Coupled heat and mass transfer during nonisothermal absorption by falling droplet with internal circulation

We considered mass and heat transfer during nonisothermal absorption of a gas by a falling droplet with internal circulation. Gas phase is assumed to be free of inert admixtures and mass transfer is liquid phase controlled. Mass flux is directed from a gaseous phase to a droplet, and the interfacial shear stress causes a fluid flow inside the droplet. Droplet deformation under the influence of interface shear stress is neglected. Absorbate accumulation and temperature increase in the bulk of liquid phase are taken into account. The problem is solved in the approximations of a thin concentration and temperature boundary layers in the liquid phase. The thermodynamic parameters of the system are assumed constant. The system of transient partial parabolic differential equations of convective diffusion and energy balance with time-dependent boundary conditions is solved by combining the similarity transformation method with Duhamel's theorem, and the solution is obtained in a form of Volterra integral equation of the second kind which is solved numerically. Theoretical results are compared with available experimental data for water vapor absorption by falling droplets of aqueous solution of LiBr.     

High-pressure cylindrical acoustic resonance diffusion measurements of methane in liquid hydrocarbons

A novel cylindrical acoustic resonance method for the measurement of gas diffusion into liquids at high pressures is described. The measurements were per formed in a vertically oriented cylindrical acoustic resonator containing both the liquid solvent and gaseous diffusant while under high-precision isothermal and isobaric control. Individual resonance modes of the liquid column, the gas column, and the two-phase coupled fluid are resolved in the fast Fourier trans form acoustic-resonance spectrum (FFT-ARS). High-resolution acoustic spectra measured at frequent time intervals reveal the changes which accompany the diffusion fusion of gas into the liquid phase. One change, namely, the growth in length of the liquid column, results in a systematic shift to higher frequencies of axial modes in the gas column. The temporal behavior of this moving boundary, together with quantitative measurement of the flow to the gas column required to sustain the constant pressure, permits determination of the gas-into-liquid diffusion coefficient. Diffusion coefficients were determined from the change in frequency as a function of time of axial resonance modes in the gas-phase virtual cylinder as the surface of the underlying liquid phase advanced due to gas absorption. Measurements of the systems methane/n-octane, methane/n-nonane, and methane/n-decane were performed as a function of temperature at a pressure of 250 psia. Comparisons is made to results obtained elsewhere and by other methods but at the same temperatures and pressure.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Moment analysis of mass-transfer kinetics in C18-silica monolithic columns

The moment analysis of elution peak profiles based on new moment equations provides information on the mass-transfer characteristics of C(18)-silica monolithic columns. The flow rate dependence of the HETP data was analyzed using the generalized van Deemter equation, after correction of these data by subtraction of the external mass-transfer contribution to band broadening. Kinetic parameters and diffusion coefficients related to the mass-transfer processes in monolithic columns were derived by taking advantage of the different flow velocity dependence of their contributions to band broadening. At high flow rates, axial dispersion and diffusive migration across the monolithic C(18)-silica skeleton contribute much to band broadening, suggesting that it remains important to reduce the influence of eddy diffusion and the mass-transfer resistance in the stationary phase to achieve fast separations and a high efficiency. Surface diffusion plays a predominant role for molecular migration in the monolithic stationary phase. Although the value of the surface diffusion coefficient (D(s)) depends on an estimate of the external mass-transfer coefficient, D(s) values of the order of 10(-7) cm(2) s(-1) were calculated for the first time for the C(18)-silica monolithic skeleton. The value of D(s) decreases with increasing retention of sample compounds. Analysis of a kind of time constant calculated from D(s) suggests that the "chromatographic corresponding particle size" is approximately 4 microm for the C(18)-silica monolithic stationary phase used in this study. The accuracy of the D(s) values determined was discussed.     

垂直降膜式吸收机内布液器的实验研究

吸收式热泵技术由于能有效利用低势热能而节约高品位的电能,已经成为一项重要的节能技术。吸收器是吸收式热泵的最重要的部件,其性能主要取决于换热管的传热与传质系数,而传热管表面液体降膜状态对传热和传质系数将产生直接影响。布液器是实现液体降膜的关键部件,而目前国内外鲜有相关研究。针对这种现状,共试制了四种规格的布液器样品,针对Φ19和Φ25的紫铜光管与强化换热管进行了管外垂直降膜布液实验,得到了各种布液器布液流量与静液柱高度关系的实验数据,并且拟合了布液器的流量系数与雷诺数的函数关系。根据实验结果提出了优化布液的方法,并用于指导热泵机组的设计。优化后的布液器已经被成功应用于国内首台供热量为1.3MW垂直降膜式吸收式热泵机组样机。     

低雷诺数下溴化锂溶液降膜吸收热质传递的数值研究

溴化锂溶液降膜吸收是吸收式空调系统中常见的热质传递形式之一。本文对溶液降膜吸收过程的热质耦合传递分析,建立了溴化锂溶液垂直降膜吸收热质传递的二维数学物理模型,采用CFD-Fluent对模型进行求解。计算得到不同Re下的液膜界面温度、液膜内浓度分布、传热传质通量及传热传质系数等。分析了Re对降膜吸收过程中热质传递的影响。结果表明:当液膜Re150时,液膜界面平均温度与平均传质系数随着Re的增大而增大,而平均传热系数随着Re的增大而减少;平均传热传质通量均是随着Re的增大而先增大后减小,存在一个最佳液膜Re使降膜吸收过程的传热传质通量达到最大,即Re=50时,平均传热和传质通量分别达到最大值7.2 k W/m~2与2.9×10~(-3)kg/(m~2·s)。     

液态Pb-Cu合金结构与扩散性质的分子动力学模拟

通过分子动力学方法模拟液态Pb-Cu合金的熔体结构,得到液态合金的对相关函数曲线、配位数和相关半径,并用于分析合金熔体内部的结构。同时将NRTL方程与分子动力学方法结合,提出一种计算合金互扩散系数的新方法,使用该方法计算得到了Pb-Cu合金的自扩散与互扩散系数,并分析了熔体结构对合金扩散性质的影响。     

Excitation of acoustic vibrations upon combustion of droplets of liquid fuel at supercritical pressure

Theoretical investigation of the excitation of acoustic vibrations upon combustion of liquid fuel droplets at a supercritical pressure of a gaseous mixture is carried out. The droplets are assumed to be spherical and mono-dispersed. The combustion is assumed to run in the diffusion regime. The binary diffusion coefficients are taken equal and independent of the concentration of the components of the gaseous mixture. The Lewis number is assumed to be unity. The flow is considered to be one-dimensional; the mixing in the transverse direction is assumed to be complete, with no mixing in the longitudinal direction. The rate of combustion at supercritical pressure of the gaseous mixture is calculated on the basis of the modified quasi-stationary theory. Expressions for the frequency and excitation increment of acoustic vibrations are obtained in this paper; the properties of the fuel and the oxidizer are explicitly taken into account.     

聚醚砜四元制膜液体系的相图计算

以Ｆｌｏｒｙ－Ｈｕｇｇｉｎｓ理论为基础，对ＰＥＳ－ＰＧ－ＮＭＰ＿Ｈ２Ｏ＿）聚醚砜丙二醇－Ｎ－甲基－２－哟咯烷酮水）四元制液体系的相图进行了计算，利用三元相图考察Ｈ２Ｏ和ＰＧ对液－液相分离的影响，在三元的理论的基础上提出了低分子量添加剂的卤元改性Ｆｌｏｒｙ－Ｈｕｇｇｉｎｓ理论，并提出了一种获得四元相图的方法，利用四元相图能较争地描述四元体系，利用改性的四元理论，能了地理解该种体系的液－液相分离行为。     

Chromatography with dynamically created liquid "stationary" phases: methanol and carbon dioxide

Liquid films composed of binary mixtures of carbon dioxide and methanol were created in empty capillary columns to produce effective stationary phases for chromatography. Under certain conditions of temperature, pressure, and stoichiometric composition, a binary mobile phase composed of CO2 and an organic liquid, such as methanol, can form two immiscible (gas and liquid) phases within a chromatographic column. The two phases can coexist in dynamic equilibrium with the liquid phase migrating through the column at a slower velocity than the gas phase. The liquid phase, composed of methanol saturated with carbon dioxide, acted as a chromatographic stationary phase while the gas phase, composed of carbon dioxide saturated with methanol, acted as a chromatographic mobile phase. The exact conditions necessary for the formation of two phase systems were determined from three-dimensional (P, T, XY) phase diagrams calculated from the Peng-Robinson cubic equation-of-state using one-parameter mixing rules. Separations of simple hydrocarbon mixtures are illustrated under various experimental conditions.     

Experimental study of diffusion instability in three-component gas mixture without density gradient

The process of binary (propane-nitrous oxide) gas mixture diffusion into carbon dioxide was experimentally studied in a two-compartment setup at various component concentrations and pressures. Regimes of mixing are determined depending on the initial concentrations of binary mixture components.     

General HETP equation for the study of mass-transfer mechanisms in RPLC

Classical HETP equations including the Van Deemter and the Knox equations, are semiempirical, approximate equations that provide apparent mass-transfer coefficients with little sound physical justifications. The conventional A and B coefficients are revisited, the former through the use of the fundamental theory of eddy diffusion due to Giddings, the latter by taking into account the intraparticle diffusion (pore and surface diffusion). Our work confirms that eddy diffusion originated from three different sources in RPLC: trans-channel, short-range interchannel, and long-range interchannel velocity biases. Accordingly, the eddy diffusion term is given by the ratio of two third-degree polynomials. Finally, the C term is the sum of two terms corresponding to the resistance to mass transfer due to diffusion through the external stationary film of liquid phase surrounding the silica particles and to the classical resistances to mass transfer due to diffusion through the silica particles. It is easily related to the physical characteristics of the phenomena involved. Experimental HETP data were derived from moment analysis for phenol on a C(18)-Sunfire column, with a mixture of acetonitrile and water as the mobile phase (15/85, v/v). The linear interstitial velocity ranged between 0.027 cm/s and 4.7 mL/min, and six temperature (21, 36, 45, 55, 67, and 77 degrees C) were applied successively. The HETP equation obtained was tested to study the mass-transfer mechanism. An excellent agreement was found between the experimental and theoretical HETP. The model allows the precise calculation of the activation energy for surface diffusion (E(S) = 31.3 kJ/mol) and the coefficient beta that relates the restriction energy for molecular diffusion on the C(18)-bonded surface to the isosteric heat of adsorption Q(st) (beta = 0.80).     

Sound-velocity measurements for HFC-134a and HFC-152a with a spherical resonator

A spherical acoustic resonator was developed for measuring sound velocities in the gaseous phase and ideal-gas specific heats for new refrigerants. The radius of the spherical resonator, being about 5 cm, was determined by measuring sound velocities in gaseous argon at temperatures from 273 to 348 K and pressures up to 240 kPa. The measurements of 23 sound velocities in gaseous HFC-134a (1,1,1,2-tetrafluoroethane) at temperatures of 273 and 298 K and pressures from 10 to 250 kPa agree well with the measurements of Goodwin and Moldover. In addition, 92 sound velocities in gaseous HFC-152a (1,1-difluoroethane) with an accuracy of ±0.01% were measured at temperatures from 273 to 348 K and pressures up to 250 kPa. The ideal-gas specific heats as well as the second acoustic virial coefficients have been obtained for both these important alternative refrigerants. The second virial coefficients for HFC-152a derived from the present sound velocity measurements agree extremely well with the reported second virial coefficient values obtained with a Burnett apparatus.Paper dedicated to Professor Joseph Kestin.     

Phase diagrams beyond the critical point

Following a path in the usual p‐T‐diagrams of one‐component systems via the supercritical region it seems that one can make a transition from the liquid to the gas phase (and in reverse) without traversing a phase boundary curve, whereas in the sub‐critical region one clearly has to pass a phase boundary curve. To solve this paradox situation, the phase diagrams of one‐component systems are analyzed with respect to the phase transition from the liquid to the gas state in the sub‐ and supercritical range. It is shown that the critical point is not an isolated point or an end point on the phase boundary curve between the gaseous and the liquid phase in a p‐T‐diagram. Instead, it marks on the boundary curve just the transition between the section of a first order phase transition in the sub‐critical range and the section of a second or higher order phase transition in the supercritical range. Thus, the present phase diagrams of one‐component systems are incomplete with respect to the phase boundary curve between liquid and gas in the supercritical region. The result is illustrated using the model of a van der Waals gas.     

Mutual diffusivity in binary mixtures of n-heptane with n-hexane isomers

This paper presents a study of the influence of branching in the binary diffusion coefficients of n-heptane + n-hexane isomers, in the liquid state. The measurements have been made with the Taylor dispersion technique, at several compositions, at 283 and 298 K, for the X + n-heptane mixtures, where X= n-hexane, 3-methylpentane, 2, 3-dimethylbutane, and 2, 2-dimethylbutane. The results show a very interesting behavior of the composition dependence of the binary diffusion coefficients, presenting a maximum, for compositions about a molar fraction of n-heptane of 0.5, which increases with the increase in the degree of branching, suggesting the possibility of order-disorder effects caused by stereochemically favored packing in the liquid phase and energetically favored segment interaction in the liquid mixtures. An attempt to apply the van der Waals model to these data could not predict the experimental binary diffusion coefficients of these systems within the experimental accuracy.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Mass transfer in a rotor dispersion-film apparatus

Results of experimental investigations of the desorption of carbon dioxide from water in a rotor dispersion-film apparatus are presented. The main factors influencing the volume mass-transfer coefficient in the liquid phase and the efficiency of mass transfer in this apparatus were determined. A comparative analysis of the apparatus investigated with other analogous apparatus has been carried out. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 2, pp. 144–148, March–April, 2007.     

Self Diffusion and Binary Maxwell–Stefan Diffusion in Simple Fluids with the Green–Kubo Method

Self-diffusion coefficients and binary Maxwell–Stefan diffusion coefficients were determined by equilibrium molecular dynamics simulations with the Green–Kubo method. The study covers five pure fluids: neon, argon, krypton, xenon, and methane and three binary mixtures: argon+krypton, argon+xenon, and krypton+xenon. The fluids are modeled by spherical Lennard-Jones pair-potentials, with parameters which were determined solely on the basis of vapor-liquid equilibrium data. The predictions of the self-diffusion coefficients agree within 5% for gas state points and about 10% for liquid state points. The Maxwell–Stefan diffusion coefficients are predicted within 10%. A test of Darken's model shows good agreement.     

Infinite Dilution Binary Diffusion Coefficients of Benzene in Carbon Dioxide by the Taylor Dispersion Technique at Temperatures from 308.15 to 328.15 K and Pressures from 6 to 30 MPa

Infinite dilution binary diffusion coefficients, D ₁₂, of benzene in carbon dioxide were measured by the Taylor dispersion technique at temperatures from 308.15 to 328.15 K and pressures from 6 to 30 MPa. The diffusion coefficients were obtained by the method of fitting in the time domain from the response curves measured with a UV–vis multidetector by scanning from 220 to 280 nm at increments of 1 or 4 nm. The wavelength dependences on the binary diffusion coefficient and the uncertainty were examined. The detector linearity, in terms of the relationship between the absorbance intensity and the product of the peak area of the response curve and CO₂ velocity, was found to fail at some characteristic absorption wavelengths such as 243, 248, 253, and 259 nm, even when the maximum absorbance intensities of the response curves were less than 0.5 and the fits were good. Although the D ₁₂ values obtained from the response curves measured at 253 nm were almost consistent with some literature data, the D ₁₂ values measured at wavelengths showing the detector linearity to be satisfactory, i.e., at 239 nm, were higher than those at 253 nm. The present D ₁₂ data at 239 nm were well represented by the Schmidt number correlation, except for those showing the anomalous decrease in a plot of D ₁₂ vs density in the density range from 250 to 500 kg·m^–3.     

Self-Diffusion and Binary Maxwell–Stefan Diffusion Coefficients of Quadrupolar Real Fluids from Molecular Simulation

Self- and binary Maxwell–Stefan (MS) diffusion coefficients were determined by equilibrium molecular dynamics simulations with the Green–Kubo method. This study covers self-diffusion coefficients at liquid states for eight pure fluids, i.e., F₂, N₂, CO₂, CS₂, C₂H₆, C₂H₄, C₂H₂, and SF₆ as well as MS diffusion coefficients for three binary mixtures N₂+CO₂, N₂+C₂H₆, and CO₂+C₂H₆. The fluids were modeled by the two-center Lennard–Jones plus point-quadrupole pair potential, with parameters taken from previous work of our group which were determined solely on the basis of vapor–liquid equilibrium data. Self-diffusion coefficients are predicted with a statistical uncertainty less than 1%, and they agree within 2–28% with the experimental data. The correction of the simulation data due to the finite size of the system increases the value of the self-diffusion coefficient typically by 10%. If this correction is considered, better agreement with the experimental data can be expected for most of the studied fluids. MS diffusion coefficients for three binary mixtures were also predicted; their statistical uncertainty is about 10%. These results were used to test three empirical equations to estimate MS diffusion coefficients in binary mixtures, i.e., the equations of Caldwell and Babb, of Darken, and of Vignes. The equations of Caldwell and Babb and of Vignes show qualitatively different behavior of the MS diffusion coefficient than that observed in the simulations. In agreement with previous work, the best results are obtained in all cases with the equation of Darken.     

Diffusion processes inβ-Zr(Al) phase: a thermodynamic approach

The diffusion behaviour in theβ -Zr(Al) solid solution phase was investigated in the temperature range 1203-1323 K using a thermodynamic approach. The Boltzmann-Matano relation used for determining interdiffusion coefficients and the Darken’s equations used for evaluating the intrinsic diffusion coefficients from velocity of movement of markers in diffusion couples were modified suitably. The composition dependent thermodynamic interdiffusion coefficients were evaluated using chemical potential gradient. Composition and temperature dependence of the thermodynamic interdiffusion coefficients were also established. The thermodynamic intrinsic diffusion coefficients of Al and Zr and their temperature dependence were determined using the modified Darken’s equations.     

Thermodynamic and transport properties of fluids and fluid mixtures in the extended critical region

A practical representation of the thermodynamic properties and the transport coefficients related to diffusion, heat conduction, and their cross-processes in pure fluids and binary mixtures near the liquid-vapor critical line is developed. Crossover equations for the critical enhancement of those coefficients incorporate the scaling laws near the critical point and are transformed to the regular background far away from the critical point. The crossover behavior of the thermal conductivity and the thermal diffusion ratio in binary mixtures is also discussed. A comparison is made with thermal-conductivity data for pure carbon dioxide, pure ethane, and carbon dioxide add ethane mixtures.