William Strieder - Academia.edu (original) (raw)

Papers by William Strieder

Research paper thumbnail of Modeling and Modification of the Electromagnetic Properties of Advanced Composite Materials

: The electromagnetic hazards involved in using composite materials in aircraft are considered. A... more : The electromagnetic hazards involved in using composite materials in aircraft are considered. Attention is focused on the problems associated with the lower conductivities of composites in comparison to those of metals. The concept of a high conductivity composite is advanced as a solution to the electromagnetic problems associated with presently available composites. The electrical properties of available advanced composite materials, primarily graphite/epoxy and boron/epoxy, are presented. Basic deterministic models relating the electrical conductivities (D.C. to 50 MHz) of composites to the fiber conductivity, the matrix conductivity and the volume fraction of the fibers are developed. The electrical behavior of as-manufactured graphite and boron fibers is also detailed. The possibility of 'doping' fibers with suitable impurities to increase conductivity without an associated decrease in specific strength is explored. Boron fibers undergo a recrystallization when heated...

Research paper thumbnail of Cold Weather Transit Technology Program. Volume 2: Physics of Ice and Snow at the Interface with Transitway Surfaces

This report is one volume of a nine-volume report associated with the Cold Weather Transit Techno... more This report is one volume of a nine-volume report associated with the Cold Weather Transit Technology (CWTT) program of the Urban Mass Transportation Administration. The objective of the program is to improve existing transportation operations during severe cold ice and snow environments and to develop new and more effective methods for assuring the dependable operation of the system in severe winter conditions. The findings of this program are intended to assist administrators, designers, planners, operators, suppliers, and others involved in the design, implementation, and operation of mass transit systems which operate in cold weather environments. This volume addresses the fundamental properties of materials which are affected by ice and snow in transit system normal operation. It presents basic research results in eight areas which focus on the fundamental information necessary to deal with the effects of ice and snow on transit systems. These eight areas are identified candida...

Research paper thumbnail of Diffusion and convection in porous catalysts

Research paper thumbnail of Cold Weather Transit Technology Program. Volume 2: Transit System Survey

This report is one of a series of reports associated with the Cold Weather Transit Technology (CW... more This report is one of a series of reports associated with the Cold Weather Transit Technology (CWTT) Program being implemented by the Urban Mass Transportation Administration (UMTA) of the U.S. Department of Transportation through a grant to the University of Notre Dame with the Vought Corporation acting as the principal contractor. Initially, the CWTT program thrust was directed to solutions to automated guideway transit (AGT) system cold weather problems in support of the Downtown People Mover (DPM) program. The CWTT program has been redirected/extended and now focuses on obtaining solutions for cold weather problems of existing transit systems. The objective of the extended/redirected CWTT program is to provide near term solutions for problems of existing transit systems operating in cold weather. This report documents the findings of a survey made to determine the extent and nature of cold weather problems that affect mass transit systems. The survey included phone conversations...

Research paper thumbnail of Heterogeneous Catalysis

Springer Tracts in Natural Philosophy, 1973

Research paper thumbnail of Approximate solutions for nonlinear gas-solid noncatalytic reactions

AIChE Journal, 1993

In the context of gas-solid noncatalytic reactions, several models have been developed in the lit... more In the context of gas-solid noncatalytic reactions, several models have been developed in the literature (for comprehensive reviews, cf. Szekely et al., 1976; Doraiswamy and Sharma, 1984). This work focuses on the sharp-interface model (SIM), which can be used to describe, once incorporated into a suitable reactor model, a variety of chemical and metallurgical processes including the roasting of zinc sulfide (Yoshida and Wen, 1970) and the combustion of coal (Baron et al., 1978). Under the assumptions of isothermal conditions, equimolar counterdiffusion of reacting and product gases and pseudo-steadystate approximation, an analytical relationship that provides the time required to reach the desired conversion of a single particle of the solid reactant can be derived in a straightforward manner for the case of a first-order reaction with respect to the gaseous reactant (Szekely et al., 1976). The assumption of a first-order reaction, however, can be valid only over a limited range of conditions and may not even be true when the gaseous reactant is adsorbed strongly on the solid surface. A number of examples of nonlinear gas-solid noncatalytic reactions are reported in the literature (Cannon and Denbigh, 1957; Habashi, 1969; Chu and Rahmel, 1979). For nonlinear kinetics, the conversion of the solid reactant as a function of time has to be computed numerically, as shown by Sohn and Szekely (1972) for power-law kinetics and by Ramachandran (1982) for Langmuir-Hinshelwood (L-H) kinetics. Since the analysis for a reactor requires solving the single particle problem repeatedly at every axial and radial position within the reactor, this can be cumbersome if the single particle problem itself has to be solved numerically. Thus, it is of interest to develop good approximate solutions for the case of nonlinear reactions. Several recent publications (Regalbuto et al., 1988, 1989, the references given there) have discussed systematic procedures to obtain good approximate solutions to nonlinear diffusion-reaction equations using the Maximum Principle (Protter and Weinberger, 1967). A unique advantage of this technique, not present in alternative methods, is that it provides rigorous upper and lower bounds on the true nu-Correspondence concerning this work should be addressed to either A. Varma or W.

Research paper thumbnail of Radiation heat transfer down an elongated spheroidal cavity

AIChE Journal, 1997

Effects of elongation on the radiation heat transport down a spheroidal cavity, located in a cond... more Effects of elongation on the radiation heat transport down a spheroidal cavity, located in a conducting solid with a difisely reflecting cavitysolid interface, are examined. A n effective conductivity A, and a void radiation conductivity A, are obtained as a function of cavity eccentricity a and surface emissivity E. To facilitate the calculations and produce readily applicable equations, a rigorous variational principle is used. Exact solutions are generated in the neighborhood of the spherical cavity (a ' + 0) for any E > 0, a long needle-shaped void (a 2 + 1) for any E > 0, and a pegect reflector (E + 0) for arbitrary elongation (0 I a I I). Signifcant differences arising from the shape change are observed. The a ' + 0 edge demonstrates a linear increase in A, with E. A t the opposite edge a ' + 1 and positive E, A, is a horizontal line independent of E , much like the long cylinder, whose conductivity is a factor of 3 2 / (9~) (= 1.13) latger. In the neighborhood of E + 0, A, is always zero for any 0 I a 2 I 1. The emissivity slope for E + 0 starts from unity at a ' = 0 and increases monotonically with elongation to a singularity 3~[ 1 6 (1a')]-' as a'-+ 1 for the long needle. A, would be to select the A, form that gives a "best"va1ue for a rigorously defined A,. One fruitful approach is to use a

Research paper thumbnail of Analysis and shape inequalities for gas-solid reactions with changing volume

AIChE Journal, 1995

ABSTRACT For gas-solid noncatalytic reactions following the sharp-interface model, some fundament... more ABSTRACT For gas-solid noncatalytic reactions following the sharp-interface model, some fundamental aspects, not discussed previously in the literature, are presented for particle shapes where diffusion processes are described by a single space dimension. A detailed structure analysis of the solution for monotone nonlinear kinetics reveals interesting differences in the dynamics of the interfacial reaction front, including local maxima and minima in the rate of reaction interface motion, depending on particle shape and expanding or shrinking particle size. Rigorous shape inequalities on the interfacial reactant concentration, the motion of the reaction front and the particle conversion for the sphere and slab, and cylinder and slab geometries are obtained for any nonlinear monotonically increasing reaction kinetics and a wide range of parameter values. By taking advantage of these inequalities, the fraction of original solids of spherical or cylindrical shape, which remains unconverted at the exit of a fluidized-bed reactor, is bounded by the corresponding quantities related to the slab shape. As an example, a first-order reaction of the gaseous reactant is considered, where expressions for the reactor are obtained analytically, without any assumptions about possible controlling regimes. These analytical bounds for reactor conversion closely approximate the numerical solutions for design purposes.

Research paper thumbnail of Radiation perpendicular to the symmetry axis of prolate and oblate cavities

AIChE Journal, 1998

ABSTRACT Thermal radiation heat transport within prolate and oblate ellipsoidal cavities was exam... more ABSTRACT Thermal radiation heat transport within prolate and oblate ellipsoidal cavities was examined. The axisymmetric anisotropy of the cavity shape gives rise to a thermal radiation conductivity tensor with principal axes components parallel (λr, ‖) and perpendicular (λr, ⊥) to the symmetry axis. The prolate (λr, ⊥) and oblate (λr, ⊥) transverse components are calculated and compared with well-known results from the kinetic theory of transport across cylindrical and within slit void geometries. The use of λr, ⊥ and λr, ⊥, along with earlier results for λr, ‖ and λr, ‖, in well-known effective conductivity equations for spheroidal inclusions within a solid matrix, provides a means to rigorously treat cavity orientation and shape in high-temperature heat transport across porous materials. To facilitate the calculations and produce readily usable equations, a variational principle is used.

Research paper thumbnail of Ligand diffusion, receptor binding, and internalization: Zeroth-order kinetics

AIChE Journal, 2000

The exact, analytical solution for steady-state diffusion and zeroth-order surface reac-() tion a... more The exact, analytical solution for steady-state diffusion and zeroth-order surface reac-() tion at a cell-wall chemoreceptor site is presented. Following Berg 1993 , and others, the receptor is modeled as a chemically acti®e circular site on an impermeable, inert cell wall. Explicit ®alues of the dimensionless site-specific rate constant mark the regions of chemical-, transitional-and diffusion-controlled kinetics. Particularly when the Michaelis-Menten constant is small relati®e to the ligand bulk concentration, this simple form of the receptor-site reaction current should pro®ide a useful model for cell growthfactor internalization, nutrient uptake, and certain cellular signaling beha®iors. Various biophysical conditions that cause site mass-transport resistance in cellular site-reaction kinetic processes are discussed. c Eq. 2a describes the active site surface kinetics at every point on the unit circular site, and the reaction rate current R is 0 a 2 :

Research paper thumbnail of Radiation heat transport in disordered media

Advances in Water Resources, 1997

Research paper thumbnail of Synthesis of reaction-bonded silicon nitride: Experiments and theory

The intrinsic kinetics of the overall reaction of silicon nitridation, as well as the individual ... more The intrinsic kinetics of the overall reaction of silicon nitridation, as well as the individual reactions that form the two phases {alpha} and {beta} at temperatures below the melting point of Si (1414 {degrees}C), are reported. A mathematical model, to represent the reaction-bonding process and to predict the overall conversion as well as the {alpha}/{beta} phase ratio evolution, is described. One promising method to synthesize silicon nitride (Si{sub 3}N{sub 4}), an advanced ceramic material with high strength and heat-resistant properties, is by direct nitridation of silicon powder compact, at temperatures below its melting point, to form a reaction-bonded body. This noncatalytic gas-solid reaction is characterized by a volume increase of the individual Si particles, pore filling of the compact and particle overlapping as the reaction proceeds. This impedes diffusion of reactant nitrogen into the interstitial space, and can result in a product with fully reacted outer layer with...

Research paper thumbnail of Series reactions A→B→C on successive spheres

Chemical Physics, 2016

Abstract The twin spherical harmonic expansion method with iterative solution of the coefficient ... more Abstract The twin spherical harmonic expansion method with iterative solution of the coefficient equations is used to generate a rigorous analytical solution for the rate of series reaction, A → B → C, occurring, respectively, on two successive spheres of radius a1 and a2, a center-to-center distance d apart. To investigate the influences of the intersphere diffusion and geometry, diffusion-controlled reactions are considered. Results are presented as a series expansion of the dimensionless reaction rate R in terms of the dimensionless center-to-center sphere separation d ¯ ( = d / ( a 1 + a 2 ) ) reciprocals, and for various sphere radius ratios γ ( = a 1 / a 2 ) . When the sphere radius ratio γ is less than unity, a maximum in the series reaction rate is found for a d ¯ of about 1.05. Also an exact value of the series dimensionless reaction rate of ln2 is obtained in the limit γ → 0 (very large a2 or very small a1) for spheres in contact. Results suggest that the plots of reaction rates for contacting spheres can be extrapolated versus γ to the ln2 limit at γ → 0, and that the rate maximum effect is large in the γ → 0 limit.

Research paper thumbnail of Effects of surface rates for the series reaction A → B → C on successive separated spherical sites

Chemical Physics

A steady - state series reaction A →B → C, consisting of a first reaction A →B on sphere 1 of rad... more A steady - state series reaction A →B → C, consisting of a first reaction A →B on sphere 1 of radius a1 with first order kinetic rate constant kA and reactant diffusivity DA, followed by a second reaction B → C on sphere 2 of radius a2 with a first order kinetic rate constant kB and a B chemical species diffusivity DB, occurs on two discrete chemically active spheres a center - to – center distance d apart. The twin spherical harmonic expansion method with a Neumann iterative solution of the coefficient equations is used to generate a rigorous solution for the rate of series reaction in terms of an expansion in the inverse dimensionless center - to - center sphere separation d (=d⁄((a_1+a_2 ))) up to the inverse thirteenth power. The expansion coefficients depend on three dimensionless parameters (γ,λ_A,λ_B), where the dimensionless inverse surface kinetic constants are λ_A=D_A⁄a_1 kA on sphere 1, λ_B=D_B⁄(a_2 k_B ) on the sphere 2, while the geometry enters as the radius ratio γ=a_1⁄a_2 . Using these results an equivalent site kinetic change is imposed, first to λ_Aon site 1, then to λ_Bon site 2, to determine which site is more influential for the overall series reaction rate. Effects of γ geometry modification at several fixed kinetic surface site rates are examined. When either one of reactive spheres is diffusion controlled, various levels of λ kinetic controls at the other site or γ site geometries are generated to study the effects of site kinetics or geometry control on the series reaction rate. As the “other site” reaction rate also increases toward diffusion control, inflection points are observed to develop as precursors to a local maximum on the series reaction rate versus sphere separation curves. An application to the isomerization of n-pentane is presented.

Research paper thumbnail of Diffusion Through a Porous Medium

Springer Tracts in Natural Philosophy, 1973

The principal object of this chapter is the estimation of the effective diffusion coefficient D e... more The principal object of this chapter is the estimation of the effective diffusion coefficient D e of a solute in a gaseous or liquid mixture when the mixture is in the presence of a suspended solid phase. Bounds on D e are calculated for an isotropic suspension whose only known statistical property is the void fraction, these are rigorously shown to be the “best possible bounds” that can be obtained with such limited information. Improved upper bounds on D e are obtained when an explicit model pore structure is generated from randomly overlapping, solid spheres.

Research paper thumbnail of Effective-medium theory of the conductivity for a random-site honeycomb lattice

Journal of Physics C: Solid State Physics

ABSTRACT The effective-medium theory for the random-site model of a percolating honeycomb lattice... more ABSTRACT The effective-medium theory for the random-site model of a percolating honeycomb lattice is formulated. The value of the critical site concentration obtained, xc=0.707, is compared with the series value xc=0.70+or-0.01 and the Monte Carlo value xc=0.688+or-0.015.

Research paper thumbnail of Effective medium theory of site percolation in a random simple triangular conductance network

Journal of Physics C: Solid State Physics

... into the effective infinite lattice, ie, figure l(a) with go = 9,. The electrical potential 4... more ... into the effective infinite lattice, ie, figure l(a) with go = 9,. The electrical potential 4(x, y) at the various sites of the infinite triangular lattice have been derived through a straightforward though tedious extension of Van Der Pol and Bremmer's ... AV = ug , - go)/[go - 9, + 2 e - 2 ~ 3 1 w ...

Research paper thumbnail of Critical exponents for conduction in a honeycomb random site lattice

Journal of Physics C: Solid State Physics

ABSTRACT Monte Carlo simulation conductivity calculations for the honeycomb random site resistor ... more ABSTRACT Monte Carlo simulation conductivity calculations for the honeycomb random site resistor lattice have been performed for lattice sizes from 200*200 at higher site fractions up to 1400*1400 near percolation. Lattice conductivity curves were compared with EMT results, also backbone beta '=0.38+or-0.02 and conductivity t=1.27+or-0.04 critical exponents were obtained.

Research paper thumbnail of Monte Carlo simulation of the conductivity of the two-dimensional triangular site network

Journal of Physics C: Solid State Physics

ABSTRACT The full conductivity curve for the triangular random site resistor network is calculate... more ABSTRACT The full conductivity curve for the triangular random site resistor network is calculated using Monte Carlo simulation. Lattice sizes range from 100*100 for higher site fractions up to 1400*1400 near percolation. Conductivity curves are compared with EMT and the conductivity exponent t=1.23+or-0.04 is obtained.

Research paper thumbnail of The Sharp Interface Model:Zero-Order Reaction with Volume Change

Industrial Engineering Chemistry Research, 1995

The sharp interface model is examined for isothermal gas-solid reactions following zero-order kin... more The sharp interface model is examined for isothermal gas-solid reactions following zero-order kinetics with respect to the gas phase and first-order kinetics with respect to the solid phase for spherical particles either shrinking or growing during reaction. It is shown that depending on the relative magnitudes of the governing parameters which include the volume expansion factor, Damkohler number, and mass Biot number, it is possible to have up to three successive transitions from one controlling regime (external mass transfer, product layer diffusion, or chemical kinetics) to another as the reaction evolves with time. This behavior gives rise to various gas concentration and solid conversion profiles. A classification of all the possible situations is made.

Research paper thumbnail of Modeling and Modification of the Electromagnetic Properties of Advanced Composite Materials

: The electromagnetic hazards involved in using composite materials in aircraft are considered. A... more : The electromagnetic hazards involved in using composite materials in aircraft are considered. Attention is focused on the problems associated with the lower conductivities of composites in comparison to those of metals. The concept of a high conductivity composite is advanced as a solution to the electromagnetic problems associated with presently available composites. The electrical properties of available advanced composite materials, primarily graphite/epoxy and boron/epoxy, are presented. Basic deterministic models relating the electrical conductivities (D.C. to 50 MHz) of composites to the fiber conductivity, the matrix conductivity and the volume fraction of the fibers are developed. The electrical behavior of as-manufactured graphite and boron fibers is also detailed. The possibility of 'doping' fibers with suitable impurities to increase conductivity without an associated decrease in specific strength is explored. Boron fibers undergo a recrystallization when heated...

Research paper thumbnail of Cold Weather Transit Technology Program. Volume 2: Physics of Ice and Snow at the Interface with Transitway Surfaces

This report is one volume of a nine-volume report associated with the Cold Weather Transit Techno... more This report is one volume of a nine-volume report associated with the Cold Weather Transit Technology (CWTT) program of the Urban Mass Transportation Administration. The objective of the program is to improve existing transportation operations during severe cold ice and snow environments and to develop new and more effective methods for assuring the dependable operation of the system in severe winter conditions. The findings of this program are intended to assist administrators, designers, planners, operators, suppliers, and others involved in the design, implementation, and operation of mass transit systems which operate in cold weather environments. This volume addresses the fundamental properties of materials which are affected by ice and snow in transit system normal operation. It presents basic research results in eight areas which focus on the fundamental information necessary to deal with the effects of ice and snow on transit systems. These eight areas are identified candida...

Research paper thumbnail of Diffusion and convection in porous catalysts

Research paper thumbnail of Cold Weather Transit Technology Program. Volume 2: Transit System Survey

This report is one of a series of reports associated with the Cold Weather Transit Technology (CW... more This report is one of a series of reports associated with the Cold Weather Transit Technology (CWTT) Program being implemented by the Urban Mass Transportation Administration (UMTA) of the U.S. Department of Transportation through a grant to the University of Notre Dame with the Vought Corporation acting as the principal contractor. Initially, the CWTT program thrust was directed to solutions to automated guideway transit (AGT) system cold weather problems in support of the Downtown People Mover (DPM) program. The CWTT program has been redirected/extended and now focuses on obtaining solutions for cold weather problems of existing transit systems. The objective of the extended/redirected CWTT program is to provide near term solutions for problems of existing transit systems operating in cold weather. This report documents the findings of a survey made to determine the extent and nature of cold weather problems that affect mass transit systems. The survey included phone conversations...

Research paper thumbnail of Heterogeneous Catalysis

Springer Tracts in Natural Philosophy, 1973

Research paper thumbnail of Approximate solutions for nonlinear gas-solid noncatalytic reactions

AIChE Journal, 1993

In the context of gas-solid noncatalytic reactions, several models have been developed in the lit... more In the context of gas-solid noncatalytic reactions, several models have been developed in the literature (for comprehensive reviews, cf. Szekely et al., 1976; Doraiswamy and Sharma, 1984). This work focuses on the sharp-interface model (SIM), which can be used to describe, once incorporated into a suitable reactor model, a variety of chemical and metallurgical processes including the roasting of zinc sulfide (Yoshida and Wen, 1970) and the combustion of coal (Baron et al., 1978). Under the assumptions of isothermal conditions, equimolar counterdiffusion of reacting and product gases and pseudo-steadystate approximation, an analytical relationship that provides the time required to reach the desired conversion of a single particle of the solid reactant can be derived in a straightforward manner for the case of a first-order reaction with respect to the gaseous reactant (Szekely et al., 1976). The assumption of a first-order reaction, however, can be valid only over a limited range of conditions and may not even be true when the gaseous reactant is adsorbed strongly on the solid surface. A number of examples of nonlinear gas-solid noncatalytic reactions are reported in the literature (Cannon and Denbigh, 1957; Habashi, 1969; Chu and Rahmel, 1979). For nonlinear kinetics, the conversion of the solid reactant as a function of time has to be computed numerically, as shown by Sohn and Szekely (1972) for power-law kinetics and by Ramachandran (1982) for Langmuir-Hinshelwood (L-H) kinetics. Since the analysis for a reactor requires solving the single particle problem repeatedly at every axial and radial position within the reactor, this can be cumbersome if the single particle problem itself has to be solved numerically. Thus, it is of interest to develop good approximate solutions for the case of nonlinear reactions. Several recent publications (Regalbuto et al., 1988, 1989, the references given there) have discussed systematic procedures to obtain good approximate solutions to nonlinear diffusion-reaction equations using the Maximum Principle (Protter and Weinberger, 1967). A unique advantage of this technique, not present in alternative methods, is that it provides rigorous upper and lower bounds on the true nu-Correspondence concerning this work should be addressed to either A. Varma or W.

Research paper thumbnail of Radiation heat transfer down an elongated spheroidal cavity

AIChE Journal, 1997

Effects of elongation on the radiation heat transport down a spheroidal cavity, located in a cond... more Effects of elongation on the radiation heat transport down a spheroidal cavity, located in a conducting solid with a difisely reflecting cavitysolid interface, are examined. A n effective conductivity A, and a void radiation conductivity A, are obtained as a function of cavity eccentricity a and surface emissivity E. To facilitate the calculations and produce readily applicable equations, a rigorous variational principle is used. Exact solutions are generated in the neighborhood of the spherical cavity (a ' + 0) for any E > 0, a long needle-shaped void (a 2 + 1) for any E > 0, and a pegect reflector (E + 0) for arbitrary elongation (0 I a I I). Signifcant differences arising from the shape change are observed. The a ' + 0 edge demonstrates a linear increase in A, with E. A t the opposite edge a ' + 1 and positive E, A, is a horizontal line independent of E , much like the long cylinder, whose conductivity is a factor of 3 2 / (9~) (= 1.13) latger. In the neighborhood of E + 0, A, is always zero for any 0 I a 2 I 1. The emissivity slope for E + 0 starts from unity at a ' = 0 and increases monotonically with elongation to a singularity 3~[ 1 6 (1a')]-' as a'-+ 1 for the long needle. A, would be to select the A, form that gives a "best"va1ue for a rigorously defined A,. One fruitful approach is to use a

Research paper thumbnail of Analysis and shape inequalities for gas-solid reactions with changing volume

AIChE Journal, 1995

ABSTRACT For gas-solid noncatalytic reactions following the sharp-interface model, some fundament... more ABSTRACT For gas-solid noncatalytic reactions following the sharp-interface model, some fundamental aspects, not discussed previously in the literature, are presented for particle shapes where diffusion processes are described by a single space dimension. A detailed structure analysis of the solution for monotone nonlinear kinetics reveals interesting differences in the dynamics of the interfacial reaction front, including local maxima and minima in the rate of reaction interface motion, depending on particle shape and expanding or shrinking particle size. Rigorous shape inequalities on the interfacial reactant concentration, the motion of the reaction front and the particle conversion for the sphere and slab, and cylinder and slab geometries are obtained for any nonlinear monotonically increasing reaction kinetics and a wide range of parameter values. By taking advantage of these inequalities, the fraction of original solids of spherical or cylindrical shape, which remains unconverted at the exit of a fluidized-bed reactor, is bounded by the corresponding quantities related to the slab shape. As an example, a first-order reaction of the gaseous reactant is considered, where expressions for the reactor are obtained analytically, without any assumptions about possible controlling regimes. These analytical bounds for reactor conversion closely approximate the numerical solutions for design purposes.

Research paper thumbnail of Radiation perpendicular to the symmetry axis of prolate and oblate cavities

AIChE Journal, 1998

ABSTRACT Thermal radiation heat transport within prolate and oblate ellipsoidal cavities was exam... more ABSTRACT Thermal radiation heat transport within prolate and oblate ellipsoidal cavities was examined. The axisymmetric anisotropy of the cavity shape gives rise to a thermal radiation conductivity tensor with principal axes components parallel (λr, ‖) and perpendicular (λr, ⊥) to the symmetry axis. The prolate (λr, ⊥) and oblate (λr, ⊥) transverse components are calculated and compared with well-known results from the kinetic theory of transport across cylindrical and within slit void geometries. The use of λr, ⊥ and λr, ⊥, along with earlier results for λr, ‖ and λr, ‖, in well-known effective conductivity equations for spheroidal inclusions within a solid matrix, provides a means to rigorously treat cavity orientation and shape in high-temperature heat transport across porous materials. To facilitate the calculations and produce readily usable equations, a variational principle is used.

Research paper thumbnail of Ligand diffusion, receptor binding, and internalization: Zeroth-order kinetics

AIChE Journal, 2000

The exact, analytical solution for steady-state diffusion and zeroth-order surface reac-() tion a... more The exact, analytical solution for steady-state diffusion and zeroth-order surface reac-() tion at a cell-wall chemoreceptor site is presented. Following Berg 1993 , and others, the receptor is modeled as a chemically acti®e circular site on an impermeable, inert cell wall. Explicit ®alues of the dimensionless site-specific rate constant mark the regions of chemical-, transitional-and diffusion-controlled kinetics. Particularly when the Michaelis-Menten constant is small relati®e to the ligand bulk concentration, this simple form of the receptor-site reaction current should pro®ide a useful model for cell growthfactor internalization, nutrient uptake, and certain cellular signaling beha®iors. Various biophysical conditions that cause site mass-transport resistance in cellular site-reaction kinetic processes are discussed. c Eq. 2a describes the active site surface kinetics at every point on the unit circular site, and the reaction rate current R is 0 a 2 :

Research paper thumbnail of Radiation heat transport in disordered media

Advances in Water Resources, 1997

Research paper thumbnail of Synthesis of reaction-bonded silicon nitride: Experiments and theory

The intrinsic kinetics of the overall reaction of silicon nitridation, as well as the individual ... more The intrinsic kinetics of the overall reaction of silicon nitridation, as well as the individual reactions that form the two phases {alpha} and {beta} at temperatures below the melting point of Si (1414 {degrees}C), are reported. A mathematical model, to represent the reaction-bonding process and to predict the overall conversion as well as the {alpha}/{beta} phase ratio evolution, is described. One promising method to synthesize silicon nitride (Si{sub 3}N{sub 4}), an advanced ceramic material with high strength and heat-resistant properties, is by direct nitridation of silicon powder compact, at temperatures below its melting point, to form a reaction-bonded body. This noncatalytic gas-solid reaction is characterized by a volume increase of the individual Si particles, pore filling of the compact and particle overlapping as the reaction proceeds. This impedes diffusion of reactant nitrogen into the interstitial space, and can result in a product with fully reacted outer layer with...

Research paper thumbnail of Series reactions A→B→C on successive spheres

Chemical Physics, 2016

Abstract The twin spherical harmonic expansion method with iterative solution of the coefficient ... more Abstract The twin spherical harmonic expansion method with iterative solution of the coefficient equations is used to generate a rigorous analytical solution for the rate of series reaction, A → B → C, occurring, respectively, on two successive spheres of radius a1 and a2, a center-to-center distance d apart. To investigate the influences of the intersphere diffusion and geometry, diffusion-controlled reactions are considered. Results are presented as a series expansion of the dimensionless reaction rate R in terms of the dimensionless center-to-center sphere separation d ¯ ( = d / ( a 1 + a 2 ) ) reciprocals, and for various sphere radius ratios γ ( = a 1 / a 2 ) . When the sphere radius ratio γ is less than unity, a maximum in the series reaction rate is found for a d ¯ of about 1.05. Also an exact value of the series dimensionless reaction rate of ln2 is obtained in the limit γ → 0 (very large a2 or very small a1) for spheres in contact. Results suggest that the plots of reaction rates for contacting spheres can be extrapolated versus γ to the ln2 limit at γ → 0, and that the rate maximum effect is large in the γ → 0 limit.

Research paper thumbnail of Effects of surface rates for the series reaction A → B → C on successive separated spherical sites

Chemical Physics

A steady - state series reaction A →B → C, consisting of a first reaction A →B on sphere 1 of rad... more A steady - state series reaction A →B → C, consisting of a first reaction A →B on sphere 1 of radius a1 with first order kinetic rate constant kA and reactant diffusivity DA, followed by a second reaction B → C on sphere 2 of radius a2 with a first order kinetic rate constant kB and a B chemical species diffusivity DB, occurs on two discrete chemically active spheres a center - to – center distance d apart. The twin spherical harmonic expansion method with a Neumann iterative solution of the coefficient equations is used to generate a rigorous solution for the rate of series reaction in terms of an expansion in the inverse dimensionless center - to - center sphere separation d (=d⁄((a_1+a_2 ))) up to the inverse thirteenth power. The expansion coefficients depend on three dimensionless parameters (γ,λ_A,λ_B), where the dimensionless inverse surface kinetic constants are λ_A=D_A⁄a_1 kA on sphere 1, λ_B=D_B⁄(a_2 k_B ) on the sphere 2, while the geometry enters as the radius ratio γ=a_1⁄a_2 . Using these results an equivalent site kinetic change is imposed, first to λ_Aon site 1, then to λ_Bon site 2, to determine which site is more influential for the overall series reaction rate. Effects of γ geometry modification at several fixed kinetic surface site rates are examined. When either one of reactive spheres is diffusion controlled, various levels of λ kinetic controls at the other site or γ site geometries are generated to study the effects of site kinetics or geometry control on the series reaction rate. As the “other site” reaction rate also increases toward diffusion control, inflection points are observed to develop as precursors to a local maximum on the series reaction rate versus sphere separation curves. An application to the isomerization of n-pentane is presented.

Research paper thumbnail of Diffusion Through a Porous Medium

Springer Tracts in Natural Philosophy, 1973

The principal object of this chapter is the estimation of the effective diffusion coefficient D e... more The principal object of this chapter is the estimation of the effective diffusion coefficient D e of a solute in a gaseous or liquid mixture when the mixture is in the presence of a suspended solid phase. Bounds on D e are calculated for an isotropic suspension whose only known statistical property is the void fraction, these are rigorously shown to be the “best possible bounds” that can be obtained with such limited information. Improved upper bounds on D e are obtained when an explicit model pore structure is generated from randomly overlapping, solid spheres.

Research paper thumbnail of Effective-medium theory of the conductivity for a random-site honeycomb lattice

Journal of Physics C: Solid State Physics

ABSTRACT The effective-medium theory for the random-site model of a percolating honeycomb lattice... more ABSTRACT The effective-medium theory for the random-site model of a percolating honeycomb lattice is formulated. The value of the critical site concentration obtained, xc=0.707, is compared with the series value xc=0.70+or-0.01 and the Monte Carlo value xc=0.688+or-0.015.

Research paper thumbnail of Effective medium theory of site percolation in a random simple triangular conductance network

Journal of Physics C: Solid State Physics

... into the effective infinite lattice, ie, figure l(a) with go = 9,. The electrical potential 4... more ... into the effective infinite lattice, ie, figure l(a) with go = 9,. The electrical potential 4(x, y) at the various sites of the infinite triangular lattice have been derived through a straightforward though tedious extension of Van Der Pol and Bremmer's ... AV = ug , - go)/[go - 9, + 2 e - 2 ~ 3 1 w ...

Research paper thumbnail of Critical exponents for conduction in a honeycomb random site lattice

Journal of Physics C: Solid State Physics

ABSTRACT Monte Carlo simulation conductivity calculations for the honeycomb random site resistor ... more ABSTRACT Monte Carlo simulation conductivity calculations for the honeycomb random site resistor lattice have been performed for lattice sizes from 200*200 at higher site fractions up to 1400*1400 near percolation. Lattice conductivity curves were compared with EMT results, also backbone beta '=0.38+or-0.02 and conductivity t=1.27+or-0.04 critical exponents were obtained.

Research paper thumbnail of Monte Carlo simulation of the conductivity of the two-dimensional triangular site network

Journal of Physics C: Solid State Physics

ABSTRACT The full conductivity curve for the triangular random site resistor network is calculate... more ABSTRACT The full conductivity curve for the triangular random site resistor network is calculated using Monte Carlo simulation. Lattice sizes range from 100*100 for higher site fractions up to 1400*1400 near percolation. Conductivity curves are compared with EMT and the conductivity exponent t=1.23+or-0.04 is obtained.

Research paper thumbnail of The Sharp Interface Model:Zero-Order Reaction with Volume Change

Industrial Engineering Chemistry Research, 1995

The sharp interface model is examined for isothermal gas-solid reactions following zero-order kin... more The sharp interface model is examined for isothermal gas-solid reactions following zero-order kinetics with respect to the gas phase and first-order kinetics with respect to the solid phase for spherical particles either shrinking or growing during reaction. It is shown that depending on the relative magnitudes of the governing parameters which include the volume expansion factor, Damkohler number, and mass Biot number, it is possible to have up to three successive transitions from one controlling regime (external mass transfer, product layer diffusion, or chemical kinetics) to another as the reaction evolves with time. This behavior gives rise to various gas concentration and solid conversion profiles. A classification of all the possible situations is made.