Showing papers on "Mass transfer published in 1992"

Ostwald Ripening of Two-Phase Mixtures

Abstract: Phase-separation processes frequently result in a polydisperse mixture of two phases of nearly equilibrium compositions and volume fractions. Such mixtures can also be created artificially by irradiating materials to create voids or, as is done in liquid phase sintering processes, by mixing together powders of different composition. Despite the nearly equilibrium state of the two-phase system, the mixture is not in its lowest energy state. This is because of the polydisperse nature of the mixture itself and the presence of a nonzero interfacial energy. Thus in the absence of elastic stress, the total interfacial area of the system must decrease with time in order for the system to reach thermodynamic equilibrium. There are many ways the system can reduce this excess interfacial area. The process of interest here is when the interfacial area is reduced via a diffusional mass transfer process from regions of high interfacial curvature to regions of low interfacial curvature. This interfacial area reduction process is commonly called coarsening, or Ostwald ripening, after the physical chemist W. Ostwald, who first described the process (I). This interfacial energy driven mass transfer process can significantly alter the morphology of the two-phase mixture. In general, the average size-scale of the mixture must increase with time and the number of second­ phase domains, or particles, must decrease with time. An example of an Ostwald ripening process is shown in Figure 1. The upper row of micro­ graphs shows the evolution of Sn-rich solid particles in an isothermal Pb­ Sn eutectic liquid as a function of time at constant magnification. Evident

Bacterial transport in porous media: Evaluation of a model using laboratory observations

Abstract: The factors that control the transport of bacteria through porous media are not well understood. The relative importance of the processes of dispersion, of immobilization of bacterial cells by various mechanisms (deposition), and of subsequent release of these trapped cells (entrainment) in describing transport has not been elucidated experimentally. Moreover, the variability of the phenomenological coefficients used to model these processes, given changes in such primary factors as grain size, organism, and ionic strength of the water, is unknown. We report results of fitting solutions of an advection-dispersion equation, modified to account for deposition and entrainment, to breakthrough curves from packed sand columns using two sizes of sand, two ionic strengths of the carrier solution, and two organisms with different sizes. A solution to the advection-dispersion equation including three processes, that is, dispersion, deposition, and entrainment, provides a match to the data that is superior to that achieved by solutions ignoring one of the processes. Fitted values of the coefficient describing deposition vary in a consistent manner with the control variables (organism, grain size, and ionic strength) and are generally within one order of magnitude of those predicted on the basis of theory.

Numerical modeling of steam injection for the removal of nonaqueous phase liquids from the subsurface. 1. Numerical formulation

Abstract: A multidimensional integral finite difference numerical simulator is developed for modeling the steam displacement of nonaqueous phase liquid (NAPL) contaminants in shallow subsurface systems. This code, named STMVOC, considers three flowing phases, gas, aqueous, and NAPL; and three mass components, air, water, and an organic chemical. Interphase mass transfer of the components between any of the phases is calculated by assuming local chemical equilibrium between the phases, and adsorption of the chemical to the soil is included. Heat transfer occurs due to conduction and multiphase convection and includes latent heat effects. A general equation of state is implemented in the code for calculating the thermophysical properties of the NAPL/chemical. This equation of state is primarily based on corresponding states methods of property estimation using a chemical's critical constants. The necessary constants are readily available for several hundred hazardous organic liquid chemicals. In part 2 (Falta et al., this issue), the code is used to simulate two one-dimensional laboratory steam injection experiments and to examine the effect of NAPL properties on the steam displacement process.

Polymerization of olefins through heterogeneous catalysis X: Modeling of particle growth and morphology

Abstract: The development of a detailed model describing particle growth in olefin copolymerization systems is presented. The Multigrain Model considers in detail monomer sorption, mass transfer, and changing porosity within the growing particle, as well as heat and mass transfer across the external film of the particle. The model predicts catalyst performance, including polymerization rates and particle morphology, in different reactor media without parameter adjustment. Internal void fractions are calculated through an examination of the relative growth rates within the growing particle. The model is used to examine the effects of mass transfer limitations, prepolymerization, and nonuniform metal distribution on the particle growth process. Model predictions of morphology show the same trends as observed experimentally.

Liquid-phase mass transfer coefficients in bioreactors.

Abstract: Liquid-phase mass transfer coefficient in bioreactors have been examined. A theoretical model based on the surface renewal concept has been devloped. The predicted liquid-phase mass transfer coefficients are compared with the experimental data for a mycelial fermentation broth (Chaetomium cellulolyticum) and model media (carboxymethyl cellulose) in a bench-scale bubble column reactor. The liquid-phase mass transfer coefficient is evaluated by dividing the volumetric mass transfer coefficient obtained experimentally by the specific surface area estimated using the available correlations. The available literature data in bubble column and stirred tank bioreactors is also used to test the validity of the proposed model. A reasonable agreement between the model and the experimental data is found.

Rate of reduction of FeO in slag by Fe-C drops

Abstract: The rate of reduction of FeO in slags by Fe-C drops plays an important role in several metallurgical processes, including iron bath smelting. In this study, the rate of this reaction was determined by measuring the volume of CO generated as a function of time, and the reaction was observed by X-ray fluoroscopy. The drops entered the slag in a nearly spherical shape, remained as single particles, and for the major portion of the reaction remained suspended in the slag surrounded by a gas halo. The rate was found to decrease with carbon content for alloys with low sulfur contents. The rate decreased significantly with increasing the sulfur content. Based on the results and a comparison of the calculated rates, for the possible rate-controlling mechanisms, a kinetic model was developed. The model is a mixed control model including mass transfer in the slag, mass transfer in the gas halo, and chemical kinetics at the metal interface. At high sulfur contents (>0.01 pct), the rate is primarily controlled by the dissociation of CO2 on the surface of the iron drop. At very low sulfur, the rate is controlled by the two mass-transfer steps and increases as the gas evolution from the particle increases.

Kinetic evaporation and condensation rates and their coefficients

Abstract: The origins and properties of evaporation and condensation coefficients are described, and results of their measurement are surveyed for water and liquid metals. Contrasts are drawn as to whether their values are likely to limit practical transfer rates at plane surfaces and on aerosols, and between evaporation and condensation. Existing theories which express condensation and evaporation rates in terms of the coefficients are described. Their failure to satisfy energy and momentum conservation as well as mass conservation at the interface is remedied by constructing a new theory which also starts with vapor molecules in Maxwell-Boltzmann distributions. The resulting rates are shown to be close to those predicted by more accurate theories in which the Boltzmann transport equation is solved.

Applying the two-resistance theory to contaminant volatilization in showers

Abstract: The two-resistance theory is applied to the transfer of volatile contaminants from shower water to indoor air by means of two transient mass balance models. Mass-transfer coefficients are calculated from reported experimental data for five full-scale shower systems. Liquid- and gas-phase coefficients differ substantially from one shower system to another although both appear to increase with water flow rate. Mass transfer in showers appears to be strongly influenced by the type of showerhead but is unaffected by the presence of a showering individual

Rate‐limited mass transfer and transport of organic solutes in porous media that contain immobile immiscible organic liquid

Abstract: A general model is presented that simulates the effect of an immobile immiscible organic liquid, as well as rate-limited solid phase sorption, on the transport of dissolved organic contaminants in heterogeneous porous media. Specific models are developed for four cases (1) immobile immiscible liquid that resides in nonadvective domains of a heterogeneous porous medium; (2) immobile immiscible liquid that resides in the advective domain; (3) homogeneous porous media wherein mass transfer within the immiscible liquid, as well as across the liquid-water interface, is rate limited; (4) homogeneous porous media with a single resistance to liquid-liquid mass transfer. The performance of the homogeneous-based, single-resistance model was evaluated by attempting to predict a break-through curve reported in the literature. Based on the successful prediction of the data, where values for all parameters were obtained independent of the data being simulated, it appears that the conceptual basis of the model is valid. Through a series of simulations, the effect of the immiscible liquid on retention was shown to be great, even at relatively low levels of saturation. Release of solute from residual saturation located within regions of relatively low hydraulic conductivity can be significantly rate limited, even when mass transfer between immiscible liquid and water is rapid. This has ramifications concerning the efficacy of remediation systems based on imposed hydraulic gradients (e.g., pump-and-treat). The model should prove useful in further investigations of the effect of immobile immiscible organic liquids on the retention and transport of organic solutes in porous media.

Transport Phenomena of Foods and Biological Materials

Abstract: INTRODUCTION. DEFINITIONS. Food and Bioengineering. Unit Operations and Physical Models. AIM AND SCOPE. GENERAL MODELS OF TRANSPORT PHENOMENA. RIGOROUS MATHEMATICAL MODELS. The Generalized Diffusion Equation (GDE). In One Dimension. Extension in Three Dimensions and Other Geometrics. Including Convection and Source Terms. Physical Meaning of the Time Derivatives. Methods of Solution of GDE. The Particular Transport Cases. Analogies. Mass and Heat Transfer. Momentum Transfer. The Steady-State Case. The General Resistance Model. Resistances in Series and in Parallel. Interfacial Transport and Transfer Coefficients. Heat Transfer. Mass Transfer. Momentum Transfer. Solution of the GDE with Interfacial Limitations. SEMIEMPIRICAL MODELS. Dimensionless Numbers. Momentum Transfer. Ratios of Diffusivities. The Peclet Number. The Grashof Number. The Graetz Number. The Stanton Number. The Psychrometric Ratio. Correlations. Forced Convection. Free or Natural Convections. Use of Correlations. PHENOMENOLOGICAL MODELS. Irreversible Thermodynamics. The Chemical Potential as a Driving Force. The Electrochemical Potential as a Driving Force. THE STEFAN-MAXWELL APPROACH. EMPIRICAL MODELS. CHARACTERIZATION AND PROPERTIES OF FOODS AND OTHER BIOLOGICAL MATERIALS. CLASSIFICATION AND RHEOLOGICAL BEHAVIOR. Foods. Microbial Cells. CASES OF TRANSPORT PHENOMENA. In Foods. In Biochemical Engineering. TRANSPORT PROPERTIES. Thermal Properties. Mass Transfer Properties. Sorption Isotherms. Mass Diffusivity. CELL STRUCTURE AND MULTIPHASE TRANSPORT. Description. Pathways of Transport. TRANSPORT PHENOMENA OF LIQUID PRODUCTS. HEAT AND MASS TRANSFER IN NON-NEWTONIAN PIPE FLOW. Laminar Flow. Turbulence. Rigorous Models. Semi-Empirical Models. AGITATED SYSTEMS. General Concepts. Dimensionless Numbers. TRANSPORT PHENOMENA IN SOLID FOODS. SIMULTANEOUS HEAT AND MASS TRANSFER. To the Product. Within the Product. The Crust. The Evaporation Zone. SHORT-CUT MODELS. The Regular-Regime Model. Constant Period. Penetration Period. Regular-Regime. Drying Curves. The Shrinking-Core Model. THE PROBLEM OF SHRINKAGE. The Approach of Crank. A Modified Crank Approach. Other Approaches. USE OF THE CHEMICAL POTENTIAL AS THE DRIVING FORCE. Early Attempts. The Bahia-Blanca Approach. IRREVERSIBLE THERMODYNAMICS AND SIMULTANEOUS TRANSPORT. TRANSPORT PHENOMENA AND THE SOURCE TERM. THE MASS TRANSFER SOURCE TERM: TRANSPORT AND REACTION. In Foods. Zero Order. First Order. Simultaneous Reactions. Other Models. Enzymatic Reactions. THE HEAT TRANSFER SOURCE TERM. Viscous Dissipation. Latent Heat. Radiation. Electrical Properties. Radiation Source Term. TRANSPORT PHENOMENA MODELS IN SOME UNIT OPERATIONS AND PROCESSING EQUIPMENT. PROCESSING EQUIPMENT FOR LIQUIDS. Heat Exchangers. Tubular. Plate. Scraped Surface. Cooking Extruders. Boilers. UNIT OPERATIONS WITH SOLIDS. BIOREACTORS. EPILOGUE. COUPLING TO THE DESIGN PROCESS. Macroscopic Balances. Correction Factors. FUTURE TRENDS. Rigorous Mathematical Modeling. Trends in Computational Capacity. Commercial Computer Programs. Phenomenological and Other Alternative Models. Irreversible Thermodynamics. The Chemical and Electrochemical Potential as Driving Forces. Rheological Studies. Heat and Mass Transfer Properties. Modeling in Biochemical Engineering. Cell Structure and Geometry. Instabilities and Modern Chaos Theory. Fundamental Transport Phenomena Modeling in Connection to Scale Up and Design Aspects. Closure.

Chemical reactors for gas-liquid systems

Abstract: Classification of gas-liquid reactors mass transfer with chemical or biochemical reaction flow of phases in gas-liquid reactors decisive design characteristics of gas-liquid reactors criteria for reactor type selection hydrodynamics and mass transfer in three-phase systems dynamic behaviour of gas-liquid reactors calculation of gas-liquid reactors.

The grafting of maleic-anhydride on high-density polyethylene in an extruder

Abstract: The grafting of maleic anhydride (MAH) on high density polyethylene in a counter-rotating twin screw extruder has been studied. As the reaction kinetics appear to be affected by mass transfer, good micro mixing in the extruder is important. Due to the competing mechanisms of increasing mixing and decreasing residence times at increasing screw speed, and due to the complicated reaction scheme. various non-linearities exist that are prohibitive for simple optimization rules. The interaction diagram presented in this paper for a twin screw extruder as a MAH grafting reactor can be used for better understanding of the influence of the extruder parameters on the reaction process.

A model and experimental study of evaporation from bare-soil surfaces

Abstract: A model is constructed for estimating evaporation from bare-soil surfaces. In the model, the evaporation is parameterized with the soil-water content for the upper 2 cm of the soil (Kondo et al.), and the heat and water transport within the soil layer below 2 cm is explicitly described by the heat conduction and moisture diffusion equations. Experiments on evaporation from loam packed in pans are also carried out. The present model well simulates the observed evaporation and vertical profiles of soil temperature and water content. Long time simulations of evaporation by the present model an compared with the force-restore method and the bucket model for a drying period of over several months. The decrease in evaporation rate for the bucket model is comparatively small. However, the evaporation by the present model and the force-restore method decreases rapidly several days after the beginning of the drying period. Differences between the evaporation by the present model and that by the force-rest...