Figure 4—-D vs. DB.
As Figure 4 demonstrates, the fractal dimensions of two different methodologies were observed to be consistent for the rest of the experiment sets despite the dissimilarity in structural and external conditions found in our experiments and that of the previous literature. In order to investigate the effect of fractal numbers (D ,DB ) on the saturation profiles, we have further adopted the methodology from the immiscible studies of Sharma et al. (2012) and generated four different profiles (Figures 5-11 ) to investigate self-similar behavior of the chemical samples.
Their descriptions are as follows:
Profile I: Log (\(l\)) vs. log (\(t\)), where (\(l\)) is the maximum distance traveled by the interface at a time (\(t\)).
Profile II: Saturation (\(x,t\)) vs. Distance, \(x\) (cm) represents the time evolution of the normalized saturation
Profile III: Saturation as a function of wave speed (\(x/t_{D}\)), where\(t_{D}\) is the dimensionless time based on the chemical injection volume.
Profile IV: Scaled saturation profiles of \({t_{D}}^{e}s(x,t)\) vs. (\({x/t_{D}}^{1+e}\)). For Figures 5-10 D was used, and to plot Figure 11, DB was used for comparison purposes.