snake-like reptational motion from... more
The dynamical behavior of cyclic macromolecules in a fixed obstacle (FO) environment is very different than the behavior of linear chains in the same topological environment; while the latter relax by a snake-like reptational motion from their chain ends the former can relax only by contour length fluctuations since they are endless. Duke, Obukhov and Rubinstein proposed a scaling model (the DOR model) to interpret the dynamical scaling exponents shown by Monte Carlo simulations of rings in a FO environment. We present a model (blob-spring model) to describe the dynamics of flexible and non-concatenated ring polymer in FO environment based on a theoretical formulation developed for the dynamics of an unentangled fractal polymer. We argue that the perpetual evolution of ring perimeter by the motion of contour segments results in an extra frictional load. Our model predicts self-similar dynamics with scaling exponents for the molecular weight dependence of diffusion coefficient and relaxation times that are in agreement with the scaling model proposed by Obukhov et al.
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In this contribution we concern ourselves with an interesting problem, namely, the dynamics of ideal flexible ring polymers constrained in an array of fixed obstacles. The fundamental issue in this problem is to understand how a... more
In this contribution we concern ourselves with an interesting problem, namely, the dynamics of ideal flexible ring polymers constrained in an array of fixed obstacles. The fundamental issue in this problem is to understand how a topologically constrained polymer chain is able to ...