IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

This study is focused on the evaluation of the thermal stability of a nanocrystalline Mg alloy, a relatively less explored topic. Guided by Darling et al. model which advises choosing of alloying elements based on their enthalpy of mixing and elastic enthalpy with respect to the parent element, Mo was chosen for stabilizing the nc Mg structure. High energy ball milling experiments were conducted on powders of Mg and Mo to achieve a composition of Mg–2at%Mo. Characterization of the ball milled powders using XRD and TEM indicated a lack of mixing of Mg and Mo and the microstructure was found to bear a mix of Mg and Mo phases. Kissinger's analysis using DSC yielded the activation energy of grain growth in the ball milled material as 73 kJ/mol which was similar to that of pure Mg, indicating that Mo did not alter the grain growth kinetics of Mg. The poor grain size stability of the nanocrystalline Mg–2Mo composition was also observed during spark plasma sintering studies conducted at 673, 723 and 773 K. The obtained results were evaluated in the light of the Murdoch and Schuh model and this revealed that the Mg–Mo alloy is not expected to be thermally stable due to the tendency of Mo to exist as a separate phase. This analysis appears to suggest that the Murdoch and Schuh model is more suitable for identifying thermally stable nanocrystalline compositions compared to the Darling et al. model. © 2020

World University root node

Department Of Chemical Engineering

Department of Metallurgical and Materials Engineering

Materialia

Theoretical and experimental studies on thermal stability of nanocrystalline Mg–Mo alloy

Coulson and Richardson’s Chemical Engineering: Volume 3A: Chemical and Biochemical Reactors and Reaction Engineering, Fourth Edition, covers reactor design, flow modelling, gas-liquid and gas-solid reactions and reactors. © 2017 Elsevier Ltd. All rights reserved.

Department Of Biotechnology

Coulson and Richardson's Chemical Engineering: Volume 3A: Chemical and Biochemical Reactors and Reaction Engineering

Coulson and richardson’s chemical engineering

Motivated by studies of the diffusion of a gas mixture in a Stefan tube, we present a hierarchy of mass transfer models with the species momentum balance and the species continuity equations as the basis. The simplifying conditions and the constitutive equations that lead to the equations of the mixture momentum balance approach are obtained. Further, the form that these equations should take for a multicomponent mixture is derived. These equations are shown to be a generalization of the Meyer–Kostin equations used to study binary diffusion in a Stefan tube. Additional simplifications that result in the so called classic approach to diffusion are identified. © 2016 Elsevier Ltd

International Communications in Heat and Mass Transfer

A hierarchy of transport models motivated by studies of the Stefan tube

The differences between the modern version of the phase rule and the one originally proposed by Gibbs are pointed out. The local analysis implied in Gibbs's approach to the phase rule is carried forward to its logical conclusion using the implicit function theorem. The results of the analysis are used to resolve the apparent contradictions in the interpretation of the phase rule, using the Gibbs-Duhem equations, for a system exhibiting an azeotrope. Specifically, the pitfalls in treating the differentials in the Gibbs-Duhem equations as variations are demonstrated. The critical role played by the rank of a submatrix in the coefficient matrix of the Gibbs-Duhem equations is highlighted. A hierarchy in the application of the phase rule is pointed out and the need for a unified framework for interpreting the phase rule is indicated. © 2012 Elsevier Ltd.

Phase rule and the azeotrope - A critique and a new interpretation

The apparent differences in the statements of the phase rule for the two sets of variables commonly used, namely, temperature, pressure, and mole fractions on the one hand and temperature, pressure, and chemical potentials on the other are resolved by developing a framework in which the phase rule may be stated and analyzed in terms of a whole class of variable sets. The framework is restricted to the case where all the components are present in all the phases. Central to the framework is the notion, due to Gibbs, of a fundamental relation for homogeneous states and the associated general equation cast in terms of intensive and specific variables. The significance of the Gibbs-Duhem equations within the context of the phase rule is brought out. The lead provided by Gibbs in his approach to the phase rule is utilized to carry out a local analysis of the equations that result from the criteria of equilibrium for the two sets of variables referred to above. The central role played by the general equations is brought out. The scope of the phase rule is widened by identifying particular sets of variables that would be suitable for uniquely defining the equilibrium state of a multiphase mixture. © 2012 American Chemical Society.

Industrial and Engineering Chemistry Research

Toward a unified framework for interpreting the phase rule

A comparative study of the kinetics of production of biodiesel from the transesterification of three non-edible vegetable oils is undertaken. A three step mechanism was used to model the kinetics in the case of Pongamia oil which was found to be a mixture tri-, di- and monoglycerides. On the other hand, an one-step model was sufficient for Jatropha and Mahua oils both of which contained largely triglycerides. The rate of transesterification at comparable temperatures and catalyst concentrations was found to be the highest for Jatropha oil followed by Mahua and then Pongamia oil. The effect of cosolvent on the rate of transesterification was noticeably higher for Mahua oil than for the other two oils but still much lower than that reported in the literature for both soybean and canola oil. Kinetics of transesterification of oils to yield biodiesel thus depends on the composition of the oil under consideration. Therefore studies are under way to examine the fine structure of the triglycerides contained in the various oils and establish a correlation with the kinetics of transesterification.

11AIChE - 2011 AIChE Annual Meeting, Conference Proceedings

Kinetics of biodiesel production from non-edible vegetable oils

The ideas used by Gibbs in defining the ideal gas mixture are brought to light in view of their fundamental significance and the fact that they have not received due attention in the literature. Specifically, the central role played by the well-known Gibbs-Duhem equation in this regard is explained. The concept of a fundamental equation and its importance in the definition of an ideal gas as well as an ideal gas mixture is elucidated. The manner in which these ideas enabled Gibbs to give a very general interpretation of Daltons law is examined in detail. © 2011 American Chemical Society.

The Gibbs-Duhem equation, the ideal gas mixture, and a generalized interpretation of Daltons Law

Engineering Sciences and Fundamentals - Core Programming Topic at the 2011 AIChE Annual Meeting

Transport properties of liquid metals

The non-edible oils of mahua and jatropha were transesterified using methanol and 1 wt % KOH as the catalyst. The effect of co-solvent and the kinetic study of the transesterification of mahua oil is being reported here for the first time. Kinetics, modeled as a single-step reaction, revealed that the order of the reaction is 2 with respect to the triglyceride concentration and 1 with respect to the methanol concentration in both oils. In the presence of co-solvent, tetrahydrofuran (THF), methanolysis of mahua oil resulted in the increase of the rate constants from 0.08 to 1.17 L2 mol-2 min-1 at 28 °C and from 0.43 to 3.18 L2 mol -2 min-1 at 45 °C. The corresponding values for jatropha oil were found to be 0.50 and 2.76 L2 mol-2 min-1 at 28 °C and 1.26 and 4.56 L2 mol-2 min-1 at 45 °C. © 2011 American Chemical Society.

GENERAL

Energy and Fuels

Kinetic studies of base-catalyzed transesterification reactions of non-edible oils to prepare biodiesel: The effect of Co-solvent and temperature

The fundamental flaws inherent in Maxwell's equal area rule are analyzed. Using an alternative principle that overcomes the limitations of Maxwell's rule, general equations are derived for determining the saturation pressure and other properties associated with the liquid-vapor phase transition given an arbitrary equation of state. The equivalence of the equation for saturation pressure to those available in the literature is proved. It is found that the alternative principle predicts saturation pressures that are significantly different from those calculated using Maxwell's rule. These results are based on numerical studies on three different equations of state and fifteen substances. Similar results are obtained for the vaporization entropy as well. © 2010 American Chemical Society.

Critical analysis of maxwell's equal area rule: Implications for phase equilibrium calculations

The validity of the hard-sphere (HS) model in determining the self-diffusion coefficient of simple fluids is studied using the Lennard-Jones (LJ) fluid as a test fluid. The latest simulation results on the LJ fluid are used along with the various perturbation theories to assess the HS model separately in the liquid, gas, and supercritical regions as a function of both density and temperature. Apart from the commonly used methods of estimating the effective hard-sphere diameter (EHSD), the Gibbs-Bogoliubov criterion, which provides an EHSD that is more representative of the intermolecular interactions, is used. This criterion gives a vastly different assessment of the HS model compared to other methods in the supercritical and liquid regions. All methods result in considerable errors in the low-density dilute gas region at lower temperatures. Next, the diffusivity of carbon dioxide is studied. Nine different sets of LJ potential parameters and three non-LJ potentials are considered. The LJ potential based on the critical constants of carbon dioxide yields diffusivities closest to the experiment. © 2008 American Chemical Society.

Lennard-jones fluid and diffusivity: Validity of the hard-sphere model for diffusion in simple fluids and application to CO2

A new method is proposed for obtaining the transformations that enable the application of the McCabe-Thiele method to the case when the saturated liquid and vapor enthalpy curves are straight but non-parallel lines. A rigorous framework which has a sound physical and mathematical basis and which brings into greater focus the central importance of the parallel enthalpy lines assumption to the McCabe-Thiele method is developed. Explicit expressions for the transformations of not only the composition and flow rate but also enthalpy are obtained. A detailed comparison of the methods adopted in this work with those in the literature is made. The specializing conditions under which the transformations in the literature emerge from a more general set are found. Extension to multi-component mixtures is demonstrated. It is shown that the framework presented here provides a rational basis for the prescriptions obtained from the "fictitious molecular weight" concept. Further, contrary to claims in the literature, the applicability of that concept to multi-component mixtures is demonstrated. Finally, the fresh perspective gained from the framework is used to widen the scope of its applicability and generalization to other separation processes such as extraction, adsorption and leaching is undertaken. © 2008 Elsevier Ltd. All rights reserved.

Transformations for a generalized McCabe-Thiele method: A retrospective and a new perspective

The mathematical problem associated with the Loschmidt tube experiment is considered with the specific purpose of resolving the discrepancies that exist in the literature regarding the solution to the problem. An outline of one method of obtaining the correct solution is presented using standard techniques.

Chemical Engineering Communications

Mathematical treatment of the Loschmidt tube experiment: Some clarifications

An unambiguous treatment of the rate of chemical transformation for homogeneous reactions is sought by pointing out the key elements of any mathematical theory of physicochemical phenomena and relating them to some of the concepts of reaction engineering. Within this framework, the rate of generation per unit volume of a species through a reaction step emerges as a primitive. The status of the species balance equation as a law (rather than a definition) and that of commonly used rate expressions as constitutive relations are brought forth. These concepts are illuminated using analogies from classical mechanics and thermodynamics.

The definition of reaction rate: A closure

The kinetics of transesterification of Pongamia oil using methanol at 60°C were studied. The forward as well as the reverse rate constants of all three steps involved in the transesterification of Pongamia oil are reported for the first time. Among the forward rate constants, the one governing the conversion of TG to DG was the highest and the one for DG to MG was the lowest. A distinct feature of the present work is the direct estimation of the equilibrium constants of all three steps by measuring the concentrations of TG, DG, and MG at very long reaction times. This reduced the number of parameters to be determined from the kinetic data by one-half, thereby leading to more accurate estimation of the rate constants. The equilibrium constant of the final step involving the conversion of MG to methyl ester and glycerol was at least an order of magnitude greater than that of the first two reaction steps. A detailed comparison was made with kinetic parameters reported in literature. The trend in the relative magnitudes of the rate constants appears to be unique to Pongamia oil. Copyright © 2006 by AOCS Press.

JAOCS, Journal of the American Oil Chemists' Society

Kinetics of base-catalyzed transesterification of triglycerides from Pongamia oil

The assumptions and results associated with the McCabe-Thiele method of distillation column analysis are brought together within a rigorous analytical framework. Within this framework, the assumption that the saturated liquid and vapor enthalpy curves are parallel lines, apart from adiabatic and isobaric operation of the distillation column, is shown to be sufficient to derive all the major results of the McCabe-Thiele method including the constant molar overflow condition. Then, using a rigorous thermodynamic analysis, a comprehensive set of conditions sufficient for the enthalpy curves to be parallel lines are obtained. Some common systems for which these assumptions hold are discussed. Finally, the conditions under which McCabe-Thiele-like methods occur in other separation processes are outlined, with pointers to a unified picture of separation processes. Copyright © Taylor & Francis Inc.

A rigorous analysis of McCabe-Thiele assumptions and their consequences: Critical role of parallel enthalpy lines

Abstract is unavailable for this paper.

Department of Humanities and Social Sciences

Advances in Chemical Physics

Molecular Theory of Liquid-Phase Vibrational Energy Relaxation

Previous studies on reactor-separator networks have focused largely on first- and second-order kinetics. A study of the effect of autocatalytic kinetics has been restricted to cases where the separator is a single-stage process. In this work, the effect of autocatalytic kinetics on the design and operation of a reactor-separator system, where the separator is a multistage distillation column, is investigated. Apart from steady-state design and stability, dynamic aspects such as response to disturbances and set-point changes are studied in detail. It was found that when the reactor holdup is maintained constant, for stable operation, the exit reactor concentration (mole fraction of the reactant A) has to be <1/2 for quadratic autocatalysis and <1/3 for cubic autocatalysis. Further, in the stable regime, the ability of the system to absorb changes in the inlet flow rate or the composition decreases as the domain of instability is approached. Regarding dynamics, we observe that the response of the system becomes slower with an increase in the base steady-state value of the exit reactor composition in the stable regime. This is correlated with the appropriate time constant, which shows a qualitatively different behavior for autocatalytic kinetics as compared to first-order or second-order kinetics. Snowball effects, which refer to sharp changes in the distillate rate due to small changes in the inlet flow rate, were also found to be dominant. For the case of variable reactor holdup, the range of stable operation is increased for quadratic autocatalysis. In general, settling times are larger when compared to the case of constant holdup, but the percentage deviations from steady-state values due to changes in the inlet flow rate and the composition are smaller. Further, snowball effects are negligible. © 2005 American Chemical Society.

Effect of autocatalytic kinetics on the steady state and dynamics of a reactor-separator system

Physics Today

Comments on the culture of the force [2] (multiple letters)

The importance of specifying the state of the inlet streams in determining the degrees of freedom (DOF) of a process is highlighted in the context of a single-stage separation unit. It is shown that, for the separation of a C-component mixture, the commonly accepted value of 2C + 6 as the DOE of an equilibrium single stage holds only if neither of the inlet streams lie on the phase envelope. The implications of this feature for the DOF of multistage processes is explored. The importance of a precise interpretation of the phase rule in arriving at the above results is emphasized. © 2005 American Chemical Society.