V
Figure 13—Dimensionless numbers vs. descriptive parameters (in log scale) (I) L/Ly, (II)tP/tT, (III) tB/tT, (IV) Nd(b), (V) Nd(f).
Figure 13 demonstrates the functional relationship between the descriptive parameters (I) L/Ly , (II) tP/tT , (III)tB/tT , (IV) Nd(b), (V) Nd(f) and dimensionless numbers (Nca * ,Nca ** , M , Nca ,We , We* ).
(I) L/Ly vs. dimensionless scaling groups. Overall trends are characterized by a decrease of L/Ly following an initial increase as the dimensionless numbers increase. The slow decrease could also be observed in the plots with Nca* andNca** , while fast decrease could be seen in the case of M , and Nca . L/Ly plotted with We* also displayed a relatively fast decrease compared to that of other dimensionless numbers. L/Ly vs. We, however, demonstrated a divergent trend from the rest of the plots characterized by a steep increase in L/Ly following a sudden dip. Considering that the magnitude of the considered viscosity term for each case is in the ratio of 2:1:0 (Nca* ,Nca** : M , Nca :We , We* , respectively), viscosity force can be attributed to being the leading factor in determining the normalized interfacial length of fingers before their stability loss. With the larger predominance of the viscosity effect, L/Ly development was shown to be delayed. Such behavior could be due to the repressed shielding effect as elaborated in the study by Nagatsu et al. (2007).
(II) tP/tT vs. dimensionless scaling groups. The general trends for the dimensionless groups plotted with normalized production port reaching time display an initial decrease followed by a stabilized phase and subsequent increase. The length of the stagnant period, however, was observed to vary and appeared to be shorter in the plots with Weand M . Considering that these two dimensionless groups do not share any variables, several factors can be considered to be the cause for the existence of the stagnant period. The chemicals responsible for the stagnant behavior are chemical samples whose contact angle and surface tension are relatively similar in range compared to that of other chemical samples which indicates the sensitivity of tP/tTto the wettability and IFT effect.
(III) tB/tT vs. dimensionless scaling groups. The general decreasing tendency can be observed in the plots except for the case oftB/tT vs. We . In the case of We , with the increase in We , tB/tT increased due to the exclusive effect of surface tension. However, its impact is immediately minimized when other variables such as wettability and viscosity effect are considered in the rest of the dimensionless numbers. In addition, the viscosity effect is observed to be responsible for the long-stagnant period which exists in the plots with Nca* ,Nca**, and M , following an initial steep decrease. The combination of surface tension and contact angle effect seems to be the responsible factor for the steep slope of decrease (with the relatively shorter period of stagnation) observed in the case ofWe* and Nca .
(IV) Nd(b) vs. dimensionless scaling groups. The increasing tendency could be observed in all cases except for We which demonstrated that the number of droplets before the “finger break” decreases with the decrease in surface tension (regardless of the viscosity which has the function of stabilizing the hydrodynamic instability). This is due to the hydrodynamic stability of fingers associated with low surface tension. However, considering that the opposite trend is observed to hold for the rest of the cases, it can be concluded that while low IFT can maintain hydrostatic stability of the fingers, it plays a minimal role in determining Nd(b) when other forces such as viscosity and wettability effect are considered.
(V) Nd(f) vs. dimensionless scaling groups. The overall decreasing tendency could be observed in the plots except in the case ofWe which again indicates that lower surface tension is associated with an increase in the number of droplets after the finger break (hydrodynamic stability loss). This is an interesting phenomenon which indicates loss of hydrodynamic stability leads to the generation of a number of droplets from the finger pinch off for the low IFT cases (Figure 14 ). There are two well-established coarsening mechanisms for emulsion: coalescence and Ostwald ripening. Coalescence occurs due to the fusion of droplets while Ostwald ripening is caused by the molecular exchange through the continuous phase. Visual data analysis of the samples clearly demonstrated that the cause of emulsion coarsening in the partial-miscibility fingering like state (brought on by hydrostatic instability) is Ostwald ripening, rather than coalescence.