Compressibility and surface tension

The viscosities of soln. of sodium and potassium carbonate have been measured by S. Arrhenius, 0. Pulvermacher, W. W. J. Nicol,12 and by A. Kanitz. The latter s values at 25° for N-, N-, arid JA -soln. ate respectively 1-2847,1-1367, and r0310 for sodium carbonate, and T1667, T0784, and 10192 for potassium carbonate. The compressibilities and surface tensions have been measured by W. 0. Kontgen and J. Schneider, and the diffusion coeff. by J. Schuhmeister, and J. C. Graham. A soln. of 2 9 mols. of sodium carbonate per litre at 10°, has a diffusion coefficient of 0 39 sq. cm. per day and one with three mols. of potassium carbonate per litre, 0 60 sq. cm. per day. 

Since the surface tension is a manifestation of intermolecular forces, it may be expected to be related to other properties derived from intermolecular forces, such as internal pressure, compressibility and cohesion energy density. This is found to be so indeed. In the first place there exists a relationship between compressibility and surface tension. According to McGowan (1967) the correlation is ... 

Several differing simple models of molten salts do indeed give reasonably close calculations of equilibrium properties, e.g., compressibility and surface tension. What these models do not do, however, is to quantitatively rationalize the data on the temperature dependence of conductance, viscous flow, and self-diffusion. The discovery by Nanis and Richards of the fact that simple liquids have heats of activation for all three properties given approximately by 3. lART presents a clear and challenging target for testing models of liquids. 

Later Reiss and Mayer (1961), Mayer (1963), and Yosim and Owens (1964) calculated some thermodynamic properties of fused salts (entropy, heat capacity, entropy of fusion, compressibility, and surface tension) on the basis of this theory. The agreement between the calculated and experimental data is reported as good and in some cases as very good. However, this model fails in the calculation of transport properties. 

A number of properties, including dielectric properties, should be considered in assessing a given polar solvent. Important bulk properties are density, vapor pressure, thermodynamic properties related to vaporization, heat capacity, viscosity, compressibility, and surface tension. Some of these are summarized in table 4.1 and are discussed briefly in this section. 

Furthermore, an extensive study of the dynamic and structural properties of water/alcohol systems by Onori and Santucci [73] based on adiabatic compressibility and surface tension measurements, infrared and near-infrared absorption spectra, and the dielectric relaxation method showed that two characteristic Umiting molar fraction values can be designated for a specific alcohol. The adiabatic compressibility is a quantity that refers to the volume unit of solution irrespective of the number of molecules therefore, the excess quantity (Ps which is... 

The expansibilities, compressibilities, and surface tensions of the mixtures are intensive properties, so they should be expressed not in terms of excess quantities but just as deviations from the linear dependence on the (mole fraction) composition. Data for the isobaric expansibilities and the adiabatic compressibilities of binary mixtures of water with many cosolvents on the list are available in [56]. The isobaric compressibilities can then be calculated from such data by Equation 3.3, using also the molar volumes of the mixtures, V = x V- + XcK -i- V. ... 

Marcus Y (2013) The compressibility and surface tension product of molten salts. J Chem Phys 139(124509) l-4... 

A Models to describe microparticles with a core/shell structure. Diametrical compression has been used to measure the mechanical response of many biological materials. A particular application has been cells, which may be considered to have a core/shell structure. However, until recently testing did not fully integrate experimental results and appropriate numerical models. Initial attempts to extract elastic modulus data from compression testing were based on measuring the contact area between the surface and the cell, the applied force and the principal radii of curvature at the point of contact (Cole, 1932 Hiramoto, 1963). From this it was possible to obtain elastic modulus and surface tension data. The major difficulty with this method was obtaining accurate measurements of the contact area. 

The applied pressure is related to the desired pore size via the Washburn Equation [1] which implies a cylindrical pore shape assumption. Mercury porosimetry is widely applied for catalyst characterization in both QC and research applications for several reasons including rapid reproducible analysis, a wide pore size range ( 2 nm to >100 / m, depending on the pressure range of the instrument), and the ability to obtain specific surface area and pore size distribution information from the same measurement. Accuracy of the method suffers from several factors including contact angle and surface tension uncertainty, pore shape effects, and sample compression. However, the largest discrepancy between a mercury porosimetry-derived pore size distribution (PSD) and the actual PSD usually... 

As shown by the applications developed so far, the characteristics of acoustic levitation make it especially suitable for use in analytical and bioanalytical chemistry — however, the earliest applications focused on the determination of mechanical and physical properties of materials such as specific density, viscosity and surface tension [93,115,116]. Ohsaka et al. developed a method for determining the viscosity of highly viscous liquids (particularly, undercooled liquids, which exist at temperatures below their freezing points [117]). Weiser and Apfel used acoustic levitation to measure mechanical properties such as density, compressibility and sound velocity in biological materials [71]. 

The filter cakes obtained from mineral and chemistry industrials are mostly wastes and sent to the transportation and storage without any thermal operations. The stability properties of the filter cakes such as tensile, shear and compression strength are very important for the deposit of slimes (5). The shear strength of the mineral filter cakes is influenced by the particle size, shape and surface tension as well as the applied pressure and the saturation degree (6, 7). It was mentioned in the recent studies that particle shape has also a very substantial effect on the shear strength of the cake. The shear strength of the mineral filter cake is defined as follows F... 

In the absence of significant electric, magnetic, motion, gravity, and surface tension effects (i.e., for stationary simple compressible systems), the change... 

Viscosity has been replaced by a generalized form of plastic deformation controlled by the yield stress Cy, which may be determined by compression experiments (e.g.. Fig. 21-117). As showm previously, yield stress is related to deformability of the wet mass and is a function of shear rate, binder viscosity, and surface tension (captured by a bulk... 

On deformation of the system, the bubbles are deformed, which increases their Laplace pressure p. Moreover, some films between particles are stretched and others are compressed, causing surface tension gradients to form, which also needs energy. Above a certain stress, yielding may occur, which means that bubbles (or drops) start to slip past each other, which generally occurs in planes about parallel to the direction of flow. Calculation of the shear modulus and the yield stress from first principles is virtually impossible because of the intricacy of the problem for a three-dimensional and polydisperse system, but trends can be predicted. One relation is that these parameters are proportional to the average apparent Laplace pressure... 

Incidentally, its viscosity and surface tension decrease to nearly negligible values as the critical temperature is approached. Over this range propane changes from a typical liquid to a fluid possessing substantially the properties of gas. As the 220°F [100°C] isotherm indicates, gaseous propane at a pressure of 1000 pounds per square inch [69 bar] is much more dense than liquid propane at 212°F [100°C] and its saturation pressure. Also, as the liquid approaches its critical temperature, it becomes highly compressible. 

The data in Fig. 5.26 confirm that the relationship between tensile strength a, agglomerate forming particle size x, and surface tension of the binder liquid a and the porosity function (1 - s)/s as per Equation 5.2 is correct and Fig. 5.27 proves that the (compression) strength of agglomerates increases linearly with the surface tension of the binder liquid as indicated by Eq. 5.2. 

Here Y denotes a general bulk property, Tw that of pure water and Ys that of the pure co-solvent, and the y, are listed coefficients, generally up to i=3 being required. Annotated data are provided in (Marcus 2002) for the viscosity rj, relative permittivity r, refractive index (at the sodium D-line) d. excess molar Gibbs energy G, excess molar enthalpy excess molar isobaric heat capacity Cp, excess molar volume V, isobaric expansibility ap, adiabatic compressibility ks, and surface tension Y of aqueous mixtures with many co-solvents. These include methanol, ethanol, 1-propanol, 2-propanol, 2-methyl-2-propanol (tert-butanol), 1,2-ethanediol, tetrahydrofuran, 1,4-dioxane, pyridine, acetone, acetonitrile, N, N-dimethylformamide, and dimethylsulfoxide and a few others. 

Supercritical fluid (SF) presents the state of some substance, which is at temperature above its critical temperature (TJ and compressed above its critical pressure (PJ, above which no applied pressure can force the substance into its liquid state (Figure 24.1). SF is characterized with specific behavior its density (from 0.1 to 0.9 g/cm at 75-500 bar) is very similar as those of liquid and it has a low viscosity, small diffusivity and surface tension which are the main characteristics of gases. 

A major difference between mechanics of solids and fluids is that fluids have veiy little shear strength. Other important properties of fluids are density, specific weight, compressibility, viscosity, surface tension, and vapor pressure. 

Figure 4.15. Evaporating film of silica sol to gel and drying schematic cross-section, (a) sol (A) concentrated sol—beginning of aggregation (c) gel compressed by surface tension (J) fracturing of gel by shrinkage (e) dried loose gel fragments. W, water surface S. solid substrate.

Other corrections - capillary shape and slip, non-uniform cross-sections (Barr, 1931), elliptical cross-section (Ito, 1951a), coiled capillaries (Ito, 1951b Dawe and Smith, 1970), wall roughness (Kawata, 1961), fluid properties effects, compressibility, non-Newtonian (Van Wazer et al, 1963), and surface tension correction (Van Wazer et al, 1963 Goncalves et al, 1991 Kawata et al, 1991) - can be found in the respective literature. 

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