Sloping angle

Figure 2.9 Phase diagram for C02, showing solid-gas (S + G, sublimation ), solid-liquid (S + L, fusion ), and liquid-gas (L + G, vaporization ) coexistence lines as PT boundaries of stable solid, liquid, or gaseous phases. The triple point (triangle), critical point (x), and selected 280K isotherm of Fig. 2.8 (circle) are marked for identification. Note that the fusion curve tilts slightly forward (with slope 75 atm K-1) and that the sublimation and vaporization curves meet with slightly discontinuous slopes (angle < 180°) at the triple point. The dotted and dashed half-circle shows two possible paths between a liquid (cross-hair square) and a gas (cross-hair circle) state, one discontinuous (dashed) crossing the coexistence line, the other continuous (dotted) encircling the critical point (see text).

From eqn. (27) it is seen that the effective initial concentration of donors nt,f (v) = (0) exp[ - (4/3)7i/ dAT determined formally by extrapolating the dependence In n(t) to t = 0 is lower than the real one by the number (per unit volume) of the donors which were located initially in the sphere of radius Rn near the acceptor and which had decayed via direct tunneling for the time t since the begining of the reaction. From eqn. (27) it also follows that, by straightening the kinetic curve in the coordinates ln[n(0/rc(0)] vs. t, one can obtain the values of RZ) and D from the segment cut off on the ordinate axis and the tangent of the slope angle. 

Consider a trapezoidal channel having side walls sloped outward from the channel bottom s flat floor. This slope angle ( ) is measured from a vertical line that begins at the channel s floor, for both side walls. Then ... 

Figure 2.9 Changes in the slope angles of the experimental plots shown in Figure 2.8 (ig(aexp)) and theoretically from Equation (2.2) (tg acaic)) as a function of the number of middle phosphate groups in PolyP molecules (nc) (o) experimental data ( ) theoretical data obtained from Equation (2.2) (Krupyanko et al., 1998).

The slope angle is the same for all lines in Fig. 5.17 and close to the value calculated (23.5). The increase in the expansion ratio observed reflects the decrease in the initial flow rate w0 (the segment on the ordinate axis cut by the line). 

Some of these results are presented in Fig. 8.3. Linear D/H( lnr) dependence was obtained in all experiments. A certain deviation was only detected at large values of the optical density. However, the slope angles of the lines (the proportionality coefficient) and the intersections with the ordinate axis, obtained from the different experiments, did not coincide though the differences were not very large, considering foam polydispersity. In all experiments the values of coefficient sf was within the range from 0.8 to 2. 

The results from the additional experiments with pressure dump [72] have shown that the main reason for change in the slope angles in the dependence considered is the inaccuracy of foam expansion ratio (dispersity) determination. 

From Eq. (10.58) it is seen that can be defined as the cross point of the VF/Vg (c o) dependence with the abscissa axis (further in the text cl,o will be denoted as C). At large surfactant concentrations when the fraction of the dispersed gas retained in the foam strongly increases, the VF/Vg ratio tends to 1. In this case the whole initial solution is transformed into a foam and further increase in the expansion ratio becomes impossible, so a considerable part of the surfactant remains in the solution, i.e. reGVg =c-cLR cL0- cmn. As indicated by the experiments, at low concentrations ct,o - Cmm there is a region where the VF /Vg (C) dependence becomes linear. The extrapolation of this linear segment gives cmjn. The slope angle of this dependence, equal to VLOn / VtTe(ti -1), can be used to estimate the adsorption, needed for the formation of a stable foam with Pf > 1, in case the value of the specific foam surface area is known. 

Although Eq. (4) was derived for a PCP with an upward slope, it is also applicable to the downward slope if 6 is taken to be negative, as long as the slope angle 9 is less than tan rj. When 6 is greater than tan on a downslope, the eapsule velocity now exceeds the air velocity F, and the capsule speed becomes... 

According to the equation (2), experimental data in [AO2] - t plot of large t is described by strait line, tangent of slope angle of which is equal to Wst, and cutting on Y-axis is equal to... 

Photolysis of CDA runs with participation of two active centers acetylalkyl radicals R and polyene radicals P , which differ hard in reaction ability. Acetic acid is formed as a result of CDA photolysis, that is why protective action of the additive may be judged by the quantity of extracted acid. Kinetic curves of acetic acid formation at irradiation of stabilized CDA films by the light with wave length of 254 nm. In all cases dependence of the amount of formed acid on the time of irradiation is a strait line from the tangent of slope angle of which the rate of acetic acid formation has been calculated. As it is shown in Figure 4.1, HC - 2 has strong protective effect on the rate of CDA - films photodestruction. 

FIGURE 5.7 Sketch of fluid particle (1) attached to an interface, (a) Fluid particle attached to solid interface a is the contact angle o is the interfacial tension of the boundary between the two fluid phases, (b) Fluid particle attached to a fluid interface O12, O13, and O23 are the interfacial tensions between the respective phases / is the slope angle of the outer meniscus at the contact line. 

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