Measurement of the concentration diffusion coefficient for Ne-Ar, Ne-Xe, Ne-H2, Xe-H2, H2-N2 and H2-O2 gas systems

The concentration diffusion coefficient, D ₁₂, is measured for the equimolar mixtures of Ne-Ar, Ne-Xe, Ne-H₂, Xe-H₂, H₂-N₂ and H₂-O₂ binary gas systems in a two-bulb metal apparatus in the temperature range 0 C to 100 C. These values are compared with the existing data on these systems and with the predictions of the kinetic theory in conjunction with the modified Buckingham exp-six potential. Unlike the thermal diffusion coefficient, with the simple theory it is possible to predict D ₁₂ within a few percent even for systems involving polyatomic gases. The smoothed experimental D ₁₂ values are also used to obtain data for the coefficients of viscosity and thermal conductivity at round temperatures and compositions for these systems.Nomenclature C ₂ ^t relative amount of a gas in the mixture in the bulb 2 at an instant t - C ₂ relative amount of the same gas in the mixture in the bulb 2 at equilibrium - D ₁₂ diffusion coefficient - X ₁ mole-fraction of the heavier component in the mixture - _mix viscosity coefficient - _mix thermal conductivity coefficient     

Inverse Estimation of the Effective Diffusion of the Filter in the In Situ Diffusion and Retention (DR) Experiment

Porous filters are often used in laboratory and in situ diffusion and retention experiments. The proper interpretation of these experiments requires knowing the effective diffusion, D _e, of the filter which is commonly determined from laboratory diffusion experiments or estimated from the filter porosity. The D _e of the filter in the in situ experiment may differ from the D _e of the filter measured in the laboratory due to pore clogging. Here, we present an inverse method to estimate the D _e of the filter of in situ diffusion experiments. The method has been tested for several sampling schemes, numbers of synthetic data, N, and standard deviations of the noise, ??. It has been applied to the following tracers used in the in situ diffusion and retention (DR) experiment performed in the Opalinus clay at Mont Terri underground research laboratory: HTO/HDO, Br^?,I^?, ²² Na⁺,¹³³ Ba²⁺,⁸⁵ Sr²⁺, Cs⁺/¹³⁷Cs⁺, and ⁶⁰Co²⁺. The estimation error increases with the standard deviation of the noise of the data and decreases with the number of data. It is smallest for sorbing tracers. The D _e of the filter can be properly estimated from 12 data collected within the first 3?days for conservative tracers as long as ????? 0.02 and for sorbing tracers as long as ??????0.05. The estimate of D _e for conservative tracers is poor when data are collected from a 10-day experiment with daily sampling. The convergence of the estimation algorithm for conservative tracers improves by starting with a value of the D _e smaller than the true value. The choice of the initial value of D _e does not affect the convergence of the estimation algorithm for sorbing tracers. Filter clogging and vertical flow though the filter can influence the tracer transport through the filter. The use of the D _e of the filter obtained from a laboratory test for the in situ experiment may result in large errors for strongly sorbing tracers. Such errors can be overcome by estimating the equivalent D _e of the filter with the proposed inverse method which will be useful for the design of in situ diffusion experiments.     

H 2 optimal filtering for bilinear systems

The filtering problem is among the fundamental issues in control and signal processing. Several approaches such as H ₂ optimal filtering and H _?? optimal filtering have been developed to address this issue. While the optimal H ₂ filtering problem has been extensively studied in the past for linear systems, to the best of our knowledge, it has not been studied for bilinear systems. This is indeed surprising, since bilinear systems are important class of nonlinear systems with well-established theories and applications in various fields. The problem of H ₂ optimal filtering for both discrete-time and continuous bilinear systems is addressed in this paper. The filter design problem is formulated in the optimization framework. The problem for the discrete-time case is expressed in terms of linear matrix inequalities which can be efficiently solved. The results are used for the optimal filtering of a bilinear model of an electro-hydraulic drive.     

Theoretical and experimental studies on the coefficient of discharge and spray cone angle of a swirl spray pressure nozzle using a power-law non-Newtonian fluid

An extension of earlier work is made in the present paper to determine both theoretically and experimentally the coefficient of discharge and spray cone angle of a swirl nozzle using a time-independent purely viscous power-law non-Newtonian fluid. The theoretical predictions are made through an approximate analytical solution of the hydrodynamics of flow inside the nozzle. Experiments are carried out with aqueous solutions of CMC (carboxymethyl cellulose sodium salt) powder of various concentrations as the working fluids. The rheological properties of the working fluids are established by a capillary tube viscometer. From both the theoretical and experimental analyses, the pertinent independent input parameters are recognised as the generalised Reynolds number at inlet to the nozzle Re_Gi, the flow behaviour index of the fluid n, length-to-diameter ratio of the swirl chamber L₁/D₁, spin chamber angle 2α and the orifice-to-swirl-chamber-diameter ratio D₁/D₁. Although the theory predicts the correct qualitative trend in all cases, it does not agree well with the experimental results. Therefore, on the basis of the theoretical results, emperical relationships between nozzle characteristics and input parameters heve been established. Finally it is recognised that, regarding the injection conditions and fluid properties, the generalised Reynolds number at nozzle inlet Re_Gi and the flow behaviour index n have inverse and direct effects, respectively, on the coefficient of discharge, but have a negligible influence on the spray cone angle. Amongst the nozzle geometries, an increase in the values of D₂/D₁ and 2α or a decrease in the value of L₁/D₁ decrease the coefficient of discharge and increase the spray cone angle.     

Mechanisms of detonation transmission in layered H2-O2 mixtures

When a plane detonation propagating through an explosive comes into contact with a bounding explosive, different types of diffraction patterns, which may result in the transmission of a detonation into the bounding mixture, are observed. The nature of these diffraction patterns and the mode of detonation transmission depend on the properties of the primary and bounding explosives. An experimental and analytical study of such diffractions, which are fundamental to many explosive applications, has been conducted in a two channel shock tube, using H₂-O₂ mixtures of different equivalence ratios as the primary and bounding or secondary explosive. The combination of mixtures was varied from rich primary / lean secondary to lean primary / rich secondary since the nature of the diffraction was found to depend on whether the Chapman-Jouguet velocity of the primary mixture,D _p, was greater than or less than that of the secondary mixture,D _s. Schlieren framing photographs of the different diffraction patterns were obtained and used to measure shock and oblique detonation wave angles and velocities for the different diffraction patterns, and these were compared with the results of a steady-state shock-polar solution of the diffraction problem. Two basic types of diffraction and modes of detonation reinitiation were observed. WhenD _p>D _s, an oblique shock connecting the primary detonation to an oblique detonation in the secondary mixture was observed. WithD _p<D _s, two modes of reinitiation were observed. In some cases, ignition occurs behind the Mach reflection of the shock wave, which is transmitted into the secondary mixture when the primary detonation first comes into contact with it, from the walls of the shock tube. In other cases, a detonation is initiated in the secondary mixture when the reflected shock crosses the contact surface behind the incident detonation. These observed modes of Mach stem and contact surface ignition have also been observed in numerical simulations of layered detonation interactions, as has the combined oblique-shock oblique-detonation configuration whenD _p>D _s. WhenD _p>D _s, the primary wave acts like a wedge moving into the secondary mixture with velocityD _p after steady state has been reached, a configuration which also arises in oblique-detonation ramjets and hypervelocity drivers.     

Measurement of the concentration diffusion coefficient for He-Ar and Ne-Kr by a two bulb method

Summary A two bulb glass apparatus was used to measure the concentration diffusion coefficient of the binary gas systems He-Ar and Ne-Kr. The coefficients were determined for equimolar mixtures at temperatures between 0°C and 70°C. The diffusion was followed as a function of time by withdrawing samples and analyzing them in a specially designed thermal conductivity analyzer with high accuracy. The diffusion coefficients agree with earlier reported experimental values and with those obtained on the basis of the Chapman-Enskog theory in conjunction with the modified Buckingham exp-six and Lennard-Jones (12-6) intermolecular potentials. The smoothed values were used to predict viscosity and thermal conductivity of these mixtures as a function of composition and temperature.     

The psychrometric problem for the evaporation of NH3 in NH3/H2 atmosphere in neutral gas absorption refrigeration units for pressures 17.5 to 27.5 bar

The present work considers the thermodynamic and transport properties of the real NH₃/H₂ gas mixture as a function of the state variables temperature, mass fraction and pressure. The relevant properties are presented in the form of analytical expressions, valid in the pressure range of 17.5 to 27.5 bar. The psychrometric problem is used to determine the mass fraction of the NH₃/H₂ gas mixture with the dry and wet bulb temperatures as input variables.

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Das Psychrometrische Problem der Verdampfung von NH₃ in NH₃/H₂ Atmosphäre bei Neutralgasabsorptionskälteanlagen für Drücke von 17,5 bis 27,5 bar

Zusammenfassung In der vorliegenden Arbeit werden die thermodynamischen und Transporteigenschaften des reellen NH₃/H₂ Gasgemisches als Funktion der Zustandsvariabeln Temperatur, Massenkonzentration und Druck betrachtet. Die verschiedenen Eigenschaften sind in Form von analytischen Ausdrücken dargestellt und gelten in dem Druckbereich von 17,5 bis 27,5 bar. Das Psychrometrische Problem wurde benutzt um mit Hilfe der Trocken- und Feuchtkugeltemperatur, als Eintrittsparameter, die Massenkonzentration des NH₃/H₂-Gasgemisches zu bestimmen.

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Abbreviations

Nomenclature A ₁,...,A₃/A₁,...,A₄/A₁,...,A₄ Enthalpy coefficients [Eq. (2)] - a _ij, a_ij, a_ij: i = 1, 4,j = 1, 4 enthalpy coefficients [Eqs. (2a), (2b)–(2j),(2k)] - B ₁,B₂,..., B₅, B₆ coefficients of the Eq. (3) concerning the mass fraction of the - NH₃/H₂ gas mixture at saturated state - b _ij: i=1, 6,j = 1, 4 coefficients of the Eqs. (3a)-(3f) - B ₁₁ cm³/mole second virial coefficient of H₂ - B ₂₂ cm³/mole second virial coefficient of NH₃ - B ₁₂ cm³/mole mixture property (mixture second virial coefficient) - C ₁,..., C₃/C₁,...,C ₃/C₁,...,C₄ specific volume coefficients [Eq.(4) - c _ij, c_ij, c_ij: i = 1, 4,j = 1,4 specific volume coefficients [Eqs. (4a)-(4j)] - c _p kJ/kg grd specific heat capacity for constant pressure - D ₁₂ cm²/sec diffusion coefficient of the real - NH₃/H₂ gas mixture - D ₁,...,D₄/D₁,...,D₄/D₁,...,D₄ coefficients [Eq. (7)] concerning the thermal conductivity of the - NH₃/H₂ gas mixture - d _ij,d_ij, d_ij: i = 1, 4,j=1,4 thermal conductivity coefficients [Eqs. (7a)-(7l)] - f _G mass fraction of the real NH₃/H₂ gas mixture - > f _sat,f _s mass fraction at saturation state - h kJ/kg specific enthalpy of the NH₃/H₂ gas mixture - H kJ/kmole molar enthalpy - H ₁₁ kJ/kmole molar enthalpy of the H₂ - H ₂₂ kJ/kmole molar enthalpy of the NH₃ - h _G kJ/kg specific enthalpy of the NH₃/H₂ gas mixture at bulk state conditions - h _s kJ/kg specific enthalpy of the NH₃/H₂ gas mixture at interface state conditions - n moles of the mixture - N _pr Prandtl number - Schmidt number - Lewis number - p bar pressure (total pressure of the NH₃/H₂ gas mixture) - r coefficient of the thermal conductivity of the NH₃/H₂ gas mixture - T °C, K temperature - m³/kg specific volume - mole fraction - ₁ moles H₂/moles mixture - ₂ moles NH₃/moles mixture Greek letters , _M kJ/m h grd thermal conductivity of the real NH₃/H₂ gas mixture - ₁ kJ/m h grd thermal conductivity of the H₂ - ₂ kJ/m h grd thermal conductivity of the NH₃ - P dynamic viscosity of the real NH₃/H₂ gas mixture - kg/m₃ density of the real NH₃/H₂ gas mixture     

2-D Simulation of Non-Isothermal Fate and Transport of a Drip-Applied Fumigant in Plastic-Mulched Soil Beds. II. Sensitivity Analysis and Model Application

Temperature dependence of selected parameters was defined and illustrated. The order of sensitivity among tested model parameters (sorption coefficient, K _D; diffusion coefficient, D _g; vapor pressure, P; degradation rate, k; Henry’s constant, H) was k > P > K _D > H > D _g for 1-day simulations and k > P and K _D > D _g > H for 2-day simulations. The most sensitive parameter for both days was k. Mass balance errors were calculated using NRMSE (normalized root mean square error) to evaluate the level of agreement. The numerical model was applied to predict fumigant movement in the soil bed.     

Calculation of convective heat flux in the vicinity of the stagnation point for partially ionized gas flow past a body

From numerical solutions of the boundary layer equations for a four-component gas mixture (E, N⁺, N₂, and N) with gas injection, approximate formulas for the heat flux as a function of the variation of λρ/c_p and h^* across the boundary layer and the magnitude of the objection are obtained (λ is the thermal conductivity of the mixture,ρ is density, c_p is the specific heat, and h^* is the enthalpy of the ideal gas state of the mixture). An effective ambipolar diffusion coefficient D^(a)(i) is introduced, making possible finite formulas for the convective heat fluxes in the “frozen” boundary layer. We study the behavior of these coefficients within the boundary layer. A formula is obtained for convective heat flux to the wall from partially ionized air for a nine-component mixture (E, O⁺, N⁺, NO⁺, O, N, NO, O₂ N₂). Even for simpler four-component gas model three effective ambipolar diffusion coefficients are necessary: $$\begin{gathered} D^{(a)} (A) = D (A, M) D^{(a)} (I) = 2D (A, M), \hfill \\ D^{(a)} (M) = [ 1 + c_e (I)] D(A, M). \hfill \\ \end{gathered} $$ Here D(A, M) is the binary diffusion coefficient of the atoms into molecules, and c_e(I) is the ion concentration at the outer edge of the boundary layer. The assumption of an infinitely large charge-exchange cross section and the other simplifying assumptions used in [1] lead to overestimation of the magnitude of the dimensionless heat flux by 7–15% for the “frozen” boundary layer case.     

Heat,Water, and Solution Transfer in Unsaturated Porous Media: I -- Theory Development and Transport Coefficient Evaluation

A detailed theory describing the simultaneous transfer of heat, water, and solute in unsaturated porous mediais developed. The theory includes three fully-coupledpartial differential equations. Heat, water, andsolute move in the presence of temperature, T; matricpressure head, _m ; solution osmotic pressure head _o ; and solute concentration C gradients. Thetheory can be applied to describe the mass and energyin radioactive waste repositories, food processing,underground energy storage sites, buried electriccables positions, waste disposal sites, and inagricultural soil. Several transport coefficients forheat, water, and solute are included in the theory. The coefficients are evaluated for a silty clay loamsoil to clarify their dependence on water content (),T, and C. The thermal vapor diffusivity D _Tv first increased as increased to0.22 m³/m³ then decreased with furtherincreases in . D _Tv was 3 orders of magnitudegreater than either isothermal vapor D _mv orosmotic vapor D _ov , diffusivities at of0.20~m³/m³, T of 50°C, and C of 0.001mol/kg. All of the liquid and vapor water transport coefficients increased with increasing T. D _Tv decreased with increasing C to a greater extent thanD _mv and D _ov . The effective thermalconductivity decreased slightly with increasing C. Thesolute diffusion coefficient D _d was 6 to 7orders of magnitude greater than the thermal soluteand salt sieving diffusion coefficients at of0.20~m³/m³, T of 50°C, and C of 0.001 mol/kg.     

Measurements of Scalar Variance, Scalar Dissipation, and Length Scales in Turbulent Piloted Methane/Air Jet Flames

One-dimensional (line) measurements of mixture fraction, temperature, and scalar dissipation in piloted turbulent partially premixed methane/air jet flames (Sandia flames C, D, and E) are presented. The experimental facility combines line imaging of Raman scattering, Rayleigh scattering, and laser-induced CO fluorescence. Simultaneous single-shot measurements of temperature and the mass fractions of all the major species (N₂, O₂, CH₄, CO₂, H₂O, CO, and H₂) are obtained along 7 mm segments with a nominal spatial resolution of 0.2 mm. Mixture fraction, ξ, is then calculated from the measured mass fractions. Ensembles of instantaneous mixture fraction profiles at several streamwise locations are analyzed to quantify the effect of spatial averaging on the Favre average scalar variance, which is an important term in the modeling of turbulent nonpremixed flames. Results suggest that the fully resolved scalar variance may be estimated by simple extrapolation of spatially filtered measurements. Differentiation of the instantaneous mixture fraction profiles yields the radial contribution to the scalar dissipation, χ _r = 2D _ξ(?ξ/?r)², and radial profiles of the Favre mean and rms scalar dissipation are reported. Scalar length scales, based on autocorrelation of the spatial profiles of ξ and χ _r , are also reported. These new data on this already well-documented series of flames should be useful in the context of validating models for sub-grid scalar variance and for scalar dissipation in turbulent flames.     

Effects of aspect ratio on the drag of a wall-mounted finite-length cylinder in subcritical and critical regimes

The effect of cylinder aspect ratio (??H/d, where H is the cylinder height or length, and d is the cylinder diameter) on the drag of a wall-mounted finite-length circular cylinder in both subcritical and critical regimes is experimentally investigated. Two cases are considered: a smooth cylinder submerged in a turbulent boundary layer and a roughened cylinder immersed in a laminar uniform flow. In the former case, the Reynolds number Re _d (??U _?? d/??, with U _?? being the free-stream velocity and ?? the fluid viscosity) was varied from 2.61?×?10⁴ to 2.87?×?10⁵, and two values of H/d (2.65 and 5) were examined; in the latter case, Re _d ?=?1.24?×?10⁴?C1.73?×?10⁵ and H/d?=?3, 5 and 7. In the subcritical regime, both the drag coefficient C _D and the Strouhal number St are smaller than their counterparts for a two-dimensional cylinder and reduce monotonously with decreasing H/d. The presence of a turbulent boundary layer causes an early transition from the subcritical to critical regime and considerably enlarges the Re _d range of the critical regime. No laminar separation bubble occurs on the finite-length cylinder immersed in the turbulent boundary layer, and consequently, the discontinuity is not observed in the C _D?CRe _d and St?CRe _d curves. In the roughened cylinder case, the Re _d range of the critical regime grows gradually with decreasing H/d, while the C _D crisis becomes less obvious. In both cases, H/d has a negligible effect on the critical value of Re _d at which transition occurs from the subcritical to critical regime.     

Diffusion of14C in dense saturated bentonite under steady-state conditions

Diffusion coefficients are critical parameters for predicting migration rates and fluxes of contaminants through clay-based barrier materials used in many waste containment strategies. Cabon-14 is present in high-level nuclear fuel waste and also in many low-level wastes such as those generated from some medical research activities. Diffusion coefficients were measured for¹⁴C (in the form of carbonate) in bentonite compacted to a series of dry bulk densities, _b, ranging from about 0.9 to 1.6 Mg/m³. The clay was saturated with a Na-Ca-Cl-dominated groundwater solution typical of those found deep in plutonic rock on the Canadian Shield. Both effective,D _e, and apparent,D _a, diffusion coefficients were determined.D _e is defined asD _{0 a} n _e, where D₀ is the diffusion coefficient in pure bulk water, _a the apparent tortuosity factor, andn _e the effective porosity available for diffusion; andD _a is defined asD _{0 a} n _e/(n _e + _b K _d ), where K_d is the solid/liquid distribution coefficient. BothD _e andD _a decrease with increasing _b:D _e values range from about 10×10^–12 m²/s at _b0.9 Mg/m³ to 0.6×10^–12 m²/s at 1.6 Mg/m³, andD _a values vary from approximately 40×10^–12 to 4×10^–12 m²/s over the same density range. The decrease inD _e andD _a is attributed to a decrease in both _a andn _e as _b increases. The data indicate thatn _e is <10% of the total solution-filled porosity of the clay at all densities.K _d values for¹⁴C with the clay range from about 0.3 to <0.1 m³/Mg; this indicates there is a small amount of¹⁴C sorbed on the clay and/or some¹⁴C is isotopically exchanged with¹²C in carbonate phases present in the clay. Finally, theD _e values for¹⁴C are lower than those of other diffusants — I^–, Cl^–, TcO₄ ^–, and Cs⁺ — that have been measured in this clay and pore-water solution. This is attributed to lower values for bothn _e andD ₀ for¹⁴C species relative to those of the other diffusants.     

Quantification of Density-Driven Natural Convection for Dissolution Mechanism in CO<Subscript>2</Subscript> Sequestration

Dissolution of CO₂ into brine causes the density of the mixture to increase. The density gradient induces natural convection in the liquid phase, which is a favorable process of practical interest for CO₂ storage. Correct estimation of the dissolution rate is important because the time scale for dissolution corresponds to the time scale over which free phase CO₂ has a chance to leak out. However, for this estimation, the challenging simulation on the basis of convection–diffusion equation must be done. In this study, pseudo-diffusion coefficient is introduced which accounts for the rate of mass transferring by both convection and diffusion mechanisms. Experimental tests in fluid continuum and porous media were performed to measure the real rate of dissolution of CO₂ into water during the time. The pseudo diffusion coefficient of CO₂ into water was evaluated by the theory of pressure decay and this coefficient is used as a key parameter to quantify the natural convection and its effect on mass transfer of CO₂. For each experiment, fraction of ultimate dissolution is calculated from measured pressure data and the results are compared with predicted values from analytical solution. Measured CO₂ mass transfer rate from experiments are in reasonable agreement with values calculated from diffusion equation performed on the basis of pseudo-diffusion coefficient. It is suggested that solving diffusion equation with pseudo diffusion coefficient herein could be used as a simple and rapid tool to calculate the rate of mass transfer of CO₂ in CCS projects.     

The Effect of Preferential Diffusion on the Soot Initiation Process in Ethylene Diffusion Flames

The influence of differential diffusion of chemical species in the soot initiation process in turbulent flows is investigated through Direct Numerical Simulations coupled to a compact global chemical mechanisms for ethylene (C₂H₄) flame combustion (Løvås et al., Combust Sci Tech 182(11):1945?C1960, 2010) featuring the important reaction steps for acetylene production. Our focus is on the formation of acetylene (C₂H₂) which is one of the most important species indicative of soot formation layers, especially in relation to the location of the H and H₂ layers. The effect of preferential diffusion is assessed by comparison of results from unity and non-unity Lewis number simulations. The results indicate that under moderate turbulent conditions, where preferential diffusion effects become prominent, and with the global scheme used preferential diffusion greatly enhances the spread of the radical H whose peak value in mass fraction is reduced by a factor of about two; the spread of H₂ is also enhanced though to a lesser extent. Importantly, the H and H₂ spread into a range of mixture fraction Z between 0.2 and 0.3 which contains the soot formation range, supporting the hypothesis that soot formation is enhanced by preferential diffusion. Nevertheless, the acetylene formation layers themselves show little adjustment in the presence of non-unity Lewis numbers suggesting that the acetylene formation is dominated under the current conditions by the direct thermal decomposition of ethylene to acetylene in the global chemistry used. The specific F _i factors that appear in flamelet models are explicitly computed; only F _H, F _H2 and F _CO show appreciable differences on the fuel lean range of mixture fraction due to non-unity Lewis numbers, suggesting that the effects of non-unity Lewis numbers could be incorporated by a selective inclusion of only a few of the F _i factors in order to save computational time.     

Rheological modeling of the diffusion process and the interphase of symmetrical bilayers based on PVDF and PMMA with varying molecular weights

The diffusion process in the molten state at a polymer/polymer interface of symmetrical and model bilayers has been investigated using a small-amplitude oscillatory shear measurement. The polymers employed in this study were poly (vinylidene fluoride) (PVDF) and poly (methyl methacrylate) (PMMA) of varying molecular weights and polydispersities. The measurements were conducted in the linear viscoelastic regime (small deformations) so as to decouple the effect of flow from the diffusion. The focus of this paper has been to investigate the effects of healing time, angular frequency (ω), temperature, and molecular weight on the inter-diffusion and the triggered interphase between the neighboring layers. The kinetics of diffusion, based on the evolution of the apparent diffusion coefficient (D _a) versus the healing time, was experimentally obtained. The transition from the non-Fickian to the normal Fickian region for the inter-diffusion at the interface was clearly observed, qualitatively consistent with the reptation model, but it occurred at a critical time greater than the reptation time (τ _rep). In non-Fickian region, effects of frequency and temperature were studied with regard to the ratio of the apparent diffusion coefficient to the self-diffusion coefficient (D _a/D _s). The D _s determined in the Fickian region was found to be consistent with Graessley’s model as well as with the literatures. And the dependence of the D_s on the frequency agreed well with the Doi–Edwards theory, in particular, scaling as $D_{\rm s} \sim \omega^{1/2}$ at ω?>?1/τ _e and $D_{\rm s} \sim \omega^{0}$ at ω?<?1/τ _rep. Our experimental results also confirmed that the dependence of the D _s on the temperature for PMMA and PVDF can be well described by the Arrhenius law. Moreover, blends of PMMAs have been proposed in order to be able to change the $\overline M_\emph{w} $ . The rheological investigations of these corresponding bilayers rendered it possible to monitor the effect of $\overline M_\emph{w} $ on the diffusion process. The obtained results gave $D_{\rm s} \sim \overline M_\emph{w}^{-1}$ , thus corroborating some earlier studies and some experimental results recently reported by Time-Resolved Neutron Reflectivity Measurements. Lastly, the thickness of the interphase and its corresponding viscoelastic properties could be theoretically determined as a function of the healing?time.     

On the dispersion of a solute in oscillating flow through a channel

The paper presents an exact analysis of the dispersion of a solute in an incompressible viscous fluid flowing slowly in a parallel plate channel under the influence of a periodic pressure gradient. Using a generalised dispersion model which is valid for all times after the solute injection, the diffusion coefficientsK _i (τ)(i=1,2,3,…) are determined as functions of timeτ when the initial distribution of the solute is in the form of a slug of finite extent. The second coefficientK ₂(τ) gives a measure of the longitudinal dispersion of the solute due to the combined influence of molecular diffusion and nonuniform velocity across the channel cross-section. The analysis leads to the novel result thatK ₂(τ) consists of a steady partS and a fluctuating partD ₂(τ) due to the pulsatility of the flow. It is shown thatS increases with increase inλ (the amplitude of pressure pulsation) for small values ofω (the frequency of the pulsation). But for largeω, S decreases with increase inλ. It is also found that for fixedλ, there is very little fluctuation inD ₂(τ) forω=1, butD ₂(τ) shows fluctuation with large amplitude whenω slightly exceeds unity. The amplitude ofD ₂(τ) then decreases with further increase inω. Thus the variation of bothS andD ₂(τ) withω is non-monotonic. Finally,? _m , the average concentration of the solute over the channel cross-section is determined for various values ofλ andω.     

Dispersion and Dispersivity Tensors in Saturated Porous Media with Uniaxial Symmetry

The coefficient of dispersion, D _ij , and the dispersivity, a _ijkl , appear in the expression for the flux of a solute in saturated flow through porous media. We present a detailed analysis of these tensors in an axially symmetric porous medium, e.g., a stratified porous medium, with alternating layers, and show that in such a medium, the dispersivity is governed by six independent moduli. We present also the constraints that have to be satisfied by these moduli. We also show that at least two independent experiments are required in order to obtain the values of these coefficients for any three-dimensional porous medium domain.     

On the dispersion of a solute in oscillating flow of a non-Newtonian fluid in a channel

The paper presents an exact analysis of the dispersion of an immiscible solute in a non-Newtonian fluid (known as an incompressible second-order fluid which shows viscoelastic behaviour) flowing slowly in a parallel plate channel in the presence of a periodic pressure gradient. Using a generalized dispersion model which is valid for all times after the solute injection, the diffusion coefficients K _i (τ)(i=1,2,3,…) are obtained as functions of time τ in the case when the initial solute distribution is in the form of a slug of finite extent. The analysis leads to the novel result that K ₂(τ) (which is a measure of the longitudinal dispersion coefficient of the solute) has a steady part S in addition to a fluctuating part D ₂(τ) due to the pulsatility of the flow. It is found that S decreases with increase in the viscoelastic parameter M for given values of the amplitude λ and frequency ω of the pressure pulsation. On the other hand, it is found that at a fixed instant τ, the amplitude of D ₂(τ) increases with increase in M for given values of λ and ω. Further it is shown that at a given instant τ, the amplitude of D ₂(τ) decreases with increase in ω for given λ and M and the profile for D ₂(τ) becomes progressively flatter with increase in ω. Finally the axial distribution of the average concentration θ _m of the solute over the channel cross-section is determined at different instants after the solute injection for several values of M, λ and ω. The present study is likely to have important bearing on the problem of dispersion of tracers in blood flow through arteries.     

Revisiting the perforation of ductile plates by sharp-nosed rigid projectiles

The process of ductile plate perforation by sharp-nosed rigid projectiles is further examined in this work through 2D numerical simulations. We highlight various features concerning the effective resisting stress (σ_r) which a finite thickness plate, with a flow stress of Y_t, exerts on the projectile during perforation. In particular, we show that the normalized resisting stress (σ_r/Y_t) can be represented as a unique function of the normalized thickness of the plate (H/D, where H is plate thickness and D is projectile diameter), for a large range of normalized thicknesses. Our simulations for very thin target plates show that the penetration process is achieved through the well-known dishing mechanism, where the target material is pushed forward by the projectile’s nose. An important observation, which emerges from our simulations, is that the transition between the dishing and the hole enlargement mechanisms takes place at a normalized thickness of about H/D = 1/3. We also find that the normalized resistive stress for intermediate plate thicknesses, 1/3 < H/D < 1.0, is relatively constant at a value of σ_r/Y_t = 2.0. This range of thicknesses conforms to a state of quasi plane stress in the plates. For thicker plates (H/D > 1) the σ_r/Y_t ratio increases monotonically to values which represent the resistance to penetration of semi-infinite targets, where the stress state is characterized by plane strain conditions. Using a simple model, which is based on energy conservation, we can predict the values of the ballistic limit velocities for many projectile/target combinations, provided the perforation is done through the ductile hole enlargement mechanism. Good agreement is demonstrated between predictions from our model and experimental data from different sources, strongly enhancing the confidence in both the validity and usefulness of our model.