Figure 16—Description of emulsion development and Nd(f).
Fu et al. (2016) stated that the pinch-off from the viscous fingering
instability results in small droplets ending up being consumed by larger
droplets through diffusive mass transfer via Ostwald ripening; however,
if the diffusive mass transfer rate cannot compete with the rate of
smaller droplet generation, it may lead to excess dissolved
concentration and a supersaturated liquid phase. And with disturbance,
droplets can be generated. However, in this study, despite the constant
injection of the solution (“disturbance”), it could be seen after a
certain period, the droplets remained—-not to be further consumed by
the surrounding larger-sized droplets (and co-existing fingers) which
implies that surface energy was sufficiently low, and further energy
minimization was not required. The cause of this behavior requires
further investigation. However, it can be speculated that the IFT
between the phases in the overall Hele-Shaw cell had reached the CMC
(Critical Micelle Concentration) value and therefore, there was not an
active chemical interaction between the liquid phases which could cause
a disturbance. In which case, droplet development (or lack thereof)
during an emulsion flow in a Hele-Shaw model can be employed as an
indicator to predict the “in-situ” CMC of injected surfactants.
Provided in Figure 17 are the micrographs and particle size
distribution histograms of the oil-in-water macroemulsion samples
produced from the injection experiments. Particle size distribution
histogram tended to have the large tail towards the left and generally
followed a lognormal distribution pattern. It can be seen that larger
sized droplets are associated with the more stable emulsion groups while
the smaller sized droplets are associated with the less stable emulsion
groups (associated with high Nf(d) ). The stability of emulsions
for the upper cases in Figure 17a was induced by the polymer.
Hydrophilic polymers are effective in preventing coalescence by
increasing the bulk phase viscosity, reducing the kinetic energy of
droplet particles, and controlling the collisions accordingly (Sadtler
et al. 2002). The cause for the coarser nature of emulsions stabilized
by polymeric solutions is not well-studied. However, it should be noted
that oil displacement was more effective in the stable emulsion case,
hence the higher oil content (and larger droplet size) observed in the
micrographs. The micrographs available in Figure 17b were captured after
adding an extra mechanical force via agitation, and before the
agitation, produced samples easily separated into two phases due to the
emulsion kinetic instability. When adding the external force to the
upper glass samples however, there was no significant change in the
droplet sizes or the droplet size distribution.