Application of dispersion theory to time domain reflectometry in soils

With time domain reflectometry (TDR) two dispersive parameters, the dielectric constant, , and the electrical conductivity, can be measured. Both parameters are nonlinear functions of the volume fractions in soil. Because the volume function of water ( _w) can change widely in the same soil, empirical equations have been derived to describe these relations. In this paper, a theoretical model is proposed based upon the theory of dispersive behaviour. This is compared with the empirical equations. The agreement between the empirical and theoretical aproaches was highly significant: the ( _w) relation of Topp et al. had a coefficient of determination r ² = 0.996 and the (_u) relation of Smith and Tice, for the unfrozen water content, _u, at temperatures below 0°C, had an r ² = 0.997. To obtain ( _w) relations, calibration measurements were performed on two soils: Caledon sand and Guelph silt loam. For both soils, an r ² = 0.983 was obtained between the theoretical model and the measured values. The correct relations are especially important at low water contents, where the interaction between water molecules and soil particles is strong.     

坡面流及土壤侵蚀动力学（II）——————土壤侵蚀

介绍了坡面土壤侵蚀的基本特征和主要类型, 综述了坡面土壤侵蚀动力学过程和预报模型等方面的研究进展, 包括土壤表层结皮、雨滴溅蚀、片流侵蚀、细沟侵蚀、坡面流输沙、土壤侵蚀界限坡度, 以及土壤侵蚀预报模型等. 并简要讨论了土壤侵蚀动力学研究的发展趋势.     

Activation energy of viscoelastic flow emulsion inks as a function of shear rate

The plastic viscosities of five production batches of a nonthixotropic pseudoplasticGestetner 217 type emulsion duplicating ink were determined at 40 RPM (700 sec^–1) using aFerranti-Shirley cone-plate viscometer. The activation energiesE were determined from the slope of anArrhenius plot over the range of 1/2 °C to 40 °C. The value ofE was not affected by batch-to-batch variations.Working with one ink only, the same procedure was then applied to shear rates from 5 to 220 RPM (87.5 to 3850 sec^–1) over the same temperature range.E was found to be constant below about 60 RPM (1000 sec^–1) but dropped rapidly with increasing shear rate above that threshold. A plot ofE vs. In shear rate gave a straight line parallel to the shear rate axis, intersected by a second straight line with a negative slope. The value ofE corresponding to the point of intersection is denotedE _L , the limiting activation energy of viscoelastic flow in a rotational shear field.It is suggested that the rate of shear corresponding toE _L is that necessary to eliminate the last traces of slippage flow in the system and to convert it to 100% laminar flow. The theoretical implications of this suggestion are discussed.Presented at the Joint Meeting of the British Society of Rheology and Research Association of British Paint, Colour and Varnish Manufacturers at Teddington, April 29, 1964.     

A method for measuring recompression shock unsteadiness applied to two supersonic wakes

The recompression shock system in blunt-base cylinder wakes at 0° and 10° angles-of-attack to an M=2.46 freestream is visualized by planar laser scattering, allowing the instantaneous position of the shock to be determined over a wide region of the flow. The recompression shock at =0° is highly branched and appears to be quite weak. The shock appears to be stronger at =10°, with far less branching. Correlation analysis for the =10° wake indicates that fluctuations in the shock position tend to be correlated over relatively long streamwise distances. Analysis of the shock angle for the angle-of-attack wake shows a significant variation in the local angle of the shock, with trends similar to those seen for the unsteadiness in the shock position.     

Thermohaline instability with thermal diffusion and horizontal gradients

The effect of thermal diffusion on an unbounded vertically stratified thermohaline fluid with compensating horizontal thermal and salinity gradients (i.e., with no horizontal density gradient) is investigated in this analysis. It is observed that the maximum growth rate of instability, the slope of the wave front and the wave number depend on the Soret parameter, S. For 1+S= ^–1, the system is stable for any value of the horizontal gradient where is the ratio of mass diffusivity to thermal diffusivity. For 1+S<0, there is convective instability when both vertical gradients are stable even in the absence of the horizontal gradient. When 1+S> ^–1, the slopes of the wave fronts tilt such that there is a diffusive set-up when stationary convection sets in and finger formation when there is oscillatory convection.     

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.     

Determination of normal stress differences in steady shear flow

Summary Using the cone- and-plate apparatus ofAdams andLodge, values of pressure gradient,r-d¯p/dr in a range 300 to 3000 dyn/cm², have been measured to an accuracy of 1% at shear rates near 10 sec^–1 in liquids of viscosity less than 200 poise. Using the constancy of pressure gradient at a given shear rate as an indicator of liquid stability, it was found that a polyisobutene liquid containing 2% of Oppanol B 200 in Oppanol B I, when stored at rest at 25 °C, was stable during a certain 7-day period after dissolution and unstable during the subsequent 30 days.     

A permeameter for unsaturated soil

A permeameter for unsaturated soil was developed by observing the way in which pore water recovers hydrostatic equilibrium. It works like an hour glass that is turned upside-down everytime the state of reference (or hydrostatic equilibrium) is reached. The hydraulic conductivity is deduced from the curves of evolution of pore-water pressure and from the distribution of partial density of water at hydrostatic equilibrium. Roman Letters a is defined by (10), kg m^–3 - A _n coefficients of the analytic solution, kgm^–3 - C ₁, C ₂, C ₃, C ₄ constants and constants of integration - D diffusivity, m² s^-1 - g gravity constant, m s^-2 - g gravity vector field - K hydraulic conductivity defined by (2), m⁵ s^-1 J^-1 - K _w hydraulic conductivity defined by (5), m ^-1 - k permeability - L length of soil sample, m - n integer in (22) - n porosity - p absolute pore water pressure, Pa - p ₀ absolute pore water pressure, Pa - p _a absolute air pressure, Pa - q volume flux or Darcy's velocity, m s^-1 - r exponent defined by (13) - S _w degree of saturation, % - t time variable, sec - u _n , v _n are defined by (22b), (22c) - x(x, y, z) space variable Greek Letters , are defined by (11), (13) - _w dynamic viscosity - water partial density, kg m^–3. It is the ratio of the mass of water to total volume of a representative elementary volume - ₀, _l water partial densities, kgm^–3 - _w density of water, kgm^–3 - _s density of solid particles, kgm^–3 - differences of partial density, kgm^–3 - p differences of water pressure, Pa - pi - , · gradient operator, divergence operator - Laplacian operator - volumetric water content, % - piezometric head, m     

A new transient method for analysis of solidification in the continuous casting of metals

Solidification processes involve complex heat and mass transfer phenomena, the modelling of which requires state-of-the art numerical techniques. An efficient and accurate transient numerical method is proposed for the analysis of phase change problems. This method combines both the enthalpy and the enhanced specific heat approaches in incorporating the effects of latent heat released due to phase change. The sensitivity and accuracy of the proposed method to both temporal and spatial discretization is shown together with closed-form solutions and the results from the enhanced specific heat approach. In order to explore the proposed method fully, a non-linear heat release, as is the case for binary alloys, is also examined. The number of operations required for the new transient approach is less than or equal to the enhanced heat capacity method depending on the averaging method adopted. To demonstrate the potential of this new finite-element technique, measurements obtained on operating machines for the casting of zinc, aluminum and steel are compared with the model predictions. The death/birth technique, together with the proper heat-transfer coefficients, were employed in order to model the casting process with minimal error due to the modelling itself.Nomenclature [A] conductance matrix - [B] matrix containing the derivative of the element shape functions - c, C _p specific heat (J kg^–1°C^–1) - effective specific heat (J kg^–1°C^–1) - f(T) local liquid fraction - f thermal load vector - H enthalpy (J kg^–1) - [H] capacitance matrix - h, h _r,h _c heat transfer coefficient (W m^–2°C^–1) - K thermal conductivity (W m^–1°C^–1) - L latent heat of solidification (J kg^–1) - l overall length (m) - N _i shape functions - Q rate of heat generation per unit volume (J m^–3) - q heat flux (W m^–2) - R residual temperature (°C) - T temperature (°C) - T _s solidus temperature (°C) - T _l liquidus temperature (°C) - T _pouring pouring temperature (°C) - T _top temperature at the top of the mould (°C) - T _w temperature of the water spray (°C) - approximated temperature (°C) - T surrounding temperature (°C) - cooling rate (°C/s) - t time (seconds) - x _i,x, y, z spatial variables (m) - t time step (s) - x element size (m) - diffusivity (m²s^–1) - density (kg m^–3) - time marching parameter - _n direction cosines of the unit outward normal to the boundary     

Thermal Conductivity of Soils at Very Low Moisture Content and Moderate Temperatures

An analysis of soil thermal conductivity data shows that, at very low moisture content, this property first varies insignificantly and then begins to increase from a certain critical moisture content, whose value tends to depend on clay mass fraction. Two simple models evaluating the critical moisture content were developed; the first one is a fraction of the permanent wilting point; the second one is a simple linear function dependent on clay mass fraction. An insignificant variation of soil thermal conductivity is observed at 20°C, within a water pressure head ranging from 1×10³ to 1×10³m, while for higher temperatures (45–50°C) from 5000 to 100000m. Three extensions of the enhanced thermal conductivity model by Sundberg, namely SUN-1, SUN-2 and SUN-3, were proposed and tested. They produce an average root mean square error of 27%, 24% and 30%, respectively, with respect to experimental data. SUN-1and SUN-2 predictions could be further improved if better estimates of thermal conductivity at the dry state and the permanent wilting point were provided. SUN-3 is a simple model which does not require information about the PWP and critical moisture content. All SUN models have a potential for implementing the latent heat transfer component.     

Viscoelasticity of a surfactant and its drag-reducing ability

There is considerable interest in the use of viscoelastic cationic surfactant-counterion mixtures in district heating and cooling systems to reduce pressure losses. A recent field test in a secondary system near Prague showed a 30+% reduction in pumping energy requirements.We have studied a number of commercial surfactants and we report here results of rheological, drag reduction and turbulence measurements on Arquad 18–50 (octadecyl trimethyl ammonium chloride (AR 18)) with an excess of sodium salicylate (NA). The concentration studied was 1.6 mM AR 18 and 4.0 mM NA which is about one third the concentration for excellent drag reduction in this surfactant's effective temperature range 30–90°C.Viscosity, , vs. shear rate,D, first normal stress difference,N ₁, vs. shear rate, drag reduction (as pressure drop,i=P/1) vs. average velocity,U _ave, in a 39.4 mm tube for AR 18, and turbulence intensity data for three drag reducing surfactants are reported.Of particular interest are the generally low turbulence intensities in all three directions which correspond to reduced heat, mass and momentum transfer rates compared to water, and the existence of large normal stress differences at 20°C for AR 18, a temperature at which no drag reduction occurs with this surfactant, indicating that normal stress effects do not correlate directly with drag reduction.The effect of time of pumping on increasing drag reduction demonstrates that this factor overwhelms the expected increase in drag reduction as temperature is raised from 18–19°C to 40.5°C.     

Drag measurements on planar riblet surfaces at high subsonic speeds

This paper presents the results of an investigation of riblet performance at high subsonic Mach numbers, and Reynolds numbers of about 20 000 based on the momentum thickness, in both zero and adverse pressure gradient boundary layers. The maximum length Reynolds number of the ribbed section was 3.4×10⁷ so the results were directly relevant to flight applications on the engine nacelles of civil airliners. Seven different sizes of riblets with heights h (equal to spacing s) ranging from 0.0007 (0.0178mm) to 0.006 (0.1524 mm) have been studied, covering a range of h+, s+ from 10 to 106. The maximum percentage skin friction reduction, as deduced from velocity profiles measured at the downstream end of the riblet surfaces, under nominally zero pressure gradient conditions was 5.5±1; rather less than that recorded in low speed studies, but consistent with a recent theoretical analysis of the effect of Reynolds number. The values of h+ required for maximum and zero skin friction reduction agreed closely with other data. In addition subsequent floating element drag balance measurements revealed little effect of yaw angles up to 15°, again in line with other findings, and also suggested that the extent of the initial development length on, and recovery length behind, the riblets was approximately 5. The adverse pressure gradient studies indicated that riblet performance was essentially unaffected by mild gradients (=0.25), but diminished to zero in a more severe gradient (=0.5).     

Traveling disturbances in rotating-disk flow

The stability curves for traveling disturbances in rotating-disk flow are computed using the sixth-order system of incompressible linear stability equations. It is found that the neutral curve has two minima for disturbances with positive frequencies as found earlier by Malik (1986) for stationary disturbances. The upper branch minimum occurs at =–2.9, R=283.6 while the lower branch minimum occurs at =7.9, R=64.46 where R is the Reynolds number. There exists a critical angle of approximately –35.34° (which is about 15° from the direction of maximum wall shear) below which all the waves are linearly damped. The results also show that at high frequencies the wave number for lower branch neutral disturbances varies with Reynolds number like R ^–1 while for stationary waves it behaves like R ^–1/2. The eigenfunction distribution suggests that the structure of the nonstationary high-frequency lower branch neutral disturbances are different from the structure of the viscous stationary disturbances.This work was sponsored under NASA Contract NAS1-18240.     

Measurement of the first normal-stress difference at high shear rates for a polyisobutylene/decalin solution “D2”

Reasonable agreement is found between values of the first normal-stress differenceN ₁ for samples of D2, a polyisobutylene/decalin solution, measured in steady shear flow using three different instruments: a Weissenberg Rheogoniometer (a cone-plate rotational rheometer), a Torsional Balance (plate-plate rotational) Rheometer, and a Stressmeter (a transverse-slot slit-die rheometer). Viscosity values are also in reasonable agreement. Ranges of variables common to at least two rheometers include values of shear stress up to 3,700 Pa and shear rate up to 20,700 s^–1 near 25 °C. The agreement supports the approximate validity of the semi-empirical HPBL equation used to calculateN ₁ from Stressmeter data over a range of shear rates up to 20,700 s^–1 near 25 °C. Time-temperature superposition behavior exhibited by Stressmeter data at temperatures in the range 21 °C to 111 °C suggest that the range of validity of the Stressmeter method for determiningN ₁ approximately may extend up to shear rates of 290,000 s^–1 at 111 °C.     

Influence of stacking sequence and interlaminar layer on stress singularities at free edge of composite laminates

Summary The topic concerning the singularity in the state of stress existing at the free edges of plane composite laminates with resin interlaminar layer, has been dealth with. The problem has been studied by means of a F.E. approach, founded on a method able to determine the free edge state of stress without aprioristical hypotheses about the presence of a singularity. Then the singularity itself has been studied through a linear-logarithmic formulation which enables, for the stacking sequences considered — all belonging to the [°/°–90°] _s family — and for all meaningful stress components, to compute the power of the singularity and the boundary layer stress intensity factor (or free edge stress intensity factor). Taking into account these parameters, various laminations and stacking sequences have been compared, in order to provide a practical measure of the severity of the singular stress field and its influence on failure modes.Then a comparative analysis has been worked out, in order to evaluate the effects due to the thickness of the resin interlaminar layer between two fiber layers.

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Sommario Si prende in considerazione il problema connesso con l'esistenza di singolarità nel campo di sforzo presente ai bordi liberi di laminati piani in materialxe composito, in presenza di uno strato di resina interlaminare.La questione viene affrontata tramite un approccio numerico agli elementi finiti, basato su di un metodo in grado di determinare il campo di sforzo al bordo libero senza assumere aprioristicamente la presenza di singolarità. La eventuale singolarità viene poi studiata mediante una trattazione logaritmico-lineare che consente di calcolare, per tutte le laminazioni prese in considerazione, (appartenenti alla famiglia [°/°–90°] _s )e per le componenti di sforzo più significative, il valore della potenza della singolarità e quello che viene definito fattore d'intensità degli sforzi al bordo libero. Sulla scorta di tali valori si confrontano le varie laminazioni e sequenze di impaccamento.Per tuttii questi aspetti viene inoltre condotta un'indagine comparativa, per valutare l'effetto dovuto allo spessore dello strato di resina interlaminare.

     

On the propagation of elastic waves through composite media

Summary With the aid of an ultrasonic pulse technique, the propagation of elastic waves (longitudinal as well as transverse) through polyurethane rubbers filled with different amounts of sodium chloride particles was studied. The velocity of both longitudinal and transverse waves was found to increase with filler content. From the measured wave velocities, the effective modulus for longitudinal waves,L, bulk modulus,K, and shear modulus,G, were calculated according to the relations for a homogeneous isotropic material. All three moduli appear to be monotonously increasing functions of the filler content over the whole experimentally accessible temperature range (–70 °C to + 70 °C forL andK;}-70 °C to about –20 °C forG) and they, moreover, reflect the glassrubber transition of the binder.Poisson's ratio,, was found to decrease with increasing filler content and show a rise at the high temperature side of the experimentally accessible temperature range (about –20 °C) as a result of the approach of the glass-rubber transition.In addition to the velocities, the attenuation of both longitudinal and transverse waves was measured in the temperature ranges mentioned. It was found that in the hard region tan _L as well as tan _G are independent of the filler content within the accuracy of the measurements. In the rubbery region, however, tan _L, increases with increasing filler content.Finally, the experimental data are compared with a simple macroscopic theory on the elastic properties of composite media.     

Heat transfer during dry spinning of fibers

Summary Heat transfer to fibers formed in dry spinning has been subjected to fundamental analysis. Solutions of the equation of energy have been derived and tested with experimental data. Results were deemed satisfactory in view of the accuracy of the experimental data. The present work is believed to yield a good representation of the heat transfer in the dry spinning process.Nomenclature h heat transfer coefficient, cal/cm² °C sec - k thermal conductivity, cal/cm °C sec - r radial distance, cm - t time, sec - Z axial distance, cm - A surface area, cm² - A _n or n-th root of - A ₀ energy required for solvent evaporation, cal/sec cm³ - C _p specific heat cal/gm °C - J ₀ Bessel function of first kind, order zero - J ₁ Bessel function of first kind, order one - J ₂ Bessel function of first kind, order two - N k/(R ² C _p V) - Q volumetric flow rate cm³/sec - R outside radius, cm - T point temperature, °C - T _S surface temperature °C - T ₀ initial fiber temperature °C - T ambient air temperature, °C - average fiber temperature, °C - ₁ average fiber temperature of preceding segment, °C - V average fiber velocity relative to air strean, cm/sec - V _r radial velocity component, cm/sec - V _z axial velocity components, cm/sec - V direction velocity component cm/sec - W weight of solvent evaporated in a given fiber segment, gms - _n a solution of the equation J ₀(X)=0 - heat of vaporization of solvent, cal/gm - dimension - r/R - density, gms/cc     

Non-equilibrium contributions to the internal energy of PVAc melts

Summary Adiabatic deformation experiments have been used as a test for the non-equilibrium thermodynamic behavior of PVAc melts. At temperatures slightly aboveT _g (i.e. 50°C and 60°C), an appreciable dependance of internal energy upon deformation history is found. The non-equilibrium contributionU represents up to 50% of the total internal energy change and plays the role of an endothermic effect. In transient shear tests,U shows an overshoot with respect to deformation. During adiabatic stress relaxation a temperature relaxation is also observed. The nonequilibrium internal energy term becomes negligible at 80°C, both during deformation and stress relaxation. At that temperature, the entropic elasticity theory holds true.

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Zusammenfassung Deformationsversuche unter adiabatischen Bedingungen wurden als Test für das thermodynamische Verhalten von PVAc-Schmelzen im Nicht-Gleichgewichts-Zustand durchgeführt. Bei Temperaturen wenig oberhalb der GlastemperaturT _g (d. h. 50°C und 60°C) wurde eine merkliche Abhängigkeit der Inneren Energie von der Deformationsvorgeschichte gefunden. Auf den NichtgleichgewichtsbeitragU entfällt bis zu 50% der Änderung der totalen Inneren Energie, und zwar kennzeichnet sie einen endothermen Effekt. Bei Anfahrversuchen zeigtU als Funktion der Scherung ein Überschießen. Während der adiabatischen Spannungsrelaxation wird ebenfalls eine Temperatur-Relaxation beobachtet. Der Nicht-Gleichgewichts-Term der Inneren Energie wird bei 80°C vernachlässigbar gering, sowohl während der Deformation als auch der Spannungsrelaxation. Bei dieser Temperatur ist somit die Theorie der reinen Entropie-Elastizität anwendbar.

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With 6 figures     

Measurements of the first normal-stress difference in a new Rheo-dilatometer for molten polymers: Triple-step-shear-strain tests for all K-BKZ constitutive equations

Following the 3rd of a triple-step-shear-strain sequence, the relaxation of the first normal-stress difference,N ₁ (t), has been measured for a sample (IUPAC A) of low-density polyethylene at 150 °C over a range of shear-strain magnitudes up to 28 shear units. A new cone-plate Rheodilatometer was used, giving sample volume change data as well as thrust and torque data during cone rotation. At 130 °C, prior measurements (described elsewhere) gave an upper limit of 0.001% for the volume change with IUPAC A; this gave an estimated error of only 1.7% in determiningN ₁(t) from time-dependent thrust data. Wagner's network-rupture model (based on a postulated strain-induced irreversible network disentanglement process) gave quantitative agreement withN ₁(t) data for IUPAC A at 150 °C over some of the ranges of time and shear-strain investigated. Wagner's earlier constitutive equation (of K-BKZ type) gave no quantitative agreement. Using a special choice of strain magnitudes in which the 3rd is half that of the 1st and 2nd, it is shown that a critical test of all K-BKZ equations can be made on the basis ofN ₁ (t) data only. This test excludes all K-BKZ equations for IUPAC A under the conditions here used. In all the present investigations, the 1st and 3rd shears had the same sign while the 2nd had the opposite sign.