Three Green element models for the diffusion–advection equation and their stability characteristics

Solutions of the transient 1-D diffusion–advection equation by three models of the Green element method (GEM) and their stability characteristics are presented. GEM is a novel approach of implementing the singular boundary integral theory so that computational efficiency is enhanced, and the theory is made more versatile. The first model, denoted as the quasi-steady Green element (QSGE) model, employs the Green’s function of the Laplacian operator in deriving its integral representation, while the second, denoted the TGE model, uses the Green’s function of the transient diffusion differential operator, and the third, denoted the ADGE model, uses the Green’s function of the diffusion–advection differential operator. The first model, which had earlier been presented, is herein compared to the other two models. Three numerical examples are used to compare the accuracies of the three models. It is observed that incorporating the Crank–Nicholson scheme into the first model not only gives optimal results of the three models, but it more readily accommodates transport with nonuniform flow velocity field and first-order rate of decay of the pollutant. Further, the mathematical simplicity of the Green’s function of the first model is an added advantage which enhances computational efficiency. The numerical stability characteristics of these models are evaluated by examining their propagation of the amplitudes and speeds of Fourier wave components in relation to their corresponding theoretical values. The results from the stability analysis confirms the superiority of the QSGE model with the Crank–Nicholson scheme.     

Mass Diffusion and Thermal Diffusivity of the Decane-pentane Mixture Under High Pressure as a Ground-based Study for SCCO Project

Thermodiffusion experiments on isomassic binary mixture of decane and pentane in the liquid phase have been performed between 25 ^°C and 50 ^°C and for pressures from 1MPa until 20MPa. By dynamic analysis of the light scattered by concentration non-equilibrium fluctuations in the binary mixture we obtained the mass diffusion coefficients of the mixture at each temperature and pressure. For the first time we were able to apply similar analysis to thermal fluctuations thus getting a simultaneous measurement of the thermal diffusivity coefficient. While mass diffusion coefficients decrease linearly with the pressure, thermal diffusivity coefficients increase linearly. In principle the proposed method can be used also for measuring the Soret coefficients at the same time. However, for the present mixture the intensity of the optical signal is limited by the optical contrast factor. This affects our capability of providing a reliable estimate of the Soret coefficient by means of dynamic Shadowgraph. Therefore the mass diffusion coefficients measurements would need to be combined with independent measurements of the thermodiffusion coefficients, e.g. thermogravitational column, to provide Soret coefficients. The obtained values constitute the on-ground reference measurements for one of the mixture studied in the frame of the project SCCO-SJ10, which aims to measure the Soret coefficients of multicomponents mixtures under reservoir conditions. Microgravity experiments will be performed on the Chinese satellite SJ10 launched in April 2016.     

Calculation of the mutual diffusion coefficient by equilibrium and nonequilibrium molecular dynamics

A nonequilibrium molecular dynamics method for the calculation of the mutual diffusion coefficient for a mixture of hard spheres is described. The method is applied to a 50-50 mixture of equidiameter particles having a mass ratio of 0.1 for the two species, at a volume of three times close-packing. By extrapolating the results to the limit of vanishing concentration gradient and infinite system size, we obtain a value in statistical agreement with the result obtained using a Green-Kubo molecular dynamics procedure, which is also described. The non-equilibrium calculation yields a mutual diffusion coefficient which decreases slightly with increasing concentration gradient. The Green-Kubo timecorrelation function for mutual diffusion displays a slow decay with time, qualitatively similar to the long-time tail which has been predicted by the hydrodynamic theory of Pomeau.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Measurement of Diffusion in Ternary Liquid Mixtures by Light Scattering Technique and Comparison with Taylor Dispersion Data

Results of diffusion coefficient measurements by dynamic light scattering (DLS) in the ternary liquid systems, glycerol–acetone–water (GAW), and cyclohexane–methanol–toluene (CMT), are reported. Data for the GAW system are compared with Taylor dispersion (TD) measurements in overlapping concentration regions close to the critical solution point at 298.15 K. A fit of the intensity autocorrelation function (ACF) could be used to predict values and explain the physical character of the corresponding diffusion coefficients. In the vicinity of the critical solution point, the DLS measurements reveal two and more hydrodynamic relaxation modes with well separated characteristic relaxation times. From the ACF, at least two effective diffusivities, D ₁ and D ₂, can be experimentally determined. Theoretical predictions reveal that they may result from pure mass diffusion and pure thermal diffusion transport processes. A possible physical meaning of the modes D ₁ and D ₂ in the ternary liquid mixtures is discussed. When we compare the transport modes from DLS with the Taylor dispersion results, only the slowest mode represents mass diffusion, and this mode agrees very well with one of the eigenvalues of Fick’s diffusion matrix. There is no relation between the mass diffusion mode from DLS and any one of the four diffusion coefficients obtained by TD.     

Estimation of interdendritic undercooling during freezing of ternary and quaternary aluminium alloys

Expressions have been developed for the maximum interdendritic supercooling during the freezing of ternary and quaternary systems. The actual undercoolings during freezing of several ternary and quaternary aluminium base alloys have been computed. Using available data for the measured diffusion coefficients and assuming reasonable values for other diffusion coefficients, it is shown that the interdendritic supercooling does not exceed one degree centigrade in all the aluminium alloys investigated. In fact, in most of the alloys it is less than a tenth of a degree centrigrade.     

Rayleigh waves at the boundary surface of modified couple stress generalized thermoelastic with mass diffusion

In this problem, we have studied propagation of Rayleigh waves in an homogeneous isotropic modified couple stress generalized thermoelastic with mass diffusion solid half space in the context of Lord–Shulman (L-S), Green–Lindsay (G-L) theories of thermoelasticity. Secular equations are derived mathematically by using appropriate boundary conditions. The values of determinant of secular equation, Rayleigh wave velocity and attenuation coefficient with respect to angular velocity for different values of wave number and relaxation times in the absence and presence of mass diffusion, are computed numerically. The numerical simulated results are depicted graphically for copper material.     

Permeation of aromatic solvent mixtures through nitrile protective gloves

The permeation of binary and ternary mixtures of benzene, toluene, ethyl benzene and p-xylene through nitrile gloves were investigated using the ASTM F739 test cell. The more slowly permeating component of a mixture was accelerated to have a shorter breakthrough time than its pure form. The larger differences in solubility parameter between a solvent mixture and glove resulted in a lower permeation rate. Solubility parameter theory provides a potential approach to interpret the changes of permeation properties for BTEX mixtures through nitrile gloves. Using a one-dimensional diffusion model based on Fick's law, the permeation concentrations of ASTM F739 experiments were appropriately simulated by the estimated diffusion coefficient and solubility. This study will be a fundamental work for the risk assessment of the potential dermal exposure of workers wearing protective gloves.     

Diffusion Modes of an Equimolar Methane–Ethane Mixture from Dynamic Light Scattering

The hydrodynamic diffusion modes of an equimolar methane–ethane mixture have been investigated by dynamic light scattering. Measurements were performed over a wide temperature range between the plait critical point at 263.55 K and 310 K along the critical isochore. Two relaxation modes have been observed which are commonly associated with pure mass diffusion and pure thermal diffusion, but in near-critical binary fluid mixtures—according to recent theory—may alternatively be interpreted as two effective diffusivities resulting from a coupling between mass and thermal diffusion. Diffusivity values for the slow mode were obtained with typical standard deviations of 1% over the whole temperature range, whereas the low amplitude of the fast mode only allowed values of this component with a large measurement uncertainty. The results are discussed in connection with literature data available for the thermophysical properties of this binary fluid mixture and regarding the various possibilities of theoretical interpretation.     

Thermo-acoustical waves in linear thermo-elastic materials

Summary Coupled waves of thermal and mechanical jumps in linear thermo-elastic materials are analysed. General linear anisotropic constitutive equations of thermo-elastic materials are derived from the Clausius-Duhem inequality and Vernotte's heat conduction law is adopted. The waves are defined to have jumps in acceleration and in temperature rate and the four-dimensional thermo-acoustical propagation condition is obtained. The differential equations which govern the variation of the wave amplitudes are obtained. For waves in linear isotropic thermo-elastic materials, there are four principal waves. Two shear waves are purely mechanical and propagate with constant amplitude, while two thermo-longitudinal waves have different propagation velocities: one is larger and other smaller than the purely mechanical longitudinal wave velocity, and their amplitudes decay, in general, exponentially in time.     

Prediction of Thermodynamic Properties of Liquid Air

In this work, a simple equation of state (EoS) has been used to predict some thermodynamic properties of air as a pseudo-pure fluid; as a ternary mixture of nitrogen, oxygen, and argon; and as a binary mixture of nitrogen and oxygen at different temperatures and pressures. A comparison with literature tabulated values has been made. The agreement of calculated densities with corresponding tabulated values is good for which the average absolute deviations are better than 0.06% if we assume air as a pseudo-pure fluid, and 0.9% and 1.2% if we consider air as a ternary mixture and as a binary mixture, respectively. To show the ability of this equation of state to predict density, the calculated densities of air have been compared with those computed by other methods.     

Taylor dispersion analysis of mixtures

Taylor dispersion analysis (TDA) is a fast and simple method for determining hydrodynamic radii. In the case of sample mixtures, TDA, as the other nonseparative methods, leads to an average diffusion coefficient on the different molecules constituting the mixture. We set in this work the equations giving, on a consistent basis, the average values obtained by TDA with detectors with linear response functions. These equations confronted TDA experiments of sample mixtures containing different proportions of a small molecule and a polymer standard. Very good agreement between theory and experiment was obtained. In a second part of this work, on the basis of monomodal or bimodal molar mass distributions of polymers, the different average diffusion coefficients corresponding to TDA were compared to the z-average diffusion coefficient (D(z)) obtained from dynamic light scattering (DLS) experiments and to the weight average diffusion coefficient (D(w)). This latter value is sometimes considered as the most representative of the sample mixture. From these results, it appears that, for monomodal distribution and relatively low polydispersity (I = 1.15), the average diffusion coefficient generally derived from TDA is very close to Dw. However, for highly polydisperse samples (e.g., bimodal polydisperse distributions), important differences could be obtained (up to 35% between TDA and D(w)). In all the cases, the average diffusion coefficient obtained by TDA for a mass concentration detector was closer to the Dw value than the z-average obtained by DLS.     

Vibrational effect on thermal diffusion under different microgravity environments

Microgravity environments may provide perspective platforms for studying the phenomenon of thermal diffusion. It is, however, noted that the residual microaccelerations (g-jitters) in space laboratories may affect the accuracy of experiments due to convections that they induce. An appropriate interpretation of experimental results from the Space relies on a thorough understanding of the influence of g-jitters on thermal diffusion. In this paper, we have modelled the thermal diffusion process under different microgravity environments using measured g-jitter data onboard the International Space Station (ISS) and FOTON-12. The fluid system consists of a rectangular cavity filled with a ternary mixture of methane, n-butane and dodecane (50∶20∶30 mol%). A lateral heating condition is applied. Various case scenarios have been studied with respect to different locations in the ISS and FOTON; and a detailed analysis is made in comparison with the ideal zero gravity (0-g) scenario. It is found that the diffusion process is only slightly affected by the g-jitters in both platforms. Recommendations are made according to the findings from this study for the improvement of the accuracy of diffusion experiments in Space.     

Comparative criteria for finite-difference formulations for problems of fluid flow

This paper concerns a technique for providing quantitative and qualitative answers to the questions related to accuracy and stability of finite-difference schemes. It is applicable to both the unsteady and the steady flows. The application of the technique provides comparative information about the amplitudes and the speeds of propagation of the numerical and analytic solutions. The difference between the two solutions is characterized in terms of a ‘false’ propagation speed and ‘false’ diffusion parameters for the numerical schemes. The technique is applied to a number of commonly used finite-difference schemes and it is concluded that the use of central differences for the convective terms and/or explicit formulations tends to increase the amplitudes and wave speeds. The opposite effects on the amplitudes and wave speeds are produced by upwind or ‘donor’ cell differences and/or implicit formulations.     

Laminar separation bubbles: Dynamics and control

This work is an experimental investigation of the dynamics and control of the laminar separation bubbles which are typically present on the suction surface of an aerofoil at a large angle of attack. A separation bubble is produced on the upper surface of a flat plate by appropriately contouring the top wall of the wind tunnel. First, a basic (unforced) separation bubble is obtained to set a benchmark for further experiments. Parametric study is done where the reference velocity is decreased to quantify its effect on the aspect ratio of the bubble. It is found that with decrease in Reynolds number, the height of the bubble increases at a greater rate than the length. This feature could be useful in characterising separation bubbles especially from the point of view of low Reynolds number aerofoil design. Artificial disturbance is introduced at two different initial amplitudes (infinitesimal and finite) upstream of separation location and hotwire anemometry is used to trace the wave packet as it is advected downstream. The evolution of wave packets is seen to take place in two distinct stages. Finite amplitude forcing causes periodic quenching of the bubble. Interestingly, even an infinitesimally small forcing is seen to modify and thereby control the separation bubble.     

Enhancement of sonodynamic tissue damage production bysecond-harmonic superimposition: theoretical analysis of its mechanism

Among the nonthermal effects of ultrasound, acoustic cavitation may have the highest potential for therapeutic applications if it can be somehow controlled. Recent in vitro and in vivo experiments have demonstrated that sonochemically active cavitation can be enhanced an order of magnitude by superimposing the second harmonic onto the fundamental in insonation. Moreover, they have shown that sonochemically active cavitation can be controlled with relative ease, thereby even in a progressive wave field. The effect of second-harmonic superimposition on the rectified diffusion through the gas-liquid interface of cavitated microbubbles is estimated theoretically. The theoretical rectified diffusion rate explained an asymmetric behavior of the threshold for producing sonodynamic tissue damage as a function of the fundamental and the second-harmonic amplitudes. The tissue damage was produced with a focused progressive wave in a liver lobe of a mouse administered with a sonodynamically active agent. The result suggests that the acceleration of the rectified diffusion is a primary mechanism of the enhancement of sonodynamically effective cavitation by second-harmonic superimposition     

Depth-averaged relations for granular-liquid uniform flows over mobile bed in a wide range of slope values

The behavior of liquid-granular flows, driven by gravity, is experimentally analyzed. Two types of free-surface uniform flow can take place, having different boundary conditions at the bottom. The first one runs over a fixed surface behaving as a solid (non-deformable) impermeable wall; the second one runs over a mobile-bed at rest, formed by the same loose grains and liquid of the flowing mixture. In the paper we will mark the differences between the two, but focus on the latter one. The experiments span over, and characterize, the possible flow regimes. In mobile-bed uniform flows it has been found that the Froude number reduces as the slope increases. Accordingly, there is an increment of the solid-concentration. These results are meaning that as slope increases a progressive dominance and thickening of frictional layers over collisional ones is taking place through the flow depth. Same behaviours have been observed by changing the type of grains in the flowing mixture. These findings contrast with the case of flows over a solid wall, where different trends are observed. Application of force balances by means of Coulomb law provides interesting confirmation of what observed and allows to take into account the surface-tension effects, which come into play when the particles on top are going to desaturate. Experimental data have also been employed to assess the applicability of kinetic theories to wet granular flows. Energy and momentum balances, under the hypothesis of no contribution in the liquid phase (except for the added mass concept) to shear stress and to the energy processes, are applied throughout the flow depth of the solid phase. Although depth-averaged quantities come out to have a trend similar to the experimental one, deficiencies in the theoretical approach, mainly due to its inability to represent frictional contacts, are clearly detected. Same conclusions may be drawn by applying the quite simple Bagnold theory. Altogether, a more appropriate theory able to deal with both collisional and frictional mechanisms, including the transition between, is demanded.     

Variation of amplitudes of thermo-acoustical waves of arbitrary form in isotropic linear thermo-elastic materials

Summary The growth and decay of the amplitudes of a thermo-longitudinal coupling wave of arbitrary form are investigated theoretically for isotropic linear thermo-elastic materials. As heat conduction law Vernotte's formula is adopted. Thomas' compatibility conditions of the second order for a singular surface of arbitrary form are used and the global behavior of the amplitude of the wave is analyzed. The geometrical effect of the wave front for the variation of amplitude depends upon the path length and the initial values of the mean and Gaussian curvatures. The thermal decay effect for the coupling wave is expressed as an exponential function of time and the damping factor is proportional to the thermal conductivity.     

Rayleigh-Lamb Waves in Transversely Isotropic Thermoelastic Diffusive Layer

Propagation of plane harmonic thermoelastic diffusive waves in a homogeneous, transversely isotropic, thin elastic layer of finite width is studied, in the context of the theory of coupled thermoelastic diffusion. According to the characteristic equation, three quasi-longitudinal waves, namely, quasi-elastodiffusive (QED) mode, quasi-mass diffusion (QMD) mode, and quasi-thermodiffusive (QTD) mode can propagate in addition to quasi-transverse waves (QSV) mode and the purely quasi-transverse motion (QSH) mode, which is not affected by thermal and diffusion vibrations, gets decoupled from the rest of the motion of wave propagation. The secular equations corresponding to the symmetric and skew symmetric modes of the layer are derived. The amplitudes of displacements, temperature change, and concentration for symmetric and skew symmetric modes of vibration of the layer are computed numerically. Anisotropy and diffusion effects on the phase velocity, attenuation coefficient, and amplitudes of displacements, temperature change, and concentration are presented graphically in order to illustrate and compare the results analytically. Some special cases of the frequency equation are also deduced and compared with the existing results.     

A mathematical model of mass transport in the lung

A mathematical model of mass transport in the lung is developed. This model is concerned with gaseous diffusion in the region distal to the terminal bronchioles, following the suggestion that in this region the airflow is small and gaseous diffusion accounts for practically all of the mass transport. Differential equations for diffusion in a ternary mixture are written in the form of state equations. The resulting two equations are solved by state variable techniques utilizing a computer program which calculates the partial pressures of oxygen and carbon dioxide in ventilated blood as a function of ventilation rate. The program includes the effects of oxygen and carbon dioxide dissociation curves as well as conducting the calculations for each lobe of the lung independently. The model shows good correlation with published data.     

Simplified Model for the Critical Thermal-Conductivity Enhancement in Molecular Fluids

This paper reviews the available information for the thermal-conductivity enhancement. This enhancement can be represented by a simplified solution of the mode-coupling theory of critical dynamics with two critical amplitudes and one cutoff wave number as fluid-specific parameters. Using corresponding states, these fluid-specific parameters are correlated in terms of their dependence on the acentric factor. A universal representation of the critical enhancement of the thermal conductivity for a large number of molecular fluids is presented.