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.