Figure 15—Surfactant and polymer-induced fingering stability (injection direction available in Figure 14).
As a continuation of the analysis above, Nd(f) is the normalized number of droplets at the final stage of the experiment. And as previously elaborated, the droplet number is a primary indicator of viscous fingering hydrostatic instability. Figure 16 displays the combination of visual and quantitative analysis results for each dimensionless number case. Nca* plot demonstrates that with an increase in the viscous forces, after reaching a specific point (>10-9), Nd(f) decreases consistently while fingers become more stable.Nca plot follows a similar trend – however, stable finger morphology driven by viscous forces appeared in the lower magnitude ranges while stable finger morphology (higher number of tip splits) dominated by surface tension came after. Overall, droplet formation was observed to be in “low to intermediate ranges” of the dimensionless numbers (Nca : 10-4~10-2,Nca* :10-9~10-6,Nca** : <10-7,We :10-5~10-3,We* :<10-2,M :10-4). Note that each finger morphology and its corresponding dimensionless number ranges were assigned to a unique color band for better visualization of the graphs.