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© 2002 Elsevier Science B.V. Postdoctoral grant from Universidad Complutense of Madrid by M.A. Izquierdo Gil and support from the Danish Directorate for Development are gratefully acknowledged., Membrane distillation (MD) has a great potential as a concentration process for temperature labile liquids such as fruit juices, etc. Besides water, also aroma compounds will permeate through the membrane depending on their volatility and how the MD process is operated on the permeate side.In this paper, an experimental and theoretical investigation of the influence of concentration polarisation and temperature polarisation on the flux and selectivity of binary aqueous mixtures of ethanol is presented for vacuum membrane distillation (VMD) processes. Experimental results include changes of the following parameters: nature of solutions, membrane material and pore size, feed temperature, recirculation flow rate. One method was proposed in order to evaluate the concentration polarisation effects from the fit of the experimental data. General models taking into account Knudsen and viscous flows were proposed, but viscous contribution resulted to be negligible under our operating conditions. Therefore, theoretical fluxes were estimated using Knudsen model and a good agreement between them and the experimental ones was found., Danish Directorate for Development, Depto. de Estructura de la Materia, Física Térmica y Electrónica, Fac. de Ciencias Físicas, TRUE, pub

© 2002 Elsevier Science B.V. The authors wish to thank CICYT (Spain), Project PB-98-07-88, for the financial support accorded to this work., Gas permeation experiments using helium, air and argon and direct contact membrane distillation (DCMD) experiments using distilled water are reported. From gas permeation experiments the characteristic parameters of the Knudsen and Poiseuille transport mechanisms were determined. Such parameters were extrapolated in order to obtain the values corresponding to water vapour and these were used to estimate theoretical fluxes in DCMD processes employing two different models, one proposed by Schofield et al. (with some improvements) and another one according to the "Dusty-Gas" literature. In both models, the different transport mechanisms: ordinary diffusion, Knudsen flow and Poiseuille flow were taken into account. A good agreement between the experimental fluxes and their theoretical predictions was found. A comparison between both models was also carried out. It was proved that in both models the viscous flow could be neglected under our experimental conditions., CICYT (Spain), Depto. de Estructura de la Materia, Física Térmica y Electrónica, Fac. de Ciencias Físicas, TRUE, pub

© 2008 Elsevier Ltd. The author wishes to thank to Professor C. Fernández Pineda for his help and support and to CICYT (Spain), Project BFM2003-07197, for the financial support accorded to this work., Single gas permeation experiments results using neon, argon, nitrogen and methane are reported. From gas permeation experiments the characteristic parameters of the Knudsen and Poiseuille transport mechanisms were determined by means of an equation derived from the "Dusty-Gas" model. The experiments were performed at different temperatures from 303.15 to 323.15K, in order to study the temperature influence on those parameters. For PVDF and PCTE membranes the influence of the temperature on K, and B. parameters was not significant. Gas influence was also investigated for both types of membrane, a slight tendency of K, to decrease with increase in molar mass and a very slight tendency of B. to increase with increase in molar mass, although these trends were not fulfilled by neon gas., CICYT (Spain), Depto. de Estructura de la Materia, Física Térmica y Electrónica, Fac. de Ciencias Físicas, TRUE, pub

© 2004 Elsevier B.V. Postdoctoral grant from Universidad Complutense of Madrid to M.A. Izquierdo-Gil, Project PB-98-07-88 (CYCYT, Spain) and support from the Danish Directorate for Development are gratefully acknowledged, Vacuum membrane distillation (VMD) has been studied as a separation process to remove volatile organic compounds from aqueous streams. A vapour pressure difference across a microporous hydrophobic membrane is the driving force for the mass transport through the membrane pores (this transport takes place in vapour phase). The vapour pressure difference is obtained in VMD processes by applying a vacuum on one side of the membrane. The membrane acts as a mere support for the liquid-vapour equilibrium. The evaporation of the liquid stream takes place on the feed side of the membrane, and the condensation on the permeate side of the membrane. The paper focus on aroma stripping using VMD; factors influencing flux and separation performance using selected model aroma compounds have been studied. Mainly the following parameters have been examined-aroma compounds: activity coefficient/vapour pressure values; membrane type: PTFE/PP/PVDF; feed flow rate; feed temperature. A comparison is made between different thermodynamic models for calculating the vapour-liquid equilibrium at the membrane/pore interface., CICYT (Spain), Danish Directorate for Development, Depto. de Estructura de la Materia, Física Térmica y Electrónica, Fac. de Ciencias Físicas, TRUE, pub

低密度気体流やマイクロ・ナノデバイス近傍の流れは、いわゆる「高クヌッセン数流れ」となり、原子・分子レベルでの計測が必要となる。ここでは、主に「高クヌッセン数流れ」の計測に適用可能な分子イメージング技術について、その原理と適用例について述べる。, JAXA Special Publication, 宇宙航空研究開発機構特別資料

The dynamics of a 2D rotating Crookes radiometer is studied using a moving mesh unified gas kinetic scheme. The whole evolution process of a fan from an initial unsteady start-up to a final steady state rotational movement in a rarefied gas environment is simulated numerically. Through the numerical study, the unsteady force distribution along a vane which dynamically drives the fan movement is captured. And a quantitative connection between total torque and rotational speed of the fan in the Knudsen number regime of 10-3 < Kn < 102 is obtained. Based on the dimensional analysis, the total radiometric torque can be decomposed into a net radiometric driving torque and a rotational resistance. Based on the numerical data, the analytical functions of the torque and angular velocity of a rotating fan in terms of Knudsen number are quantitatively constructed. This relationship is used to explain the experimental observation of the Knudsen number shift for the appearance of the maximum torque and the maximum rotational speed in the transitional flow regime. (C) 2012 American Institute of Physics. [http://dx.doi.orgt10.1063/1.4765353]

The dynamics of a 2D rotating Crookes radiometer is studied using a moving mesh unified gas kinetic scheme. The whole evolution process of a fan from an initial unsteady start-up to a final steady state rotational movement in a rarefied gas environment is simulated numerically. Through the numerical study, the unsteady force distribution along a vane which dynamically drives the fan movement is captured. And a quantitative connection between total torque and rotational speed of the fan in the Knudsen number regime of 10-3 < Kn < 102 is obtained. Based on the dimensional analysis, the total radiometric torque can be decomposed into a net radiometric driving torque and a rotational resistance. Based on the numerical data, the analytical functions of the torque and angular velocity of a rotating fan in terms of Knudsen number are quantitatively constructed. This relationship is used to explain the experimental observation of the Knudsen number shift for the appearance of the maximum torque and the maximum rotational speed in the transitional flow regime. (C) 2012 American Institute of Physics. [http://dx.doi.orgt10.1063/1.4765353]

The behavior of a slightly rarefied monatomic gas between two parallel plates whose temperature grows slowly and linearly in time is investigated on the basis of the kinetic theory of gases. This problem is shown to be equivalent to a boundary-value problem of the steady linearized Boltzmann equation describing a rarefied gas subject to constant volumetric heating. The latter has been recently studied by Radtke, Hadjiconstantinou, Takata, and Aoki (RHTA) as a means of extracting the second-order temperature jump coefficient. This correspondence between the two problems gives a natural interpretation to the volumetric heating source and explains why the second-order temperature jump observed by RHTA is not covered by the general theory of slip flow for steady problems. A systematic asymptotic analysis of the time-dependent problem for small Knudsen numbers is carried out and the complete fluid-dynamic description, as well as the related half-space problems that determine the structure of the Knudsen layer and the coefficients of temperature jump, are obtained. Finally, a numerical solution is presented for both the Bhatnagar-Gross-Krook model and hard-sphere molecules. The jump coefficient is also calculated by the use of a symmetry relation; excellent agreement is found with the result of the numerical computation. The asymptotic solution and associated second-order jump coefficient obtained in the present paper agree well with the results by RHTA that are obtained by a low variance stochastic method.

The dynamics of a 2D rotating Crookes radiometer is studied using a moving mesh unified gas kinetic scheme. The whole evolution process of a fan from an initial unsteady start-up to a final steady state rotational movement in a rarefied gas environment is simulated numerically. Through the numerical study, the unsteady force distribution along a vane which dynamically drives the fan movement is captured. And a quantitative connection between total torque and rotational speed of the fan in the Knudsen number regime of 10-3 < Kn < 102 is obtained. Based on the dimensional analysis, the total radiometric torque can be decomposed into a net radiometric driving torque and a rotational resistance. Based on the numerical data, the analytical functions of the torque and angular velocity of a rotating fan in terms of Knudsen number are quantitatively constructed. This relationship is used to explain the experimental observation of the Knudsen number shift for the appearance of the maximum torque and the maximum rotational speed in the transitional flow regime. (C) 2012 American Institute of Physics. [http://dx.doi.orgt10.1063/1.4765353]

Relaxations from a uniform mass/heat flow and flows driven by an external force/temperature-gradient for a rarefied gas between two parallel plates are studied on the basis of the kinetic theory of gases. By numerical computations of the linearized Bhatnagar–Gross–Krook model of the Boltzmann equation, it is demonstrated that the reciprocity among these elemental flows derived from a general reciprocity theory for time-dependent problems [S. Takata, J. Stat. Phys. 140, 985 (2010)] holds at any time and any Knudsen numbers. Moreover, a propagation of the discontinuity of the velocity distribution function (VDF) in the relaxation problems and that of the derivative discontinuity of the VDF in the driven-flow problems are demonstrated. Their relation is also clarified.

The behavior of a slightly rarefied monatomic gas between two parallel plates whose temperature grows slowly and linearly in time is investigated on the basis of the kinetic theory of gases. This problem is shown to be equivalent to a boundary-value problem of the steady linearized Boltzmann equation describing a rarefied gas subject to constant volumetric heating. The latter has been recently studied by Radtke, Hadjiconstantinou, Takata, and Aoki (RHTA) as a means of extracting the second-order temperature jump coefficient. This correspondence between the two problems gives a natural interpretation to the volumetric heating source and explains why the second-order temperature jump observed by RHTA is not covered by the general theory of slip flow for steady problems. A systematic asymptotic analysis of the time-dependent problem for small Knudsen numbers is carried out and the complete fluid-dynamic description, as well as the related half-space problems that determine the structure of the Knudsen layer and the coefficients of temperature jump, are obtained. Finally, a numerical solution is presented for both the Bhatnagar-Gross-Krook model and hard-sphere molecules. The jump coefficient is also calculated by the use of a symmetry relation; excellent agreement is found with the result of the numerical computation. The asymptotic solution and associated second-order jump coefficient obtained in the present paper agree well with the results by RHTA that are obtained by a low variance stochastic method.

A self-similar reaction front develops in reactive ion etching when the ions penetrate channels of shallow height h. This relates to the patterning of microchannels using a single-step etching and bonding, as described by Rhee et al. [Lab Chip 5, 102 (2005)] . Experimentally, we report that the front location scales as xf ? ht1/2 and the width is time-invariant and scales as ? ? h. Mean-field reaction-diffusion theory and Knudsen diffusion give a semiquantitative understanding of these observations and allow optimization of etching times in relation to bonding requirements., ChemE/Chemical Engineering, Applied Sciences

Performance of the Knudsen pump is studied numerically to find out effective configurations not only for the finally achieved separation and compression rates, but also for its time efficiency. A system of convection–diffusion equations with transmission conditions, which have been derived from the Boltzmann equation under the narrow channel approximation, is used for simulations of various configurations. A comparison with the experiment of evacuation from a tank is also made to demonstrate the practical ability of that system.

Relations between different problems described by the linearized Boltzmann equation (LBE) are discussed on the basis of the classical symmetry of LBE and kinetic boundary condition. The theory is developed for the system of arbitrary Knudsen number (Kn) from the view point of the Green function. After showing the main idea of the approach to steady problems for bounded and unbounded domains, its extension to unsteady problems in a fixed bounded domain is given. In particular, in the latter, recovery of Kubo formula for the viscosity and thermal conductivity in the fluctuation–dissipation theorem and its extension to the systems of arbitrary Kn are shown. A comment on the extension to gas mixtures is also given.

A self-similar reaction front develops in reactive ion etching when the ions penetrate channels of shallow height h. This relates to the patterning of microchannels using a single-step etching and bonding, as described by Rhee et al. [Lab Chip 5, 102 (2005)] . Experimentally, we report that the front location scales as xf ? ht1/2 and the width is time-invariant and scales as ? ? h. Mean-field reaction-diffusion theory and Knudsen diffusion give a semiquantitative understanding of these observations and allow optimization of etching times in relation to bonding requirements., ChemE/Chemical Engineering, Applied Sciences

Relations between different problems described by the linearized Boltzmann equation (LBE) are discussed on the basis of the classical symmetry of LBE and kinetic boundary condition. The theory is developed for the system of arbitrary Knudsen number (Kn) from the view point of the Green function. After showing the main idea of the approach to steady problems for bounded and unbounded domains, its extension to unsteady problems in a fixed bounded domain is given. In particular, in the latter, recovery of Kubo formula for the viscosity and thermal conductivity in the fluctuation–dissipation theorem and its extension to the systems of arbitrary Kn are shown. A comment on the extension to gas mixtures is also given.

Performance of the Knudsen pump is studied numerically to find out effective configurations not only for the finally achieved separation and compression rates, but also for its time efficiency. A system of convection–diffusion equations with transmission conditions, which have been derived from the Boltzmann equation under the narrow channel approximation, is used for simulations of various configurations. A comparison with the experiment of evacuation from a tank is also made to demonstrate the practical ability of that system.

Thermal transpiration is a rarefied gas flow driven by a wall temperature gradient and is a promising mechanism for gas pumping without moving parts, known as the Knudsen pump. Obtaining temperature measurements along capillary walls in a Knudsen pump is difficult due to extremely small length scales. Meanwhile, simplified analytical models are not applicable under the practical operating conditions of a thermal transpiration device, where the gas flow is in the transitional rarefied regime. Here, we present a coupled gas-phonon heat transfer and flow model to study a closed thermal transpiration system. Discretized Boltzmann equations are solved for molecular transport in the gas phase and phonon transport in the solid. The wall temperature distribution is the direct result of the interfacial coupling based on mass conservation and energy balance at gas-solid interfaces and is not specified a priori unlike in the previous modeling efforts. Capillary length scales of the order of phonon mean free path result in a smaller temperature gradient along the transpiration channel as compared to that predicted by the continuum solid-phase heat transfer. The effects of governing parameters such as thermal gradients, capillary geometry, gas and phonon Knudsen numbers and, gas-surface interaction parameters on the efficiency of thermal transpiration are investigated in light of the coupled model.

Thermal transpiration is a rarefied gas flow driven by a wall temperature gradient and is a promising mechanism for gas pumping without moving parts, known as the Knudsen pump. Obtaining temperature measurements along capillary walls in a Knudsen pump is difficult due to extremely small length scales. Meanwhile, simplified analytical models are not applicable under the practical operating conditions of a thermal transpiration device, where the gas flow is in the transitional rarefied regime. Here, we present a coupled gas-phonon heat transfer and flow model to study a closed thermal transpiration system. Discretized Boltzmann equations are solved for molecular transport in the gas phase and phonon transport in the solid. The wall temperature distribution is the direct result of the interfacial coupling based on mass conservation and energy balance at gas-solid interfaces and is not specified a priori unlike in the previous modeling efforts. Capillary length scales of the order of phonon mean free path result in a smaller temperature gradient along the transpiration channel as compared to that predicted by the continuum solid-phase heat transfer. The effects of governing parameters such as thermal gradients, capillary geometry, gas and phonon Knudsen numbers and, gas-surface interaction parameters on the efficiency of thermal transpiration are investigated in light of the coupled model.

Thermal transpiration is a rarefied gas flow driven by a wall temperature gradient and is a promising mechanism for gas pumping without moving parts, known as the Knudsen pump. Obtaining temperature measurements along capillary walls in a Knudsen pump is difficult due to extremely small length scales. Meanwhile, simplified analytical models are not applicable under the practical operating conditions of a thermal transpiration device, where the gas flow is in the transitional rarefied regime. Here, we present a coupled gas-phonon heat transfer and flow model to study a closed thermal transpiration system. Discretized Boltzmann equations are solved for molecular transport in the gas phase and phonon transport in the solid. The wall temperature distribution is the direct result of the interfacial coupling based on mass conservation and energy balance at gas-solid interfaces and is not specified a priori unlike in the previous modeling efforts. Capillary length scales of the order of phonon mean free path result in a smaller temperature gradient along the transpiration channel as compared to that predicted by the continuum solid-phase heat transfer. The effects of governing parameters such as thermal gradients, capillary geometry, gas and phonon Knudsen numbers and, gas-surface interaction parameters on the efficiency of thermal transpiration are investigated in light of the coupled model.

Thermal transpiration is a rarefied gas flow driven by a wall temperature gradient and is a promising mechanism for gas pumping without moving parts, known as the Knudsen pump. Obtaining temperature measurements along capillary walls in a Knudsen pump is difficult due to extremely small length scales. Meanwhile, simplified analytical models are not applicable under the practical operating conditions of a thermal transpiration device, where the gas flow is in the transitional rarefied regime. Here, we present a coupled gas-phonon heat transfer and flow model to study a closed thermal transpiration system. Discretized Boltzmann equations are solved for molecular transport in the gas phase and phonon transport in the solid. The wall temperature distribution is the direct result of the interfacial coupling based on mass conservation and energy balance at gas-solid interfaces and is not specified a priori unlike in the previous modeling efforts. Capillary length scales of the order of phonon mean free path result in a smaller temperature gradient along the transpiration channel as compared to that predicted by the continuum solid-phase heat transfer. The effects of governing parameters such as thermal gradients, capillary geometry, gas and phonon Knudsen numbers and, gas-surface interaction parameters on the efficiency of thermal transpiration are investigated in light of the coupled model.

A gas-kinetic model with multiple translational temperature for the continuum and near continuum flow simulations is proposed. The main purpose for this work is to derive the generalized Navier-Stokes equations with multiple temperature. It is well recognized that for increasingly rarefied flowfields, the predictions from continuum formulation, such as the Navier-Stokes equations lose accuracy. These inaccuracies may be partially due to the single temperature assumption in the standard Navier-Stokes equations. Here, based on an extended Bhatnagar-Gross-Krook (BGK) model with multiple translational temperature, the numerical scheme for its corresponding Navier-Stokes equations is also constructed. In the current approach, the energy exchange between x, y, and z directions is modeled through the particle collision, and individual energy equation in different direction is obtained. The kinetic model, newly constructed is an enlarged system in comparison with Holway's ellipsoid statistical BGK model (ES-BGK). The detailed difference is presented in this paper. In the newly derived "Navier-Stokes" equations from the current model, all viscous terms are replaced by the temperature relaxation terms. The relation between the stress and strain in the standard Navier-Stokes equations is recovered only in the limiting case when the flow is close to the equilibrium, such as small temperature differences in different directions. In order to validate the generalized Navier-Stokes equations, we apply them to the study of Couette and Poiseuille flows with a wide range of Knudsen numbers. In the continuum flow regime, the standard Navier-Stokes solutions are precisely recovered. In the near continuum flow regime, the simulation results are compared with the direct simulation Monte Carlo solutions. The anomalous phenomena in the pressure and temperature distributions from the standard Navier-Stokes equations in the Poiseuille flow case at Kn=0.1 are well resolved by the generalized N

A gas-kinetic model with multiple translational temperature for the continuum and near continuum flow simulations is proposed. The main purpose for this work is to derive the generalized Navier-Stokes equations with multiple temperature. It is well recognized that for increasingly rarefied flowfields, the predictions from continuum formulation, such as the Navier-Stokes equations lose accuracy. These inaccuracies may be partially due to the single temperature assumption in the standard Navier-Stokes equations. Here, based on an extended Bhatnagar-Gross-Krook (BGK) model with multiple translational temperature, the numerical scheme for its corresponding Navier-Stokes equations is also constructed. In the current approach, the energy exchange between x, y, and z directions is modeled through the particle collision, and individual energy equation in different direction is obtained. The kinetic model, newly constructed is an enlarged system in comparison with Holway's ellipsoid statistical BGK model (ES-BGK). The detailed difference is presented in this paper. In the newly derived "Navier-Stokes" equations from the current model, all viscous terms are replaced by the temperature relaxation terms. The relation between the stress and strain in the standard Navier-Stokes equations is recovered only in the limiting case when the flow is close to the equilibrium, such as small temperature differences in different directions. In order to validate the generalized Navier-Stokes equations, we apply them to the study of Couette and Poiseuille flows with a wide range of Knudsen numbers. In the continuum flow regime, the standard Navier-Stokes solutions are precisely recovered. In the near continuum flow regime, the simulation results are compared with the direct simulation Monte Carlo solutions. The anomalous phenomena in the pressure and temperature distributions from the standard Navier-Stokes equations in the Poiseuille flow case at Kn=0.1 are well resolved by the generalized N

A gas-kinetic model with multiple translational temperature for the continuum and near continuum flow simulations is proposed. The main purpose for this work is to derive the generalized Navier-Stokes equations with multiple temperature. It is well recognized that for increasingly rarefied flowfields, the predictions from continuum formulation, such as the Navier-Stokes equations lose accuracy. These inaccuracies may be partially due to the single temperature assumption in the standard Navier-Stokes equations. Here, based on an extended Bhatnagar-Gross-Krook (BGK) model with multiple translational temperature, the numerical scheme for its corresponding Navier-Stokes equations is also constructed. In the current approach, the energy exchange between x, y, and z directions is modeled through the particle collision, and individual energy equation in different direction is obtained. The kinetic model, newly constructed is an enlarged system in comparison with Holway's ellipsoid statistical BGK model (ES-BGK). The detailed difference is presented in this paper. In the newly derived "Navier-Stokes" equations from the current model, all viscous terms are replaced by the temperature relaxation terms. The relation between the stress and strain in the standard Navier-Stokes equations is recovered only in the limiting case when the flow is close to the equilibrium, such as small temperature differences in different directions. In order to validate the generalized Navier-Stokes equations, we apply them to the study of Couette and Poiseuille flows with a wide range of Knudsen numbers. In the continuum flow regime, the standard Navier-Stokes solutions are precisely recovered. In the near continuum flow regime, the simulation results are compared with the direct simulation Monte Carlo solutions. The anomalous phenomena in the pressure and temperature distributions from the standard Navier-Stokes equations in the Poiseuille flow case at Kn=0.1 are well resolved by the generalized N

Vacuum membrane distillation (VMD) has been studied as a separation process to remove volatile organic compounds from aqueous streams. A vapour pressure difference across a microporous hydrophobic membrane is the driving force for the mass transport through the membrane pores (this transport takes place in vapour phase). The vapour pressure difference is obtained in VMD processes by applying a vacuum on one side of the membrane. The membrane acts as a mere support for the liquid-vapour equilibrium. The evaporation of the liquid stream takes place on the feed side of the membrane, and the condensation on the permeate side of the membrane. The paper focus on aroma stripping using VMD; factors influencing flux and separation performance using selected model aroma compounds have been studied. Mainly the following parameters have been examined-aroma compounds: activity coefficient/vapour pressure values; membrane type: PTFE/PP/PVDF; feed flow rate; feed temperature. A comparison is made between different thermodynamic models for calculating the vapour-liquid equilibrium at the membrane/pore interface. (C) 2004 Elsevier B.V. All rights reserved.

The effect of pore surface roughness on Knudsen diffusion in nanoporous media is investigated by dynamic Monte Carlo simulations and analytical calculations. A conceptual difference is found between the roughness dependence of the macroscopic, transport diffusivity and the microscopic, self-diffusivity, which is reminiscent of diffusion in zeolites, where a similar difference arises due to adsorption effects and intermolecular interactions. Because of the dependence of the self-diffusivity on molecular residence times, self-diffusion may be roughness dependent, while transport diffusion is not. Detailed proofs are given. The differences become significant when the pore surface is rough down to molecular scales, as is the case, e.g., for many common sol–gel materials. Simulations are in good agreement with analytical calculations for several tested rough, fractal pore structures. These results are important for the interpretation of experimental diffusion measurements and for the study of diffusion-reaction processes in nanoporous catalysts with a rough internal surface., DelftChemTech, Applied Sciences

The effect of pore surface roughness on Knudsen diffusion in nanoporous media is investigated by dynamic Monte Carlo simulations and analytical calculations. A conceptual difference is found between the roughness dependence of the macroscopic, transport diffusivity and the microscopic, self-diffusivity, which is reminiscent of diffusion in zeolites, where a similar difference arises due to adsorption effects and intermolecular interactions. Because of the dependence of the self-diffusivity on molecular residence times, self-diffusion may be roughness dependent, while transport diffusion is not. Detailed proofs are given. The differences become significant when the pore surface is rough down to molecular scales, as is the case, e.g., for many common sol–gel materials. Simulations are in good agreement with analytical calculations for several tested rough, fractal pore structures. These results are important for the interpretation of experimental diffusion measurements and for the study of diffusion-reaction processes in nanoporous catalysts with a rough internal surface., DelftChemTech, Applied Sciences

This dissertation deals with the development of a method to predict the orbital lifetimes of uncontrolled free tethers and tether-trailing satellites originating in low-to-moderate altitude Earth orbits. The problem is solved by application of the empirical method. Two mathematical models to simulate the orbital evolution of tethered systems are developed. In both models the system is discretized into a series of interconnected point masses, orbiting an oblate Earth and transiting an oblate, rotating, temporally and globally averaged atmosphere. For aerodynamic drag calculations, tether segments are modeled as right circular cylinders, and any end-body is modeled as a sphere. Drag coefficients vary as a function of shape and Knudsen number. In the multibody model, connections between masses are elastic, and the system is free to assume any orientation. Newtonian equations of motion are numerically integrated. In the orbital element propagation model, connections between masses are inelastic, and the system is constrained to remain aligned along the local vertical. Gauss' form of Lagrange's Planetary Equations, in terms of equinoctial elements, are used to propagate the orbital elements describing the orbit of the system's center of mass., AFIT/CI/CIA-92-017D

This work continued to investigate thermionic energy conversion in the Knudsen (collisionless) operating mode. A SAVTEC-type converter with an interelectrode spacing of 18-22 microns was tested over a range of emitter temperatures up to about 1700 K. Maximum performance followed the predictions of vacuum-mode analysis for emitter temperatures below 1580 K. Above that temperature the converter operated in the unignited mode, with partial space-charge neutralization by surface ionization of cesium. It was found that collisionless and diffusion mode theories could be extended into the regime of maximum output power for the unignited mode (spacing and electron mean-free path about equal) to give good agreement with the experimental data. The Knudsen-mode thermionic converter with a structured emitter was also investigated. Analysis has shown that associative ionization between barium and cesium is unlikely to be the cause of the current enhancement observed in previously published work. An analysis which considered the trapping of positive ions in the emitter slots has given good qualitative agreement with published data. Work is continuing on this analysis. Parts for a structured emitter variable spacing converter have been constructed and are being assembled. Keywords: Thermionic energy conversion; Knudsen operating mode; Structured emitter; SAVTEC diodes.

This work studied discharge processes in Knudsen mode (collisionless), thermionic energy converters. Mechanisms for reducing the effects of electron space charge in such devices are essential for thermionic converters to produce useful current and power densities. The mechanisms studied are: reduction of space-charge through a very close interelectrode gap (less than 10 microns); transport and retention of positive cesium ions generated by surface ionization; transport of positive cesium ions generated in an arc external to the electrodes; and the mechanism for enhanced current output due to a structured emitter in a mixed barium-cesium vapor. The experimental work used SAVTEC (Self-Adjusting, Versatile Thermionic Energy Converter) diode structures which were tested in a chamber containing 0.1 - 1.0 torr of cesium vapor. Comparison of measured volt-ampere curves with theory gave excellent agreement and indicated an interelectrode gap of 6.5 microns at an emitter temperature of 1250 K. A theoretical model of the collisionless thermionic diode was developed which included surface ionization, auxiliary ions from an external source, and trapping of charged particles in potential wells due to infrequent collisions. Studies showed that trapping of positive ions leads to a large, beneficial increase in current density. Using a diffusion analysis to couple this model to models of collision-dominated discharges gave predictions of the performance of SAVTEC devices in the presence of an auxiliary discharge, and led to design criteria for electrode size in order for auxiliary ionization to be effective.

The vapor pressure and the heat of vaporization of barium were measured using the Knudsen target technique. A recording microbalance was used to measure both the effusion rate and the recoil force exerted by the beam onto the target. The measured vapor pressure may be presented by log P(atm) = 5.145 - 9597/T. Mass spectrometric investigation was conducted with the time-of-flight mass spectrometer which produced a second-law heat of vaporization.

Relative values of the vaporization coefficients of C, C2, and C3, the predominant vapor species of graphite, were evaluated by comparing the ratios between the ion intensities of different carbon vapor species obtained in a free (Langmuir) vaporization experiment and in an equilibrium (Knudsen) vaporization experiment. The measurements of the ion intensities of carbon vapor species over the spectrographic electrode grade graphite were carried out using a RF induction heating furnace coupled with a Bendix Time-of-Flight mass spectrometer. The data in literature on pyrolytic graphite was also analyzed; an interpretation of the vaporization coefficients of pyrolytic graphite is difficult as the pyrolytic graphite vaporizes predominantly from cracks, etc.

A model for the exchange of nitrogen isotopes taking place between two pellets of aluminum nitride in a Knudsen cell by means of gas-solid reactions has been proposed, and the differential equations describing the kinetics of exchange in terms of vaporization, condensation, and flow rates has been solved. The equation was fitted to data of Hoch and Ramakrishnan (Reference 3). Values of vaporization and condensation and reaction rate constants have been determined. It was also determined that the best fit to the data requires that reaction zone be defined to be equal to the thickness of 10,000 layers of atoms. The vaporization coefficients, and condensation coefficient were found to be equal to each other. (Author), Supersedes Rept. no. AFML-TR-68-120 dated Aug 68, AD-676 296.

The free-molecular flow rates through untapered circular tubes of finite lengths are determined for several length to radius ratios (L/R). The governing equations, which are derived on the assumptions that the reflection from the wall is diffuse and the arrival rates of molecules at an elemental area follow the 'cosine law' distribution, are evaluated numerically. The Clausing integral equation, which determines the flux of molecules at an element of the interior wall of the tube, is solved on an IBM 7094 by an iterative scheme. An analysis of the Clausing integral equation provides very useful information on the behavior of its solution, and this, together with the mass conservation principle for checking the numerical results, particularly for higher values of L/R. Knowing the distribution of the flux of molecules along the interior wall of the tube, the flux of molecules arriving from the wall at both exit and entrance planes are computed by straightforward numerical integration. The total flux rates through the exit plane are shown to agree with those obtained by DeMarcus by a variational technique for certain values of L/R. (Author)

The vaporization of CuI was studied using Knudsen effusion-mass spectrometric techniques. The ionic species in the mass spectrum were identified and assigned to the appropriate parent molecules in the equilibrium vapor. Partial pressures for each of the components of the equilibrium vapor were determined as a function of temperature. Second law heats of sublimation were determined and two structural transformations occurring in the solid were characterized. The possibility of a temperature dependent ionization cross section for some of the species is discussed. (Author)

In the last decade, shale reservoirs emerged as one of the fast growing hydrocarbon resources in the world unlocking vast reserves and reshaping the landscape of the oil and gas global market. Gas-condensate reservoirs represent an important part of these resources. The key feature of these reservoirs is the condensate banking which reduces significantly the well deliverability when the condensate forms in the reservoir below the dew point pressure. Although the condensate banking is a well-known problem in conventional reservoirs, the very low permeability of shale matrix and unavailability of proven pressure maintenance techniques make it more challenging in shale reservoirs. The nanoscale range of the pore size in the shale matrix affects the gas flow which deviates from laminar Darcy flow to Knudsen flow resulting in enhanced gas permeability. Furthermore, the phase behaviour of gas-condensate fluids is affected by the high capillary pressure in the matrix causing higher condensate saturation than in bulk conditions. A good understanding and an accurate evaluation of how the condensate builds up in the reservoir and how it affects the gas flow is very important to manage successfully the development of these high-cost hydrocarbon resources. This work investigates the gas Knudsen flow under condensate saturation effect and phase behaviour deviation under capillary pressure of gas-condensate fluids in shale matrix with pore size distribution; and evaluates their effect on well productivity. Supplementary MATLAB codes are provided elsewhere on OpenAIR: http://hdl.handle.net/10059/2145

In the last decade, shale reservoirs emerged as one of the fast growing hydrocarbon resources in the world unlocking vast reserves and reshaping the landscape of the oil and gas global market. Gas-condensate reservoirs represent an important part of these resources. The key feature of these reservoirs is the condensate banking which reduces significantly the well deliverability when the condensate forms in the reservoir below the dew point pressure. Although the condensate banking is a well-known problem in conventional reservoirs, the very low permeability of shale matrix and unavailability of proven pressure maintenance techniques make it more challenging in shale reservoirs. The nanoscale range of the pore size in the shale matrix affects the gas flow which deviates from laminar Darcy flow to Knudsen flow resulting in enhanced gas permeability. Furthermore, the phase behaviour of gas-condensate fluids is affected by the high capillary pressure in the matrix causing higher condensate saturation than in bulk conditions. A good understanding and an accurate evaluation of how the condensate builds up in the reservoir and how it affects the gas flow is very important to manage successfully the development of these high-cost hydrocarbon resources. This work investigates the gas Knudsen flow under condensate saturation effect and phase behaviour deviation under capillary pressure of gas-condensate fluids in shale matrix with pore size distribution; and evaluates their effect on well productivity. Supplementary MATLAB codes are provided elsewhere on OpenAIR: http://hdl.handle.net/10059/2145