Monotonic decreasing response surface

Figures 2.2, 2.3 and 2.4 show relationships between y, and Xj that always increase or always decrease over the domains shown. The lowest and highest values of the response y, lie at the limits of the x, factor domain. Figure 2.2 is a response surface that is monotonic increasing that is, the response always increases as the factor level increases. Figures 2.3 and 2.4 show response surfaces that are monotonic decreasing the response always decreases as the factor level increases.

There are some informations about monotonous decrease of the equilibrium surface tension, dilatational elasticity, and adsorption of lysozyme for non-ionic surfactant decyl dimethyl phosphine oxide (Cj DMPO) as the concentration of surfactant increases in the mixture. However, in the case of mixtures of non-ionic surfactants with more flexible proteins like P-casein, the elasticity of the interfacial layer decreases before passing through a maximum as the concentration of surfactant increases [7], Possibly, the weaker interfacial network formed by P-casein as compared to globular proteins determines the dilatational response of the mixtures. The same picture was shown for the system P-casein mixed with dodecyl dimethyl phosphine oxide (C,2DMPO). For all studied frequencies (0.005-0.1 Hz) the elasticities for adsorption layers have a maximum about 4x10" mol/1 Cj2DMPO concentration. It was shown the obtained values are very close to those measured for the surfactant alone. Thus, in this concentration region the surfactant dominates the surface layer. In our case we have... 

Figure 8 Ellipsometric isotherm of the nonionic C12-DMP betain. The ellipsometric isotherm decreases in a monotonic fashion and is proportional to the surface excess as can be seen in the inset, which compares the surface excess according to Gibbs and the ellipsometric response, (redrawn from [20])...

On the other hand, a step decrease in feed hydrogen resulted in a relatively very rapid and monotonic decline to the final steady-state ethylene concentration. It should be noted that the sum of all hydraulic and mixing lags for this system is of the order of 75 s and the diffusional relaxation time (R /Dg) is much smaller than one second. Hence, the extremely slow response observed in the step-up experiment and its asymmetry compared to the step-down result suggest that non-linear dynamics of the gas phase-catalyst surface interaction play a major role in unsteady reactor behavior. 

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