Logarithmic coordinates

Values of n and k for the suspensions used are given in Table 5.2. Experimental results are shown in Figure 5.8 as wall shear stress R as a function of wall shear rate (dn /dyfr o using logarithmic coordinates. 

At low values of the Reynolds number, less than about 10, a laminar or viscous zone exists and the slope of the power curve on logarithmic coordinates is — 1, which is typical of most viscous flows. This region, which is characterised by slow mixing at both macro-arid micro-levels, is where the majority of the highly viscous (Newtonian as well as non-Newtonian) liquids are processed. 

The behaviour of te,2 (tj) is qualitatively different. In the dense media this dependence also satisfies the Hubbard relation (6.64), and in logarithmic coordinates of Fig. 6.6 it is rectilinear. As t increases, it passes through the minimum and becomes linear again when results (6.25) and (6.34) hold, correspondingly, for weak and strong collisions ... 

As shown in Fig. 6 [19], for the lubricant with higher viscosity (kinetic viscosity from 320 mm /s to 1,530 mm /s), the film is thick enough so that a clear EHL phenomenon can be observed, i.e., the relationship between the film thickness and speed is in liner style in the logarithmic coordinates. 

Figure 5. True stress-at-break plotted on doubly logarithmic coordinates against the strain-at-break. Conditions 30°C extension rates from 9.4 X 103 to 9.4 min 1. Quantity A introduced for clarity.

Several useful methods are available for extrapolating equilibrium data for a given system to various temperatures and pressures. One convenient method is by use of a reference substance plot. Here, the adsorption equilibrium partial pressure of the adsorbate is plotted against a pure substance vapor pressure, preferably that of the adsorbate. If logarithmic coordinates are used on both axes, lines of constant adsorbent loading, isosteres, are linear for most substances. Therefore, only two datum points are required to establish each isostere. 

In figure 1 the dependence pA(t) in double logarithmic coordinates, corresponding to the relationship (2), for solid state imidization reaction without filler at the four mentioned above imidization temperatures 7) are shown. As can be seen, the received dependences are linear and according to their slope the value ds can be obtained. The 7) increase in the range 423-523... 

Carman found that when R jpu was plotted against Re using logarithmic coordinates, his data for the flow through randomly packed beds of solid particles could be correlated approximately by a single curve (curve A, Figure 4.1), whose general equation is ... 

Figure 4.19 Temperature dependence of the dipolar Ti relaxation time in semi logarithmic coordinates at the Larmor frequency coq- The dashed T i curve corresponds to a higher Larmor frequency. The regions with and 1 <<0)qT ...

Plots of the fractional remaining activity C /C q against incubation time on semi-logarithmic coordinates give straight lines, as shown in Figure 3.3. The values of the inactivation constant k calculated from the slopes of these straight lines are as follows ... 

In Figure 4.4 the dimensionless cell concentrations X are plotted on semi-logarithmic coordinates against the dimensionless cultivation time for... 

Cl) against time on semi-logarithmic coordinates produces a straight line, from the slope of which can be calculated the value of... 

These results could be complemented well with the curve slopes in the double logarithmic coordinates as plotted in Fig. 6.33(a) using idea of the intermediate critical exponent a(t), equation (4.1.68). In the traditional chemical kinetics its asymptotic limit ao = a(oo) = 1 is achieved already during the presented dimensionless time interval, t 104. For non-interacting particles and if one of two kinds is immobile, Da = 0, it was earlier calculated analytically [11] that the critical exponent is additionally reduced down to ao = 0-5. However, for a weak interaction (curve 1) it is observed that in the time interval t 104 amax 0.8 is achieved only for a given n(0) = 0.1, i.e., the... 

The group on the left side of this equation is a form of dimensionless film thickness and has been termed the Nusselt film thickness parameter Nt (D12). Equation (97) indicates that a plot of Nt against Nne on double-logarithmic coordinates should give a straight line of slope for the... 

Fig. 1. Body weight versus metabolic rate plotted on logarithmic coordinates...

Figure 1 shows a plot of the reduced tensile relaxation modulus, Ep(t), against the time, t, in logarithmic coordinates for Kraton 102 cast from benzene. Similar plots were prepared for the results obtained on specimens cast from cyclohexane and tetrahydrofuran solution, respec-... 

Figure 3 shows the plot of the reduced tensile creep compliance, Dp(t), against t in logarithmic coordinates for the creep tests on Sheet I. A similar plot was made for the data obtained from Sheet II, and, in addition, for the relaxation data shown in Figure 1 after conversion to creep data using the relation (7) ... 

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