60th Annual Report on Research 2015

Two-phase flow in constrictions

Rheology of foams and concentrated emulsions impacts many industries, including enhanced oil recovery. The use of foams or emulsions is particularly attractive for mobility control. Our research objectives are to 1) identify conditions for the stability of surfactant- and nanoparticle-laded emulsions flowing through constrictions with size equal to or smaller than droplet diameter. 2) Determine the degree of reversibility and dispersion of the emulsion’s microstructure, and if initially irreversible structures self-organize into reversible patterns after cycles of oscillations.

Results:

1. Stability of surfactant-laden emulsions flowing through narrow constrictions.

We have continued the characterization of the breakup probability of concentrated emulsions flowing into a narrow constriction with a cross section smaller than that of a single droplet. The dispersed phase was water, and the continuous phase was a hydrofluoroether containing a fluorinated surfactant at 2% w/w concentration. The drops were generated using a microfluidic flow-focusing device, and then collected to increase the volume fraction to >80%. Varying the geometry of the constriction as well as the droplet volume allowed us to identify a preliminary dimensionless number that the breakup probability was dependent on. Figure 1 shows that the data appeared to collapse when the velocity of the applied flow at measured at the constriction (Uc) was scaled with b, a confinement factor that we had defined to scale with (R/R_h)³, where R is the radius of the drop and R_h is the hydraulic radius of the constriction.

Figure 1: (Left) Breakup probability of the drops as a function of velocity of flow measured at the constriction Uc for various droplet sizes and constriction dimensions. (Right) Breakup probability as a function of Uc scaled with a confinement factor b.  

The droplet volumes used varied from 30 pL to 50 pL, the height of the channel varied from 25 to 30 mm, and the width of the constriction varied from 25 to 40 mm. Work is still in progress to verify this scaling. In addition, we have varied the viscosity ratio l between the drops and the continuous phase. We changed the viscosity ratio by mixing glycerol into water at different concentrations. Figure 2 shows that breakup probability increased when the drops were increasingly viscous compared with the continuous phase.

Figure 2: Breakup probability as a function of flow rate for different viscosity ratios l.

2. Stability of Nano-particles laden droplets

We have synthesized nanoparticles as effective emulsifiers to replace surfactants. The stabilization of droplets depended on particle size and surface chemistry. To better quantify the adsorption of nanoparticles to W/O interface, we have measured the changes in the interfacial tension between W/O in the presence of the nanoparticles. Our results show that if the particles possessed the appropriate surface chemistry for stabilization of W/O emulsions, the interfacial tension should decrease below 40 mN/m.

Figure 3: Interfacial tension between water (or LB) and HFE-7500 containing various concentrations of nanoparticles “F-SiO2 NPs”. The NPs were 52.1 ± 10 nm in diameter, and they were dispersed in the fluorous phase, and the plateau indicates adsorbed NPs were likely to be saturated at interface.

3. Degree of reversibility and dispersion of the emulsion’s microstructure:

We continued to characterize the transition from reversible to chaotic behavior in an oscillatory shear flow of water-in-oil emulsions. The emulsion was injected through a microchannel and was forced to rearrange due to a central constriction in the channel. When injected into the channel, the drops first arranged into a 2D hexagonally-packed crystal and followed discrete trajectories as they flowed. The taper geometry of the channel led to “rearrangement zones” where number of rows of drops decreased from N to N-1. At the flow conditions applied (Reynolds number Re and capillary number Ca at the constriction were Re ~ 0.06 and Ca ~ 10^-4 respectively), the drops were un-deformed and appeared mostly as circles. In the rearrangement zones, the reduction in the number of rows of drops occurred via a cascade of T1 events. A T1 is an elementary rearrangement process involving the exchange of neighbors among 4 drops, consisting of one pair of “diverging” drops (drops #2 and #4 as shown in Figure 4) and one pair of “converging” drops (drops #1 and #3). The sequence of T1 had the following three characteristics: i) they occurred at a fixed x-location in the channel. ii) Within a rearrangement zone, only one T1 took place at a time. iii) The T1s propagated from one channel wall to the other, thereby reducing the number of rows of drops by one. We have found that the reversibility of the flow relied on the properties of such T1 events.

Figure 4:  The flow of the emulsion in the channel occurred via a sequence of T1 events.

Impact of the research:

The study on droplet stability is useful for understanding the behavior of concentrated emulsions in applications such as mobility control in enhanced oil recovery, and for extrapolating critical parameters such as injection rates to ensure the stability of the fluids going through small pore throats. Understanding hydrodynamic reversibility and discovering any self-organization of the fluid structure allows one to elucidate the origin of hysteresis and history dependence of the microstructure. One could potentially prime the foams or emulsions prior to actual use to fine-tune their bulk properties.

The research has resulted in publication in a peer-reviewed journal Soft Matter, and two conference presentations in American Physical Society Division of Fluid Dynamics Annual meeting 2014. The work has enabled research in my lab on two-phase flow and supported a graduate student who is interested in a career in two-phase flow and interfacial phenomena.