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.