Unit Length

In Chapter III, surface free energy and surface stress were treated as equivalent, and both were discussed in terms of the energy to form unit additional surface. It is now desirable to consider an independent, more mechanical definition of surface stress. If a surface is cut by a plane normal to it, then, in order that the atoms on either side of the cut remain in equilibrium, it will be necessary to apply some external force to them. The total such force per unit length is the surface stress, and half the sum of the two surface stresses along mutually perpendicular cuts is equal to the surface tension. (Similarly, one-third of the sum of the three principal stresses in the body of a liquid is equal to its hydrostatic pressure.) In the case of a liquid or isotropic solid the two surface stresses are equal, but for a nonisotropic solid or crystal, this will not be true. In such a case the partial surface stresses or stretching tensions may be denoted as Ti and T2-... 

The independent combination of ai symmetry (normalized to produce vectors of unit length) are... 

The surface tension of a liquid, -y, is the force per unit length on the surface that opposes the expansion of the surface area. In the literature the surface tensions are expressed in dyn cm 1 dyn cm = 1 mN in the SI system. For the large majority of compounds the dependence of the surface tension on the temperature can be given as... 

Assuming a Gaussian profile, the extent of band broadening is measured by the variance or standard deviation of a chromatographic peak. The height of a theoretical plate is defined as the variance per unit length of the column... 

In this expression, called Pick s first law, the proportionality constant D is the diffusion coefficient of the solute. Since J = (l/A)(dQ/dt) and c = Q/V, where Q signifies the quantity of solute in unspecified units, it follows that D has the units length time", or m sec in the SI system. The minus sign in Eq. (9.69)... 

In spectrophotometry the absorbance per unit length of path through the sample e is defined as... 

Resistivity/Conductivity. The resistivity or specific resistance of a material is the electric resistance offered by an element of the material having unit length and unit cross-sectional area. The current iatensity is proportional to the voltage across its path, and is iaversely proportional to resistance. This relationship is expressed by Ohm s law, where I = current ia amperes, E = poteatial ia volts, and R = resistance ia ohms. 

Typical textile fibers used, for example, in a needle-punched filter fabric, are a blend of 3.3- and 6.6-dtex (3- and 6-denier) polyester staple. These fibers are - 5 cm long, have diameters ranging from 18 to 25 pm, mass-per-unit-length or linear density values ranging from - 350 to 650 mg per 1000 m, and length-to-width ratios in the order of 1000 to 1. 

Flexibility and Stress-Intensification Factors. The flexibihty factor k (>1.0) is defined as the ratio between the rotation per unit length of the part in question produced by a given moment to the rotation of a straight pipe (of the same size and schedule) produced by the same moment. A close approximation of the flexibiUty factor that agrees quite well with theory and experiment for bends is as follows ... 

In the macroscopic heat-transfer term of equation 9, the first group in brackets represents the usual Dittus-Boelter equation for heat-transfer coefficients. The second bracket is the ratio of frictional pressure drop per unit length for two-phase flow to that for Hquid phase alone. The Prandd-number function is an empirical correction term. The final bracket is the ratio of the binary macroscopic heat-transfer coefficient to the heat-transfer coefficient that would be calculated for a pure fluid with properties identical to those of the fluid mixture. This term is built on the postulate that mass transfer does not affect the boiling mechanism itself but does affect the driving force. 

System System units Length of hank, yd Count ... 

Knitted fabric constmction characterization is discussed in ASTM D3887. Characterization of knitted fabrics includes yield (area per weight), width, length, and yam count (number of courses and wales per unit length). The type of knit is also specified, eg, warp knit or weft knit. Yarn analysis may be difficult on account of problems in raveling individual yams from the knitted stmcture, particularly warp knits. 

The monolayer resulting when amphiphilic molecules are introduced to the water—air interface was traditionally called a two-dimensional gas owing to what were the expected large distances between the molecules. However, it has become quite clear that amphiphiles self-organize at the air—water interface even at relatively low surface pressures (7—10). For example, x-ray diffraction data from a monolayer of heneicosanoic acid spread on a 0.5-mM CaCl2 solution at zero pressure (11) showed that once the barrier starts moving and compresses the molecules, the surface pressure, 7T, increases and the area per molecule, M, decreases. The surface pressure, ie, the force per unit length of the barrier (in N/m) is the difference between CJq, the surface tension of pure water, and O, that of the water covered with a monolayer. Where the total number of molecules and the total area that the monolayer occupies is known, the area per molecules can be calculated and a 7T-M isotherm constmcted. This isotherm (Fig. 2), which describes surface pressure as a function of the area per molecule (3,4), is rich in information on stabiUty of the monolayer at the water—air interface, the reorientation of molecules in the two-dimensional system, phase transitions, and conformational transformations. 

Linear Density. Linear density is defined as the weight per unit length (usually defined as denier), weight in grams of 9000 m or Tex, gram weight of 1000 m of yam or cord (26). Tex is often used as dTex (Tex x 10) and is related to denier because dTex = denier x 1.111. 

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