Density surface

The downhole density of oil (at reservoir conditions) can be calculated from the surface density using the equation ... 

The X-ray instrumentation requires a commercial small angle X-ray camera, a standard fine structure X-ray generator and a sample manipulator if scanning is requested. The essential signal is the relative difference between the refraction level Ir and the absorption level Ia. Both levels are measured simultaneously by two scintillation detectors. At fixed angles of deflection this signal depends solely on the inner surface density factor C and thickness d of the sample [2] ... 

The algorithm leads to computation of the width 2a, and the depths d, dj, dj, d, d , d at six equidistant points along the y -axis of the cross-section of a crack, as well as the surface density of charge m=4 ju c at the crack walls. In its formulation from Fig.3, the algoritlun is adapted to cracks with a constant width. 

The data from Table 2 show that the algorithm developed in allows sizing of different cracks with complex cross-sections and unknown shapes for orientation angles not exceeding 45°. It is seen that the width 2a and the parameter c (or the surface density of charge m=4 r // e at the crack walls) are determined with 100% accuracy for all of the Case Symbols studied. The errors in the computation of the depths dj and di are less than 4% while the errors in the computation of d, dj, d, and d are less than 20% independent of the shape of the investigated crack and its orientation angle O <45°. 

Still another manifestation of mixed-film formation is the absorption of organic vapors by films. Stearic acid monolayers strongly absorb hexane up to a limiting ratio of 1 1 [272], and data reminiscent of adsorption isotherms for gases on solids are obtained, with the surface density of the monolayer constituting an added variable. 

Fig. XI-7. Volume fraction profile of 280,000-molecular-weight poly(ethylene oxide) adsorbed onto deuterated polystyrene latex at a surface density of 1.21 mg/m and suspended in D2O, from Ref. 70.

For other purposes, obtaining a measure of the adsorbate surface density directly from the experiment is desirable. From this perspective, we introduce a simple model for the variation of the surface nonlinear susceptibility with adsorbate coverage. An approximation that has been found suitable for many systems is... 

From a purely phenonienological perspective, this relationship describes a constant rate of change in the nonlhiear susceptibility of the surface with increasing adsorbate surface density N. Within a picture of... 

If we consider the optical response of a molecular monolayer of increasing surface density, the fomi of equation B 1.5.43 is justified in the limit of relatively low density where local-field interactions between the adsorbed species may be neglected. It is difficult to produce any rule for the range of validity of this approximation, as it depends strongly on the system under study, as well as on the desired level of accuracy for the measurement. The relevant corrections, which may be viewed as analogous to the Clausius-Mossotti corrections in linear optics, have been the... 

Here the ijk coordinate system represents the laboratory reference frame the primed coordinate system i j k corresponds to coordinates in the molecular system. The quantities Tj, are the matrices describing the coordinate transfomiation between the molecular and laboratory systems. In this relationship, we have neglected local-field effects and expressed the in a fomi equivalent to simnning the molecular response over all the molecules in a unit surface area (with surface density N. (For simplicity, we have omitted any contribution to not attributable to the dipolar response of the molecules. In many cases, however, it is important to measure and account for the background nonlinear response not arising from the dipolar contributions from the molecules of interest.) In equation B 1.5.44, we allow for a distribution of molecular orientations and have denoted by () the corresponding ensemble average ... 

Free surface density functions calculated at step 8 are used as the initial conditions to update the current position of the surface using the following integration... 

The strength of dispersion interaction of a solid with a gas molecule is determined not only by the chemical composition of the surface of the solid, but also by the surface density of the force centres. If therefore this surface density can be sufficiently reduced by the pre-adsorption of a suitable substance, the isotherm may be converted from Type II to Type III. An example is rutile, modified by the pre-adsorption of a monolayer of ethanol the isotherm of pentane, which is of Type II on the unmodified rutile (Fig. 5.3, curve A), changes to Type III on the treated sample (cf. Fig. 5.3 curve B). Similar results were found with hexane-l-ol as pre-adsorbate. Another example is the pre-adsorption of amyl alcohol on a quartz powder... 

The rate of evaporation of ions from a heated surface is given by Equation 7.3, in which Q, is the energy of adsorption of ions on the filament surface (usually about 2-3 eV) and Cj is the surface density of ions on the surface (a complete monolayer of ions on a filament surface would have a surface density of about 10 ions/cm" ). 

As ions and neutrals evaporate from a heated filament surface, the amount of sample decreases and the surface densities (C, Cq) must decrease. Therefore, Equation 7.1 covers two effects. The first was discussed above and concerns the changing value for the ratio n+/n° as the temperature of the filament is varied, and the other concerns the change in the total number of ions desorbing as the sample is used up. The two separate effects are shown in Figure 7.8a,b. Combining the two effects (Figure 7.8c) reveals that if the temperature is increased to maintain the flow of ions, which drops naturally as the sample is used up (time), then eventually the flow of ions and neutrals becomes zero whatever the temperature of the filament because the sample has disappeared from the filament surface. 

Schematic illustrations of the effect of temperature and surface density (time) on the ratio of two isotopes, (a) shows that, generally, there is a fractionation of the two isotopes as time and temperature change the ratio of the two isotopes changes throughout the experiment and makes difficult an assessment of their precise ratio in the original sample, (b) illustrates the effect of gradually changing the temperature of the filament to keep the ratio of ion yields linear, which simplifies the task of estimating the ratio in the original sample. The best method is one in which the rate of evaporation is low enough that the ratio of the isotopes is virtually constant this ratio then relates exactly to the ratio in the original sample.

Natural convection occurs when a solid surface is in contact with a fluid of different temperature from the surface. Density differences provide the body force required to move the flmd. Theoretical analyses of natural convection require the simultaneous solution of the coupled equations of motion and energy. Details of theoretical studies are available in several general references (Brown and Marco, Introduction to Heat Transfer, 3d ed., McGraw-HiU, New York, 1958 and Jakob, Heat Transfer, Wiley, New York, vol. 1, 1949 vol. 2, 1957) but have generally been applied successfully to the simple case of a vertical plate. Solution of the motion and energy equations gives temperature and velocity fields from which heat-transfer coefficients may be derived. The general type of equation obtained is the so-called Nusselt equation hL I L p gp At cjl... 

At X-ray fluorescence analysis (XRF) of samples of the limited weight is perspective to prepare for specimens as polymeric films on a basis of methylcellulose [1]. By the example of definition of heavy metals in film specimens have studied dependence of intensity of X-ray radiation from their chemical compound, surface density (P ) and the size (D) particles of the powder introduced to polymer. Have theoretically established, that the basic source of an error of results XRF is dependence of intensity (F) analytical lines of determined elements from a specimen. Thus the best account of variations P provides a method of the internal standard at change P from 2 up to 6 mg/sm the coefficient of variation describing an error of definition Mo, Zn, Cu, Co, Fe and Mn in a method of the direct external standard, reaches 40 %, and at use of a method of the internal standard (an element of comparison Ga) value does not exceed 2,2 %. Experiment within the limits of a casual error (V changes from 2,9 up to 7,4 %) has confirmed theoretical conclusions. 

The experiment testing was realized on the steel samples having zinc coating. The samples were made of steel tape used for cables protection having surface density 100 and 200 g/nf, which corresponds to the thickness of zinc costing about 14 and 28 micrometers. The measurements on the base of the presented above procedure has given the thicknesses of 20 and 25 micrometers. 

A quantity related to the disappearance yield for a particle of a species which covers a solid surface with a surface density 9 (A), is the disappearance cross-section, ctd (A) ... 

Because measuring A can be problematic, quantification is normally performed by relative sensitivity factor (RSF) methods. If a species A on the surface is detected by the ion X , the ratio of the detected ion current /a(X ) to the primary ion current 7pi and the surface density 9 (A) is called the practical sensitivity factor Sp (X (A)) ... 

By using RSFs it is possible to determine surface densities of other species, if the surface density of the reference species 9 (B) is known. 

Fig. 17. Adhesion energy G measured as a function of the surface density of the interfacial chains. It may noted that the strength measured in a peel test (a) is about 5 times larger than that measured using the JKR method (b). Further, a maximum exists in the value of G as function of the surface chain density. This is because of swelling effects at larger values of surface chain density. The open symbols represent the data for elastomer molecular weight Mo = 24,000 and the closed symbols represent the data for Mo = 10,000.

As with block copolymers, the important parameters are the surface density and length of the copolymer chains. Toughening of the interface may occurs as a result of pull-out or scission of the connector chains, or of fibril or craze formation in matrix. This last mechanism gives the highest fracture toughness, F, and tends to occur at high surface density of chains. 

Fig. 11. Laboratory OSB board density profile as a function of board thickness when using 10 s and 50 s press closing times. Note the much higher peaks of surface density for the 10 s case, and the more even density profile for the slower press closing time.

Overall board density will strongly affect core layer plasticization and density profile (Fig. 12), as at the highest overall board density a steep density gradient appears between the surface and core layers of the board. This is due to the greater difficulty encountered by the steam to penetrate and plasticize it. At lower density, the greater mat permeability enables a faster steam throughflow of the board, comparable to a steam injection process. The final result is similar as the overall board density is closer in value to both core and surface densities. 

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