Papers by Siddharth Chatterjee
Royal Society Open Science, 2017
The surface of a turbulent liquid is visualized as consisting of a large number of chaotic eddies... more The surface of a turbulent liquid is visualized as consisting of a large number of chaotic eddies or liquid elements. Assuming that surface elements of a particular age have renewal frequencies that are integral multiples of a fundamental frequency quantum, and further assuming that the renewal frequency distribution is of the Boltzmann type, performing a population balance for these elements leads to the Danckwerts surface age distribution. The basic quantum is what has been traditionally called the rate of surface renewal. The Higbie surface age distribution follows if the renewal frequency distribution of such elements is assumed to be continuous. Four age distributions, which reflect different start-up conditions of the absorption process, are then used to analyse transient physical gas absorption into a large volume of liquid, assuming negligible gas-side mass-transfer resistance. The first two are different versions of the Danckwerts model, the third one is based on the uniform and Higbie distributions, while the fourth one is a mixed distribution. For the four cases, theoretical expressions are derived for the rates of gas absorption and dissolved-gas transfer to the bulk liquid. Under transient conditions, these two rates are not equal and have an inverse relationship. However, with the progress of absorption towards steady state, they approach one another. Assuming steady-state conditions, the conventional one-parameter Danckwerts age distribution is generalized to a two-parameter age distribution. Like the two-parameter logarithmic normal distribution, this distribution can also capture the bell-shaped nature of the distribution of the ages of surface elements observed experimentally in air–sea gas and heat exchange. Estimates of the liquid-side mass-transfer coefficient made using these two distributions for the absorption of hydrogen and oxygen in water are very close to one another and are comparable to experimental values reported in the literature.
Royal Society Open Science, 2018
The recently derived steady-state generalized Danckwerts age distribution is extended to unsteady... more The recently derived steady-state generalized Danckwerts age distribution is extended to unsteady-state conditions. For three different wind speeds used by researchers on air-water heat exchange on the Heidelberg Aeolotron, calculations reveal that the distribution has a sharp peak during the initial moments, but flattens out and acquires a bell-shaped character with process time, with the time taken to attain a steady-state profile being a strong and inverse function of wind speed. With increasing wind speed, the age distribution narrows significantly, its skewness decreases and its peak becomes larger. The mean eddy renewal time increases linearly with process time initially but approaches a final steady-state value asymptotically, which decreases dramatically with increased wind speed. Using the distribution to analyse the transient absorption of a gas into a large body of liquid, assuming negligible gas-side mass-transfer resistance, estimates are made of the gas-absorption and dissolved-gas transfer coefficients for oxygen absorption in water at 25°C for the three different wind speeds. Under unsteady-state conditions, these two coefficients show an inverse behaviour, indicating a heightened accumulation of dissolved gas in the surface elements, especially during the initial moments of absorption. However, the two mass-transfer coefficients start merging together as the steady state is approached. Theoretical predictions of the steady-state mass-transfer coefficient or transfer velocity are in fair agreement (average absolute error of prediction = 18.1%) with some experimental measurements of the same for the nitrous oxide-water system at 20°C that were made in the Heidelberg Aeolotron.
A simple and holistic model based on a linear driving force approximation for
describing the unst... more A simple and holistic model based on a linear driving force approximation for
describing the unsteady-state transport of moisture in the thickness direction of paper is formulated that accounts for the parallel diffusion of moisture in the pore and fibre phases, as well as external mass-transfer resistance. The transport model is able to correlate measurements of the transient weight change and average relative humidity (RH) of stacks of bleached kraft paperboard sheets subjected to ramp changes of the external
RH with an average error of 9.3%.
A theoretical model describing the unsteady-state transport of moisture in the thickness directio... more A theoretical model describing the unsteady-state transport of moisture in the thickness direction of paper is formulated that accounts for the parallel diffusion of moisture in the pore and fiber phases, as well as external mass-transfer resistance. Using values of the effective water-vapor
and bound-water diffusion coefficients of a bleached kraft paperboard (BKP), which were estimated from steady-state moisture flux measurements in the first part of our work (see the preceding article in this issue), and no fitting parameter, the predictions of the dynamic moisture transport
model are found to be in good agreement with measurements of the transient weight change and relative humidity (RH) profile of stacks of BKP sheets subjected to ramp changes of the external RH under a variety of experimental conditions.
A theoretical analysis using the surface-renewal and film-penetration models, which includes gas-... more A theoretical analysis using the surface-renewal and film-penetration models, which includes gas-phase resistance to mass transfer, is presented for the rate of absorption of a gas and its transfer to the bulk liquid in the case where the solute gas undergoes a first-order chemical reaction in the liquid phase. It reveals that (a) the fraction of absorbed gas transported to the bulk liquid depends upon the Hatta number (Ha) in case of the surface-renewal model and on Ha and a dimensionless hydrodynamic parameter in case of the film-penetration model; (b) the widely assumed law of addition of resistances is valid for the surface-renewal and film-penetration models; and (c) the reaction influences both the overall mass-transfer coefficient and the nature of the driving force, i.e., the increased rate of absorption due to reaction is not solely due to the enhancement factor multiplying the liquid-phase mass-transfer coefficient for physical absorption as has been conventionally assumed in the literature. It also shows that in a gas-liquid reactor the film and surface-renewal models give close predictions for both the rate of absorption and concentration of dissolved gas in the liquid leaving the reactor. For values of Ha ≥ 0.5, the bulk-liquid concentration of dissolved gas predicted by both models is negligible compared to its interfacial concentration.
A theoretical model using the surface-renewal concept is developed for describing cross-flow ultr... more A theoretical model using the surface-renewal concept is developed for describing cross-flow ultrafiltration under dynamic and steady-state conditions. The model can predict the local permeate flux and concentration profile of dissolved solute in the filter. The rate of surface renewal (S) at the membrane surface and the diffusion coefficient (D) of the solute in the solvent are the two parameters of the model. The model is able to correlate literature data of transient permeate flux in the ultrafiltration of skim milk with an average root-mean-square error of 9.9%. The values of S and D, estimated from the model, are 0.84 - 1.74 * 10-3 s-1 and 0.55 - 2.07 * 10-9 m2/s, respectively.
Separation and Purification Technology, Jan 1, 2004
This book, written by several experts, provides a summary of the evolutionary and revolutionary d... more This book, written by several experts, provides a summary of the evolutionary and revolutionary developments in the field of computer-aided process engineering (CAPE) over the last two decades from a software architecture and technology perspective. The book is one of the results of the CAPE-OPEN and Global CAPE-OPEN projects undertaken by the EU very recently. Following the book, this review is composed of several sections. Part I, written by the editors (Braunschweig and Gani), gives a general introduction to the contents of the book. A distinction is drawn between CAPE methods, which are a collection of computer-aided methodologies, techniques, and algorithms and CAPE tools which are software made by transforming CAPE methods for a range of applications and uses. The authors also give road maps through the book for readers with different interests.
CURRENT SCIENCE, Jan 1, 2012
This article explores Einstein’s views on the nature of scientific theory, and is directed toward... more This article explores Einstein’s views on the nature of scientific theory, and is directed towards students and researchers in the physical sciences and engineering. A majority of scientific theories belong to the constructive
type whose axiomatic foundation consists of empirically observed principles and imaginary or speculative hypotheses. On this base is erected a logical superstructure (e.g. calculus) whose object is to make concrete predictions which can be tested against experiential data. A favourable comparison will point to validity of the hypotheses while an unfavourable one will require their revision. A constructive theory holds temporarily and will eventually be replaced with a more comprehensive approach. In contrast, in a
theory of principle, the axiomatic foundation consists solely of principles of nature that are derived from human experience. Unless these principles are found to be false in the future, the security of such a theory is
guaranteed. An example of a constructive theory is the kinetic theory of gases while classical thermodynamics and the theory of relativity belong to the class of principle theories.
International journal of …, Jan 1, 2006
Evaporative cooling of water in a small porous clay vessel was studied under controlled humidity ... more Evaporative cooling of water in a small porous clay vessel was studied under controlled humidity conditions. In steady-state experiments performed at an ambient temperature of 23 °C, the cooling effect increased from 4.7 to 8.3 °C as the ambient relative humidity decreased from 60 to 15%. External heat and mass transfer coefficients, estimated from the steady-state measurements, were used in mathematical models to predict the experimentally observed transient temperature variation of the water under ramp changes of the ambient relative humidity. With a prototypical cool chamber containing water tested in Kolkata, India under an ambient temperature of 34.5-35 °C, the cooling effect reached a maximum of 7 °C between 3 and 3:30 PM and then declined to 4.5 °C around 6 PM.
Industrial & Engineering Chemistry …, Jan 1, 2008
A two-parameter model, which utilizes the hybrid film-penetration concept, is developed for descr... more A two-parameter model, which utilizes the hybrid film-penetration concept, is developed for describing exothermic physical absorption of a gas into a liquid. The model is applied to the absorption of dry saturated water vapor into aqueous lithium bromide solution, which system is used in absorption cooling. The conventional film and penetration models predict constant values of 0.55 and 6.59 K for the interfacial temperature rise, respectively, and also suggest that the rate of absorption at the gas-liquid interface will be depressed by 3 (film model) and 40% (penetration model) compared to assumed isothermal absorption at the bulk liquid temperature. The holistic film-penetration model resolves this large discrepancy between the film and penetration models, which are fragmentary perspectives of the absorption process.
Industrial & engineering chemistry …, Jan 1, 2003
A theoretical model describing the unsteady-state transport of moisture in the thickness directio... more A theoretical model describing the unsteady-state transport of moisture in the thickness direction of paper is formulated that accounts for the parallel diffusion of moisture in the pore and fiber phases, as well as external mass-transfer resistance. Using values of the effective water-vapor
and bound-water diffusion coefficients of a bleached kraft paperboard (BKP), which were estimated from steady-state moisture flux measurements in the first part of our work (see the preceding article in this issue), and no fitting parameter, the predictions of the dynamic moisture transport
model are found to be in good agreement with measurements of the transient weight change and relative humidity (RH) profile of stacks of BKP sheets subjected to ramp changes of the external RH under a variety of experimental conditions.
Carbon, Jan 1, 1990
A new model for the retention of toxic gas by modifed carbon in fixed-bed operations is presented... more A new model for the retention of toxic gas by modifed carbon in fixed-bed operations is presented. The retention of the toxic gas is assumed to be effected through two independent pathways: physical adsorption and chemical reaction between the toxic gas and carbon impregnants with the reaction taking place instantaneously. Reasonable agreement was obtained between experiments and predictions on breakthrough time and effluent concentration histories based on the model.
Chemical Engineering Science, Jan 1, 1989
Separations Technology, Jan 1, 1991
Industrial & engineering chemistry …, Jan 1, 2003
A theoretical model describing the steady-state transport of moisture in the thickness direction ... more A theoretical model describing the steady-state transport of moisture in the thickness direction of a stack of paperboard sheets placed in a diffusion cup that accounts for the parallel diffusion of water vapor in the pore space and of bound water in the fiber phase is presented. The predictions of the model compare favorably with experimental measurements of the moisture transmission rate through a bleached kraft paperboard stack, average moisture content of the stack, relative humidity profile in the stack, and average moisture content of the individual sheets of the stack under steady-state conditions.
Carbon, Jan 1, 1989
ABSTRACT
Chemical Engineering …, Jan 1, 2009
A mathematical description is presented for xylan solubilization during hydrothermal pretreatment... more A mathematical description is presented for xylan solubilization during hydrothermal pretreatment of sugar maple and aspen wood chips. It assumes first-order kinetics with Arrhenius-type temperature dependence of the reaction rate constants and includes limitations on the transport of reaction products formed in the wood pores to the bulk liquor. The model is calibrated with experimentally measured yields of residual xylan, xylooligomers, and xylose obtained in the autohydrolysis of sugar maple wood chips under pretreatment conditions of 152−175 • C, reaction times of 0−6 h, and liquor to solid ratio of 6:1 in a batch digester. It is validated against experimental data obtained from the autohydrolysis of aspen wood chips at 160 • C under similar experimental conditions as those used for sugar maple. The model can also satisfactorily correlate data of deacetylation of xylan and formation of products (free acetyl groups and acetyl groups attached to xylooligomers in the hydrolyzate) in the autohydrolysis of sugar maple and aspen wood chips with fair accuracy.
Industrial & engineering chemistry research, Jan 1, 2001
Everett's domain and Mualem's capillary-radii similarity models of hysteresis were used to charac... more Everett's domain and Mualem's capillary-radii similarity models of hysteresis were used to characterize the moisture sorption equilibria of a bleached kraft paperboard of mean basis weight 230 g/m 2 . The models predicted the experimental equilibrium moisture content (EMC) of the paperboard for the case of desorption scanning (similarity model only), adsorption scanning, spiral, and loop trajectories inside the main sorption hysteretic loop with good precision. Over an RH range of 15-90%, the root-mean-square deviation between the predicted and experimental EMCs was 0.11-0.83% (domain model) and 0.21-0.64% (similarity model). However, the similarity model is easier to use and requires data of only the two boundary isotherms that envelop the main hysteretic loop. The similarity method obviates the need of taking additional labor-intensive and time-consuming scanning curve data that is necessary to develop the moisture distribution function of the domain model and predicts higher-order EMC trajectories that lie inside the main hysteretic loop in a consistent fashion. * Phone: (315) 470-6517. Fax: (315) 470-6945. 10.
Holzforschung, Jan 1, 2009
A mathematical description is presented for xylan solubilization during hydrothermal pretreatment... more A mathematical description is presented for xylan solubilization during hydrothermal pretreatment of sugar maple and aspen wood chips. It assumes first-order kinetics with Arrhenius-type temperature dependence of the reaction rate constants and includes limitations on the transport of reaction products formed in the wood pores to the bulk liquor. The model is calibrated with experimentally measured yields of residual xylan, xylooligomers, and xylose obtained in the autohydrolysis of sugar maple wood chips under pretreatment conditions of 152−175 • C, reaction times of 0−6 h, and liquor to solid ratio of 6:1 in a batch digester. It is validated against experimental data obtained from the autohydrolysis of aspen wood chips at 160 • C under similar experimental conditions as those used for sugar maple. The model can also satisfactorily correlate data of deacetylation of xylan and formation of products (free acetyl groups and acetyl groups attached to xylooligomers in the hydrolyzate) in the autohydrolysis of sugar maple and aspen wood chips with fair accuracy.
The Canadian Journal of …, Jan 1, 1987
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Papers by Siddharth Chatterjee
describing the unsteady-state transport of moisture in the thickness direction of paper is formulated that accounts for the parallel diffusion of moisture in the pore and fibre phases, as well as external mass-transfer resistance. The transport model is able to correlate measurements of the transient weight change and average relative humidity (RH) of stacks of bleached kraft paperboard sheets subjected to ramp changes of the external
RH with an average error of 9.3%.
and bound-water diffusion coefficients of a bleached kraft paperboard (BKP), which were estimated from steady-state moisture flux measurements in the first part of our work (see the preceding article in this issue), and no fitting parameter, the predictions of the dynamic moisture transport
model are found to be in good agreement with measurements of the transient weight change and relative humidity (RH) profile of stacks of BKP sheets subjected to ramp changes of the external RH under a variety of experimental conditions.
type whose axiomatic foundation consists of empirically observed principles and imaginary or speculative hypotheses. On this base is erected a logical superstructure (e.g. calculus) whose object is to make concrete predictions which can be tested against experiential data. A favourable comparison will point to validity of the hypotheses while an unfavourable one will require their revision. A constructive theory holds temporarily and will eventually be replaced with a more comprehensive approach. In contrast, in a
theory of principle, the axiomatic foundation consists solely of principles of nature that are derived from human experience. Unless these principles are found to be false in the future, the security of such a theory is
guaranteed. An example of a constructive theory is the kinetic theory of gases while classical thermodynamics and the theory of relativity belong to the class of principle theories.
and bound-water diffusion coefficients of a bleached kraft paperboard (BKP), which were estimated from steady-state moisture flux measurements in the first part of our work (see the preceding article in this issue), and no fitting parameter, the predictions of the dynamic moisture transport
model are found to be in good agreement with measurements of the transient weight change and relative humidity (RH) profile of stacks of BKP sheets subjected to ramp changes of the external RH under a variety of experimental conditions.
describing the unsteady-state transport of moisture in the thickness direction of paper is formulated that accounts for the parallel diffusion of moisture in the pore and fibre phases, as well as external mass-transfer resistance. The transport model is able to correlate measurements of the transient weight change and average relative humidity (RH) of stacks of bleached kraft paperboard sheets subjected to ramp changes of the external
RH with an average error of 9.3%.
and bound-water diffusion coefficients of a bleached kraft paperboard (BKP), which were estimated from steady-state moisture flux measurements in the first part of our work (see the preceding article in this issue), and no fitting parameter, the predictions of the dynamic moisture transport
model are found to be in good agreement with measurements of the transient weight change and relative humidity (RH) profile of stacks of BKP sheets subjected to ramp changes of the external RH under a variety of experimental conditions.
type whose axiomatic foundation consists of empirically observed principles and imaginary or speculative hypotheses. On this base is erected a logical superstructure (e.g. calculus) whose object is to make concrete predictions which can be tested against experiential data. A favourable comparison will point to validity of the hypotheses while an unfavourable one will require their revision. A constructive theory holds temporarily and will eventually be replaced with a more comprehensive approach. In contrast, in a
theory of principle, the axiomatic foundation consists solely of principles of nature that are derived from human experience. Unless these principles are found to be false in the future, the security of such a theory is
guaranteed. An example of a constructive theory is the kinetic theory of gases while classical thermodynamics and the theory of relativity belong to the class of principle theories.
and bound-water diffusion coefficients of a bleached kraft paperboard (BKP), which were estimated from steady-state moisture flux measurements in the first part of our work (see the preceding article in this issue), and no fitting parameter, the predictions of the dynamic moisture transport
model are found to be in good agreement with measurements of the transient weight change and relative humidity (RH) profile of stacks of BKP sheets subjected to ramp changes of the external RH under a variety of experimental conditions.