Dimensionless absorption

The human effective permeability Pcff in Eq. (59) is expressed in centimeters per hour. In terms of the dimensionless absorption number An, Eq. (58) can be written as... 

Dressman et al. [13] developed a dimensionless absorption potential (AP) model based on the concept that the fraction of dose absorbed, assuming negligible luminal instability and first-pass metabolism, is a function of drug lipophilicity (log P0/w), solubility (Sw), and dose (D), as defined in Eq. 2.7. 

III) Mass transfer is described by a modified Maxwell-Stefan theory by assuming n.4 l and dAgnA l (the absorption flux is sufficiently small). In this case eq. (22) can be reduced to the following explicit expression for the dimensionless absorption flux by linearization of the exponential terms (see Appendix A) ... 

On the basis of inspection of eqs (27)-(29) and combination of the results for cases (a)-(d) the following general approximate explicit expression for the dimensionless absorption flux can be formulated ... 

Fig. 8. Dimensionless absorption flux as function of reaction rate constant for mass transfer with bimolecular chemical reaction in case all K,j equal 1 x 10 m/s except K g = 1 X 10" m/s). The kinetics are given by eqs (38a)-(38c).

Figure 6. Frequency dependence of dimensionless absorption. Dimensionless collision frequency y = 0.3. (a) Calculation from rigorous formulas (70a) and (70b) (solid lines) and from the PL-RP approximation, Eqs. (78-80b) (dashed lines). Curves 1 refer to P = ji/8 and curves 2 to (3 = ti/4. Vertical lines mark the values of the absorption-peak frequencies estimated by Eqs. (85) and (86). (b) Comparison of the total absorption (solid line) with contribution of the precessional component (dashed line). Calculation for the PL-RP approximation, P = ji/8.

Figure 13. Dimensionless absorption versus normalized frequency calculated rigorously (solid lines), from the PL-RP approximation (dashed lines), and for the hybrid model (dashed-and-dotted lines). The cone angle P = tt/8 and the reduced collision frequency y = 0.2. The reduced well depth u = 3.5 (a) and 5.5 (b). Left and righ vertical lines mark the frequency peaks estimated, respectively, in the rotational and librational ranges.

We account for only the torque proportional to the string s expansion AL, which produces the main effect considered in this work. For calculation we employ the spectral function (SF) Lstr(Z), which is linearly connected with the spectrum of the dipolar ACF (see Section II), with Z x Y being the reduced complex frequency. Its imaginary part Y is in inverse proportion to the lifetime tstr of the dipoles exerting restricted rotation. The dimensionless absorption Astr is related to the SF Lstr as... 

We shall show now that (i) The R-band arises due to rotational motion of a polar H-bonded molecule determined by the elastic force constant k. (ii) The dimensionless absorption Astr(v) (463) agrees qualitatively with the g(vstr) frequency dependence found in Section IX.B. (iii) The used SD model describes a small isotopic shift of the R-band also in terms of the ACF method. 

Figure 62. Solid lines contribution of the structural-dynamical model to the dimensionless absorption Astr(v) calculated in the R-band by the ACF method, (a) Calculation for H20, the dimensionless collision frequency Y = 0.6, r/L = 0.27,/) = 2.07. (b) Calculation for D20 with Y = 1.3, r/L = 0.4,/j = 3.54. Dotted lines total absorption calculated for the composite HC-SD model. Temperature 22.2°C. The peak ordinates are set equal to 1.

The following molecular constants are used in further calculations density p of a liquid the static (es) and optical (n ) permittivity moment of inertia /, which determine the dimensionless frequency x in both HC and SD models the dipole moment p the molecular mass M and the static permittivity 1 referring to an ensemble of the restricted rotators. The results of calculations are summarized in Table XXIII. In Fig. 62 the dimensionless absorption around frequency 200 cm 1, obtained for the composite model, is depicted by dots in the same units as the absorption Astr described in Section B. Fig. 62a refers to H2O and Fig. 62b to D2O. It is clearly seen in Fig. 62b that the total absorption calculated in terms of the composite model decreases more slowly in the right wing of the R-band than that given by Eq. (460). Indeed, the absorption curve due to dipoles reorienting in the HC well overlaps with the curve generated by the SD model, which is determined by the restricted rotators. 

At the end of the simulation time, the mass that was absorbed and the mass that has exited from the end of the tube can be computed. Further, the dimensionless absorption number An can be computed [153] from... 

Figure 40 (a-d) Frequency dependences of the dimensionless absorption A(x). Solid lines denote absorption due elastic translations of charges and dashed lines due to elastic reorientations. Calculation according to strict theory (a) c = 0.4 (b) c = 0.2 for curves 1 and 2 (c) c = 0.15 for curves 5 and 6 and c — 0.1 for curves 7 and 8 (d) c = 0.05. Approximate calculation (b) for c = 0.2 (curves 3 and 4). Vertical lines refer to the Lorentz line centers estimated as xq = /, xfl = p. (e) Amplitude of angular vibration versus rotary force constant, horizontal line depicts the quantity (158). 

In Fig. 45a we show the dimensionless absorption calculated for the librational band for the parameters, typical for liquid water. Here distinction of the planar model (solid lines) from the spatial one (dashed line) turns out to be noticeable. For ice (Fig. 45b) the indicated distinction becomes less. 

Figure 46 Dimensionless absorption frequency dependences, calculated for the planar (solid lines) and spatial (dashed lines) hat models, (a) Calculation for liquid water at 27°C with the parameters / = 23°, u = 8, / = 0.8, y = 0.3. (b) Calculation for ice at -7°C with the parameters P = 23.5°, u = 8.5,/ = 0.15, y = 0.8...

It follows from (280) that at high frequencies, such that x y, the spectral function L(z), which is proportional to the dimensionless absorption coefficient, equal to x Im[/ (x)]. 

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