The importance of water migration in the measurement of the thermal conductivity of unsaturated frozen soils

The transport of heat in frozen soil may occur by conduction and by the convective transport of sensible and latent heat arising from the flow of water in the vapor, liquid and solid states. Theory describing the coupled flow of heat and of water in the liquid and vapor states is used to derive a definition of apparent thermal conductivity (the convective transport of heat in the movement of ice in unstaturated soils is assumed to be negligible). Calculations suggest that, at temperatures close to 0°C, the transport of latent heat may exceed the contribution of heat flow by conduction. Under these conditions, the apparent thermal conductivity will be much greater than the thermal conductivity calculated from the thermal conductivities and volume fractions of the components.Insufficient published data prevent a rigorous evaluation of the theory. However the functional dependence on temperature of both thermal conductivity and the apparent thermal conductivity are calculated for a Tomakomai soil at different subzero temperatures. These values are compared to the apparent thermal conductivities of this soil which were measured at a water content in the unfrozen state of 0.48 cm³ cm^?3 and at temperatures ranging from ?0.7°C to ?10°C using the line heat source technique. The dependence of apparent thermal conductivity on subzero temperature, as calculated from theory, compares favourably to the dependence which was observed for this soil.     

Effect of cooling rate on freezing of a saturated soil

Assuming that overburden pressure does not constitute a limiting factor for frost heaving and that all pore spaces among particles have the same size, we have discussed the freezing of such idealized soil saturated with water under conditions where the temperature of the ground surface falls at a given rate. From the law of conservation of mass and heat alone, we obtained a necessary condition for three kinds of frozen soil: (1) a frozen soil with an ice layer due to segregational freezing; (2) homogeneously frozen soil containing no visible ice layers resulting from in situ freezing of pore water; and (3) a frozen soil with rhythmic ice banding.     

The cryopumping of water vapour in the continuum pressure region

Pumping speed measurements in the continuum pressure region, P>10^?3 torr, have been made for water vapour impinging on copper spheres and coils cooled to liquid nitrogen temperatures. Water vapour flow rates between 0.06 mg s^?1 and 420 mg s^?1 were used. The volumetric pumping speed was constant over the pressure range 2 × 10^?3 torr to 2 × 10^?2 torr and was, as expected, higher than that obtained in the free molecular flow region. Above 2 × 10^?2 torr the pumping speed decreased and possible reasons for this were investigated and are discussed. These included the effects of inadequate heat transfer from the liquid nitrogen refrigerant to the cryopump, a poor thermal conductivity of the cryodeposit, and an impurity, nitrogen gas, in the water vapour.     

Forced convection heat transfer to liquid helium I in the nucleate boiling region

Heat transfer and critical heat fluxes to helium boiling in a 2 mm id copper tube (100 mm long) were measured in the pressure range 1.1–1.5 atm and at mass velocities 18–96 kg m^?2s^?1. Corresponding Reynolds numbers are (1.2–6.2) × 10⁴. Experimentally obtained heat transfer coefficients show satisfactory agreement with those calculated according to the Kutateladze equation but with less pronounced pressure dependence. It was found that in the boiling region developed quality did not influence the heat transfer coefficient. An expression was obtained, which describes with ±10% error, the dependence of critical heat flux on mass flow rate in the pressure range 1.1–1.5 atm and mass quality 0.33–0.6.     

Numerical analysis of coupled water,heat and stress in saturated freezing soil

Clapeyron equation can be applied in freezing soil to describe the relationship among temperature, water pressure and ice pressure when ice and water coexist in phase equilibrium. The mathematical deduction shows that the driving force that makes the unfrozen water in soil moves from high temperature area to low temperature area is determined by gravity, temperature and pore pressure. Upon proposing the concept of separating void ratio as a judge criterion for the formation of ice lenses, adjusting the hydraulic conductivity to describe the unfrozen water gathering at the front of ice lenses and the growth of ice lens, a mathematical model of coupled water, heat and stress is established. A typical process of coupled water, heat and stress that happens in a saturated freezing soil column is simulated by COMSOL Multiphysics simulation software. The amount of frost heave is calculated, and the result of simulation gives the distribution bar graph of ice lenses and distribution curves of temperature, equivalent water content and pore pressure, and shows how they change.     

The adsorption force theory of frost heaving

Presented in this paper are the theorization of a traditional concept of the mechanics of frost heaving, as well as a critical review of the recent developments in this field. The key to the theorization is the following: (1) the film water adsorbed on soil particles can build up an internal solid-like stress, and (2) the flow of film water is different from the conventionally accepted flow of pore water. It is expected that modern continuum mechanics will, in the future, improve the theory of film water which, in this paper, has been formulated by use of the classical method.The freezing film water, trying to retrieve the loss of its thickness to the frozen ice, generates a suction force that draws water to the freezing front where the frost-heaving pressure pushes up the overburden. The temperature of the freezing film water that has generated the solid-like stress, is lower than the temperature of the freezing pore water. This distribution of freezing temperatures in the region of film and pore waters explains the observation that the freezing front causing frost heaving is not a planar surface but a three-dimensional zone diffused in the direction of heat transfer. Frost-heaving pressure can be derived as part of the solution of the boundary-value problem of the frost-heaving differential equations.     

Vibrational, giant dielectric and AC conductivity properties of agglomerated CuO nanostructures

We report frequency, temperature dependent dielectric response and AC conductivity of nanocrystalline CuO. These nanoparticles were prepared using sol–gel technique. Prepared particles were made as a pellet using hydraulic pressure and thermally heat treated at 950 °C. X-ray diffraction study showed that the prepared particles were crystalline in nature. Fourier transform infrared (FTIR) studies confirm the presence of Cu–O bond. Force constant and bond length is calculated which are 2.17 N cm^?1 and 1.98 Å respectively. Frequency dependent dielectric studies were done at different temperatures. Measurements show the giant dielectric value (~10³) and it increases with increase of temperature. AC conductivity measurements reveal that the conduction depends on both frequency and temperature, this agrees well with Correlated Barrier Hopping model.     

Using soil freezing characteristic curve to estimate the hydraulic conductivity function of partially frozen soils

We propose using the soil freezing characteristic curve (SFCC), instead of the soil water characteristic curve (SWCC), to estimate the hydraulic conductivity of partially frozen soils. Shortcomings associated with the use of the SWCC to estimate the hydraulic conductivity function of partially frozen soils are discussed. The hydraulic conductivity function for partially frozen Devon Silt is derived using the SFCC and the empirical relationships for hydraulic conductivity estimation method developed by Fredlund et al. (1994). The SFCC for Devon Silt is determined from unfrozen water content measurement using time domain reflectometry and temperature measurements inside the soil sample. The results using this novel approach compare well with results presented by others that use different methods to determine the hydraulic conductivity function of partially frozen soils.     

Macroscopic behavior of freezing saturated silty soils

The macroscopic behavior of freezing saturated silty soils was studied through a series of nine laboratory experiments. Under the range of test conditions, the heaving rate remained near-constant throughout a given experimental run as long as the overburden load was unchanged; water flow varied throughout the early period of experiments and then also stabilized at a near-constant rate; and ice lenses were found to grow predominantly at the freezing front but also occasionally on its cold side.Because the amount of water frozen in the soil per unit time is shown to be largely independent of the growth of visible ice lenses, segregation ice probably forms pervasively throughout the soil samples, frequently on a scale too small to be visibly detected. An experimentally demonstrated consequence of this pervasive segregation ice is the low strength of apparently unlensed, newly thawed soils, relative to the same soil at the same water content which has never been frozen.     

Thermal and hydrodynamic considerations of ice slurry in heat exchangers

This article focuses on the behavior in heat exchangers of an ice slurry composed of fine ice particles inside an ethanol–water solution. The heat transfer and friction characteristics were studied in two double pipe heat exchangers, one with a smooth surface and another with an improved surface. Heat transfer coefficients and pressure drops were experimentally investigated for the slurry flowing in the internal tube with ice mass fractions ranging from 0 to 30% and with flow velocities between 0.3 and 1.9 m s^?1. For some flow velocities, the results showed that an increase in the ice fractions caused a change in the slurry flow structure influencing the evolution of the pressure drops and the heat transfer coefficients. Critical ice fraction values were determined corresponding to a change flow structure from laminar to turbulent motion revealed by the evolution of the friction factor.     

Effects of solidification rate on segregation and fluid flow tendency in mushy zone of directionally solidified superalloy Inconel 718

Abstract

The microstructure and composition of the interdendritic liquid along the mushy zone of superalloy Inconel 718 that was directionally solidified at various solidification rates between 2 and 100 μm s^?1 have been investigated by SEM and EDAX techniques. The interdendritic liquid segregation profiles along the mushy zone are presented. The liquid density difference and Rayleigh number in the interdendritic liquid were calculated and analysed as well. It was found that when the solidification rates increased in the range 10–70 μm s^?1, segregation of Nb decreased, but segregation of Mo was most serious at 20 μm s^?1. The liquid density difference increased the most for rates from 20 to 40 μm s^?1 as temperature decreased. The maximum relative Rayleigh number was highest at 10°C below the liquidus temperature at 20 μm s^?1, which indicated the conditions where fluid flow most easily occurred for Inconel 718. The relative Rayleigh number synthetically considers the factors affecting fluid flow and can give a reasonable prediction for fluid flow tendency.     

Sorption of Pb(II), Cr(III), Cu(II), As(III) to peat,and utilization of the sorption properties in industrial waste landfill hydraulic barrier layers

The low conductivity landfill barrier layers protect the groundwater and soil by limiting the water flow through the bottom layers of the landfill material. Many materials used in hydraulic barrier layers also have sorption properties which could be used to reduce environmental risks. The adsorption of lead, chromium, copper, and arsenic to peat was studied with a batch-type test and a column test for compacted peat, both without pH adjustment in acidic conditions. Peat adsorbed all the metals well, 40 000 mg/kg of lead, 13 000 mg/kg of chromium, and 8400 mg/kg of copper in the column test. Arsenic was only tested in a batch-type test, and in that peat adsorbed 60 mg/kg of arsenic. The column test showed heavy metals to be adsorbed on the surface layers of the compacted peat sample, on the first centimeter of the sample. The adsorption was much greater in the column test than in the batch-type test, partly due to the different pH conditions and the buffer capacity of the peat in the column test. The liquid/solid ratio of the column experiment represented a time period of approximately 40 years in a landfill, under Finnish climate conditions. The hydraulic conductivity of the peat decreased as it was compressed, but it already met the hydraulic conductivity limits set by European Union legislation for the hydraulic barrier layer (1 × 10⁻⁹ m/s at a pressure of 150 kPa for a 5-m layer), with a pressure of 50 kPa. The results show that peat would be an excellent material to construct compacted, low hydraulic conductivity layers with adsorption properties in, e.g. industrial waste landfills.     

High temperature kinetics of metal-oxygen reactions by solid oxide electrolyte cells: An application to nickel

Chronopotentiometric curves, generated by galvanostatic single steps, applied to a solid electrolyte cell, have been analysed on the basis of a dimensionless equation derived on the assumption that a scale of oxide grows at one of the electrode-electrolyte interfaces. This process is rate limiting for developing the charge transfer-diffusion overvoltage; Wagner's theory on tarnishing, under retarding electric field conditions, has been assumed for treating the kinetics of the growing scale. The kinetic model developed has been tested for the reaction of solid nickel (positive electrode) at 1268 K with oxygen partial pressures ranging from 3.9 × 10^?11 Atm [equilibrium pressure of Ni(s)-NiO(s) system] to 1.7 × 10^?10 Atm.Both the rate and the rate constant of the scale formation go through the maximum but at different times, while the rate constant dependence of the oxygen partial pressure agrees with the theory. The maximum rate constant value was found to be 9.8 × 10⁸ molecules cm^?1 s^?1. The calculated scale thicknesses were between 6 and 24 nm.     

Stability of the interphase surface in the freezing of moist ground

It is suggested that the formation of ice layers should be regarded as a consequence of a loss of stability of the motion of the freezing front. The kinetics of the freezing process is investigated and a stability criterion is obtained.Notation s(t) coordinate of the moving front - L length of the specimen - k moisture conductivity - W moisture content - heat of phase transition - W_H amount of unfrozen water - q flow of moisture from the melted zone into the frozen zone - v velocity of motion of the front - T_i temperature - Q_i heat flux - _i thermal conductivity - a_i thermal diffusivity (i=1 is the frozen zone and i=2 is the melted zone) - mass transfer coefficient - T_H the initial temperature Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 96–101, July, 1980.     

Performance characteristics of an apparatus based on the curve-fitting method for measuring thermal properties at cryogenic temperatures

This paper describes the performance characteristics of a new test apparatus and the measured results using the apparatus. It has been developed on the basis of Harmathy's curve-fitting method to measure, in a short time, the physical properties of the nonmetallic materials for a cryogenic storage tank. The apparatus has been used to measure the heat capacity, thermal conductivity, and thermal diffusivity of the materials at the same time in the temperature range of approximately ?180°C to +50°C.With this apparatus the thermal conductivity can be measured over a wide range of approximately 0.01 kcal m^?1 h^?1°C^?1 to 10 kcal m^?1 h^?1°C^?1 in the range of ?180°C to +50°C. The materials investigated were structural materials such as concrete, wood, frozen soil, and autoclaved lightweight concrete (ALC) and such insulation materials as calcium silicate, phenolic foam, and polyurethane foam.     

The modelling of the freezing process in fine-grained porous media: Application to the frost heave estimation

The solution of the moving-boundary problem, related to heat- and mass-transfer processes in freezing, fine-grained, porous media under phase-transition conditions is presented. It is assumed that a freezing zone, characterized by a wide temperature range of phase transitions, is formed. Therefore a three-zone model is developed. The preservation of the term ∂L/∂t(L is the ice content) in the system of equations has made it possible to determine the ice distribution within the frozen and the freezing zones. For loamy soils the dependence of the freezing process on the characteristic parameters, the Stefan and Lewis numbers, was analyzed. It was found that increasing the enthalpy of phase transition, i.e., decreasing the Stefan number Ste, resulted in diminution of the frozen zone but, at the same time, the ice content within this zone increased. Intensification of the migration process, i.e., increasing the Lewis number Le, also led to diminution of the frozen zone, in which the ice content and, consequently, the total moisture (including ice) were increased. For large Lewis numbers the freezing zone was observed to decrease. When the water migration process is absent (Le = 0), the calculations, which were based on the described model show that in the course of freezing the redistribution takes place only between moisture and ice contents. The total moisture remains constant and equal to the initial water content. The theoretical conceptions and results derived from the analytical solution are in agreement with experimental findings. The presented model predicts the freezing process in porous media and satisfactorily reflects observed phenomena. The utilization of the considered problem solution to the prediction of the frost heave phenomenon in soils freezing processes shown that the calculated frost heave curve matches the experimental results very closely indicating that the model can well reproduce the frost heaving process associated with the freezing. Propagation of the freezing front in the test is predicted the experimental results with reasonable accuracy.     

Simulation of 3D flow in porous media by boundary element method

In the present paper problem of natural convection in a cubic porous cavity is studied numerically, using an algorithm based on a combination of single domain and subdomain boundary element method (BEM). The modified Navier–Stokes equations (Brinkman-extended Darcy formulation with inertial term included) were adopted to model fluid flow in porous media, coupled with the energy equation using the Boussinesq approximation. The governing equations are transformed by the velocity–vorticity variables formulation which separates the computation scheme into kinematic and kinetic parts. The kinematics equation, vorticity transport equation and energy equation are solved by the subdomain BEM, while the boundary vorticity values, needed as a boundary conditions for the vorticity transport equation, are calculated by single domain BEM solution of the kinematics equation. Computations are performed for steady state cases, for a range of Darcy numbers from 10^?6 to 10^?1, and porous Rayleigh numbers ranging from 50 to 1000. The heat flux through the cavity and the flow fields are analyzed for different cases of governing parameters and compared to the results in some published studies.     

Three-dimensional measurement of ice crystals in frozen dilute solution

A Micro-Slicer Image Processing System (MSIPS) has been applied to observe the ice crystal structures formed in frozen dilute solutions. Several characteristic parameters were also proposed to investigate the three-dimensional (3-D) morphology and distribution of ice crystals, based on their reconstructed images obtained by multi-slicing a frozen sample with the thickness of 5 μm. The values of characteristic parameters were determined for the sample images with the dimension of 530×700×1000 μm. The 3-D morphology of ice crystals was found to be a bundle of continuous or dendrite columns at any freezing condition. The equivalent diameter of ice crystals were in the range of 73–169 μm, and decreased exponentially with increasing freezing rate at the copper cooling plate temperature of −20 to −80 °C. At the T_cp −40 °C, the volumes of ice crystals were in the range of 4.6×10⁴ μm³ to 3.3×10⁷ μm³, and 36 ice columns were counted in the 3-D image.     

Plutonium dioxide catalyzed reaction between H<Subscript>2</Subscript> and O<Subscript>2</Subscript>

The kinetic characteristics of the reaction between H₂ and O₂ were calculated to more adequately simulate the radiolysis of water adsorbed on PuO₂. The rate constants of this reaction were determined via comparison of the calculated results with the published experimental data. It was found that, with the amount of the adsorbed water increasing from 2 × 10^?4 to 5 × 10^?3%, the rate constant of the reaction decreases from 6.0 × 10^?4 to 1.7 × 10^?5 mol^?1 s^?1. At the water content over 5 × 10^?3%, the rate constant is ≤1 × 10^?5 mol^?1 s^?1. A new mathematical model of the radiation-chemical and physicochemical processes occurring in the PuO₂-H₂O system was presented; the amounts of hydrogen and oxygen yielded by α-radiolysis of the adsorbed water were calculated, taking into account the reaction between H₂ and O₂.     

Uniaxial compressive strength of frozen silt under constant deformation rates

Uniaxial compressive strength tests were conducted on remolded, saturated Fairbanks frozen silt under various constant machine speeds, temperatures and dry densities. Test results show that the peak strength σ_m of frozen silt is not sensitive to dry density (or water content) at ?2°C, especially at relatively high strain rates, but is very sensitive to temperature and applied strain rate. However, the failure strain (strain at σ_m) is not sensitive to temperature and strain rate within a wide range of strain rate, but is very sensitive to dry density. It has been found that the initial yield strength σ_y consistently increases with decreasing dry unit weight. The initial yield strain (strain at σ_y) is almost independent of dry density and temperature, but varies with strain rate. Its magnitude ranges from 0.2 to 0.6% as strain rate varies from 1.1 × 10^?6 to 5.7 × 10^?3 s^?1, which is very close to the strain at yield for fine-grained polycrystalline ice (Hawkes and Mellor, 1972; Mellor and Cole, 1982). The initial tangent modulus of frozen silt is found to be nearly independent of strain rate, but the 50% strength modulus is closely related to strain rate. The test results indicate that there is a definite relationship between the two moduli.