Microfluidic dispersion of mineral oil-seawater multiphase flows in the presence of dialkyl sulfonates, polysorbates, and glycols

2.1 Chemicals

Sorbitan monooleate, polyoxyethylene sorbitan trioleate, dioctyl sulfosuccinate sodium salt, di(propylene glycol) butyl ether (mixture of isomers), and sea salts were obtained from Sigma-Aldrich (St. Louis, MO, USA). 1,2-propanediol, sodium benzoate, and kerosene (low odor) were purchased from Alfa Aesar (Ward Hill, MA, USA). Polyoxyethylene sorbitan monooleate was acquired from VWR International (West Chester, PA, USA). Mineral oil (white, light) was obtained from Avantor Performance Materials (Phillipsburg, NJ, USA). All chemicals were used without further purification.

2.2 Experimental setup

The experimental setup is schematically illustrated in Figure 1. Dispersant, mineral oil, and seawater were delivered into a 6-μl microfluidic chip (0.15×0.15×340 mm; Micronit Microfluidics, Enschede, The Netherlands) using three syringe pumps (PHD 2000, Harvard Apparatus, Holliston, MA, USA), one 0.5-ml glass syringe, and two 5-ml glass syringes (SEG Analytical Science, Austin, TX, USA). The syringes and the microfluidic chip were connected using fluidic Connect 4515 (Micronit Microfluidics), 150-μm ID tubing (Perkinelmer, Waltham, MA, USA), 500-μm ID tubing (Idex Heath & Science, Oak Harbor, WA, USA), and PEEK ferrules (Idex Heath & Science, Oak Harbor, WA, USA). A StereoZoom Microscope (VWR International) with a USB digital camera (DV-500) was used for imaging. The camera was linked to a computer.

Figure 1

(A) Schematic flow diagram of the experimental setup used to study the stability of mineral oil-seawater multiphase flows in the presence of model dispersants. Photographs of (B) the enlarged 6-μl microfluidic chip and (C) the packaged system with fluid delivery and exiting connections are also provided.

2.3 Reagent preparation

Seawater was prepared by dispersing 3.5 wt% sea salts into deionized water. Using commercial sea salts provides a reproducible solution of known composition, and it minimizes biological effects. Table 1 shows the typical composition of seawater. Model dispersant was also prepared by first mixing the components according to the molar fractions shown in Table 2. Kerosene was then added to the mixture. Samples were named based on their kerosene contents: Model Dispersant I, 75 wt% kerosene; Model Dispersant II, 50 wt% kerosene; and Model Dispersant III, 25 wt% kerosene.

Table 2

Molar composition of model dispersant less kerosene.

Chemical name	Molecular structure	Molar content (mol %)
Sorbitan monooleate		18.0
Polyoxyethylene sorbitan monooleate		9.5
Polyoxyethylene sorbitan trioleate		3.1
Dioctyl sulfosuccinate sodium salt		8.7
Di(propylene glycol) butyl ether, mixture of isomers		10.1
1,2-Propanediol		50.6

2.4 Residence time distribution measurements

The residence time distributions (RTDs) of the seawater single-phase and seawater-oil-dispersant multiphase were measured using an inline UV-vis setup, as shown in Figure 2. Syringe pumps and 5-ml SGE glass syringes were used to refill seawater and oil into the microfluidic chip. Sodium benzoate with a concentration of 0.04 wt% in seawater was used as the tracer and was injected into the seawater phase by a microscale injector before the two phases contact. The distribution of tracer was measured using the UV-vis setup at the outlet of the microfluidic chip. The microfluidic chip, microscale injector, and the UV-vis setup were connected by 0.005” tubing to reduce the dead volume. Both lamps on the light source were allowed to warm up for at least 20 min before operating the experiments.

Figure 2

(A) Schematic diagram of continuous inline UV-vis spectroscopy used for RTD measurements. (B) Microscale injector with a 0.75-µl sample loop (6 cm of 0.005” ID red tubing) and (C) flow cell with integrated 400-µm ID quartz capillary.

4.1 Mineral oil-seawater microfluidic slug-length distribution

Mineral oil and seawater were delivered into the 6-μl microfluidic chip at identical flow rates ranging from 1 to 10 μl/min. No model dispersant was injected in the initial set of experiments. Depending on the flow rates of mineral oil and seawater, different slug length distributions of two phases were estimated, which is consistent with the work of others [48, 49]. Figure 3A illustrates an example of the mineral oil slug length images obtained using the StereoZoom Microscope, and the mineral oil slug length number distribution calculated is shown in Figure 3B. Here, samples of 100 consecutive mineral oil slugs for each flow rate were chosen to estimate their distributions. As the slug length analysis shows, the flow rate has a strong influence on the slug length distribution. Increasing the flow rate decreases the slug lengths of both the mineral oil and the seawater phases, as depicted in Figures 3A and 3B. Larger flow rates result in larger rates of pressure buildup and, therefore, more rapid insertion of one phase into the other. As a consequence, both phases segment into a greater number of slugs [49, 50]. One observes that the mineral oil slugs are a fraction larger than the water slugs, which results from the hydrophilic microfluidic channel surface. There exists a thin water film between the mineral oil slugs and the microchannel wall. That is, the thin water film connects all the water slugs while all the mineral oil slugs are discrete. The corresponding film thickness, h, is estimated using Bretherton′s Law [51]:

Figure 3

Characterization of mineral oil-seawater multiphase flow through a microfluidic device in the absence of dispersants. (A) Photographs of mineral oil slug lengths obtained using a StereoZoom Microscope. (B) Estimation of the mineral oil slug length number distribution at different injection rates. (C) Dimensionless characterization of the mean capillary and the mean Reynolds numbers.

where the Capillary number Ca=μu/γ, μ is the viscosity of the liquid, and γ is the interfacial tension of the liquid. In our system, the mean Capillary number is in the order of 10^-3 (see Table 3) and the water film thickness estimated by Equation (11) is 0.68 to 3.14 μm. The mean Capillary number is below the critical value (10^-2), so the shear stress alone is not sufficient to break up the slugs. The slug length is determined by the flow rate of mineral oil and the seawater in our model system [52]. Plotting Ca_mean as a function of Re_mean yields Figure 3C. The slope, Ca_mean/Re_mean=μ²/(d_Eργ), is estimated to be 3.0×10^-3. Previously reported values of 0.47×10^-4(for a T-shaped junction) and 0.63×10^-4 (for a Y-shaped junction) estimated for toluene dispersed in deionized water [48] are indications of the characteristic difference of the seawater-mineral oil viscous forces. Increasing viscous forces increases the Ca_mean/Re_mean ratio [48].

Table 3 further summarizes the experimental conditions achieved in the 6-μl microfluidic chip and the corresponding dimensionless quantities. Reynolds number ranged from 0.19 to 1.8, and thus, laminar was established for residence times ranging from 0.30 to 3.0 min. For mineral oil and seawater flow rates of 5.00 μl/min each (total flow rate of 10.00 μl/min), the equivalent mean residence time is 0.60 min and the mean mineral oil slug length is approximately 900 μm. The Weber number, We=d_Eρu²/γ, where ρ is the density of the liquid, ranges from 0.11 to 11.3 (×10^-4). Therefore, the liquid-liquid surface tension dominates over the inertial forces, and again, slug flow is expected [48, 53]. Spilled crude oil on the ocean surface forms a thin film influenced by interfacial tension, viscous, and gravitational forces [54]. In stormy seas, the near-surface turbulence of waves generates oil droplets through natural dispersion [55], and We values >10 predict natural droplet break-ups [53, 56]. When one considers calm seas, the thin crude oil film velocity on the ocean surface is approximately 3.5% of wind speeds [57], ranging from 1.0 to 9.0 m/s [58]. Suspended crude oil droplets can exhibit broad size distributions in thin films (e.g., 1 to 1000 μm) [55]. Estimations of the corresponding We values based on previously reported data give maximum and minimum values of 1.9×10^-3 and 2.4×10^-5, respectively, for droplet sizes of 1 μm. Maximum and minimum We values of 1.9 and 2.4×10^-2, respectively, correspond to 1000-μm droplets. As a consequence, interfacial forces govern, both our laboratory scale study and calm sea conditions, over inertial forces. As we will soon learn, introducing model dispersants into the mineral oil-seawater multiphase flow has a profound impact on the stability of the phase behavior and on the molecular dispersion.

4.2 Influence of model dispersants on the slug length

The influence of dispersant on the slug size distribution was evaluated in the next set of experiments. Seawater, analogous to the base case, was injected into the 6-μl microfluidic chip at a flow rate of 5 μl/min. Each model dispersant was also injected separately at flow rates ranging from 0.02 to 1.0 μl/min. The combined flow rate of the mineral oil and the dispersant was 5 μl/min in each test. Microscope photographs of the mineral oil-seawater multiphase flows for different injection rates of Model Dispersant I are shown in Figure 4. Interestingly, one observes in the figure a transition in the stability as the flow rate of the model dispersant increased from 0.02 μl/min (Figure 4A) to 0.04 μl/min (Figure 4B) to 0.06 μl/min (Figure 4C). For Model Dispersant I flow rates <0.04 μl/min, uniform mineral oil slugs were observed. At flow rates >0.04 μl/min, mineral oil slug lengths became stochastic. Increasing the flow rate to 0.20 μl/min dispersed mineral oil droplets in the continuous seawater phase, and thus, the mineral oil-seawater multiphase flow took a form of bubbly flow as shown in Figures 4D, 5A, and 5B for flow conditions. A stop-flow technique was applied to estimate the static droplet diameters, ranging from 7 to 70 μm, for the bubbly flow regime (see Figure 5C) for dispersant injection rates of 0.30 μl/min. Increasing the injection rate to 1.0 μl/min further reduced the droplet diameters, as shown in Figure 5D. The transition to bubbly flow, a significant discovery, is preliminary indication of a critical dispersant concentration necessary to achieve high interfacial surface areas. To facilitate better understanding of the transition, we define the dimensionless dispersant flow rate, Θ_D, as

Figure 4

Microscope photographs of the mineral oil-seawater multiphase flow through a microfluidic device for different injection rates of Model Dispersant I: (A) F_D=0.02 μl/min, (B) F_D=0.04 μl/min, (C) F_D=0.06 μl/min, and (D) F_D=0.20 μl/min (F_W=5 μl/min; F_O+F_D=5 μl/min for all tests).

Figure 5

Photographs of mineral oil-seawater phase separation (with Model Dispersant I) through a microfluidic device under flow, (A) F_D=0.30 μl/min and (B) F_D=1.0 μl/min, and static conditions, (C) F_D=0.30 μl/min and (D) F_D=1.0 μl/min, where F_W=5 μl/min and F_O+F_D=5 μl/min for all tests.

where the total flow rate, F_T, is the sum of the mineral oil (F_O), dispersant (F_D), and seawater (F_W) flow rates.

Estimation of the mean slug length (L_mean) for different Θ_D values (Figure 6) elucidates the mass of dispersant needed to destabilize the mineral oil slugs. As can be seen in Figure 6, increasing Θ_D values from 0 to approximately 0.003 has no influence on L_mean values for Model Dispersant I. However, L_mean values for Model Dispersants I, II, and III began to decrease for Θ_D values of 0.003, 0.0015, and 0.001, respectively. By Θ_D values of 0.010, the L_mean of mineral oil droplets was 0.126 mm (I), 0.108 mm (II), and 0.064 mm (III). The plateau values illustrated in Figure 6 reveal that the mineral oil slug is stable until the concentration of the model dispersants is greater than a critical concentration. The critical concentrations of Model Dispersant I, II, and III are observed for dispersant flow rates of 0.012, 0.02, and 0.04 μl/min, respectively. The corresponding dimensionless mass ratios of each model dispersant to the mineral oil are 7.7×10^-3 (I), 4.1×10^-3 (II), and 2.6×10^-3 (III). The resultant ratios undergird that increasing the kerosene mass fraction increases the critical mass ratio whereby emulsion formation is expected.

Figure 6

Mean mineral oil slug length (L_mean) as a function of the dimensionless dispersant injection rate (Θ_D×10³) measured by analyses of microscope images. The transition from stable, well-characterized slug flows to the bubbly microfluidic regime is illustrated each for Model Dispersant I, II, and III.

The mineral oil slugs remain stable prior to achieving the critical concentration of dispersant as the surface tension decreases and the dispersant molecules construct a monolayer at the liquid-liquid interfaces. Dispersant molecules accumulate at the interface until the critical concentration is achieved, whereby the surface tension decreases to its minimum limit and the slugs start to break up. As Θ_D values increase beyond the critical values, the dispersant molecules need additional mineral oil-water interface to occupy, which results in the transformation of mineral oil slugs into dispersed mineral oil droplets (i.e., an emulsion). In marine environments, wave motions govern the phase behavior of crude oil slicks. Identifying the critical mass addition of dispersants that effectively break up oil slicks into dispersed droplets is key to minimizing environmental risks and to maximizing the crude oil surface-to-volume ratio (i.e., maximizing the bacteria consumption rate) before crude oil slicks have enough time to reach coastal shorelines.

4.3 RTDs of single-phase and multiphase flows

Experimental analysis of dispersion in multiphase microfluidics, which builds on the classical RTD theory previously derived, offers additional insights on the mineral oil-seawater system. As a first step, the dispersion in single-phase seawater within the microfluidic device was investigated. A tracer molecule, 0.04 wt% sodium benzoate in seawater, was injected into the carrier seawater solvent. Figure 7 shows the absorbance of sodium benzoate in seawater at different concentrations. The maximum absorbance wavelength of 225 nm was chosen to increase the signal-to-noise ratio, which improves the precision of the measurements especially at low absorbance. Flow rates of seawater single-phase flow of 2.00, 4.00, 10.00, and 20.00 μl/min were studied. Estimations of the dimensionless RTD function, E(θ), by Equation (4) were made, and the results are reported in Figures 8A and 8B. The corresponding parameters were calculated using Equations (5) through (7) and (10), and they are reported in Table 4. As the flow rate increased from 2.00 to 20.00 μl/min, the mean residence time decreased from 8.35±0.19 to 0.85±0.003 min (see Table 4), and the peak width of the absorbance decreased (Figure 8A) while the peak width of E(θ) curves increased (Figure 8B). Furthermore, Table 4 confirms that increasing the flow rate increases the vessel dispersion number and Bo because differences between the centerline fluid velocity and the zero wall velocity (i.e., the no-slip boundary condition at the microchannel wall) are greater.

Figure 7

UV-vis absorbance of sodium benzoate in seawater.

Figure 8

RTD measurements of mineral oil and seawater flows. (A) Absorbance as a function of time for seawater injections and (B) their corresponding E(θ) values as a function of dimensionless time (θ). (C) Absorbance as a function of time for mineral oil-seawater multiphase flows and (D) their corresponding E(θ) values as a function of dimensionless time (θ).

Dispersion of the tracer molecule in multiphase flow was evaluated next under the same flow rate conditions and using Equations (4), (5), and (8) through (10). Figures 8C and 8D illustrate the absorbance and the resulting E(θ) curves for total flow rates of 2.00, 4.00, 10.00, and 20.00 μl/min. As shown in Figure 8D and Table 5, (D*/uL) values are independent of the flow rate, which is not surprising in well-mixed segmented flow. Values of (D*/uL)~0.003, significantly less than those reported in Table 4 for single-phase flow, confirm that segments of mineral oil dispersed in seawater confine the tracer molecule. The result is in agreement with previously reported observations for gas-liquid flows [46, 59]. Values of Bo ranging from 400 to 4000 in both the single-phase and multiphase flows confirm the convective flux to dominate the diffusive flux in the radial direction. Eliminating the diffusive and the convective communication between segments in the axial direction, as we will soon see, creates an ideal microfluidic condition that can be exploited to identify when the addition of dispersants breaks up the slugs into dispersed droplets (i.e., an emulsion).

Analyses of the tracer molecule′s absorbance in liquid-liquid mineral oil-seawater multiphase flow offer additional insight on the influence of the model dispersants. As shown in Figure 9A, the tracer molecule absorbance injected into the seawater carrier solvent (in the absence of any model dispersant) generates a histogram distribution with alternating absorbance from one immiscible phase to the other. Figures 9B, 9C, and 9D illustrate the destabilization of the multiphase segmented flow as Θ_D values increase from 0.5×10^-3 to 4×10^-3 to 10×10^-3. Not only does the maximum absorbance increase with increasing Θ_D values but also stochastic peaks outside the distribution function appear as the droplets are dispersed. Replotting the E(θ) curves by substituting data of Figures 9A, 9C, and 9D into Equation (4) yields Figure 10. The maximum of the dimensionless distribution function E(θ) decreases as Θ_D values increase from 0 to 0.004 to 0.010, which signifies axial communication between the immiscible liquid-liquid segments. Recall that axial dispersion was observed neither in Figures 8C and 8D nor in the results of Table 5. As the slugs break up into dispersed droplets, via the addition of Model Dispersant I, axial dispersion is made possible. Table 6 further exemplifies the observation as the resulting calculated (D*/uL) and Bo values increase from 3.0×10^-3 to 4.0×10^-3 and from 2100 to 2800, respectively, with increasing Θ_D values in the range from 0 to 0.010. Our general observations support that changes in the Bodenstein number measured in immiscible liquid-liquid segmented flows indicate the dispersant-induced transition from stable slug flow to the bubbly flow regime. Understanding the criteria, as previously stated, is key to minimizing environmental risks and to maximizing the crude oil surface-to-volume ratio before crude oil slicks have enough time to reach coastal shorelines.

Figure 9

RTDs of mineral oil-seawater multiphase flows with (A) no dispersant (F_w=F_O=5 μl/min; F_D=0; Θ_D(×10³)=0) and for varying dimensionless injection rates of Model Dispersant I: (B) Θ_D(×10³)=0.5, (C) Θ_D(×10³)=4, and (D) Θ_D(×10³)=10.

Figure 10

Dimensionless E(θ) curves of mineral oil-seawater multiphase flow for different dimensionless dispersant injection rates.

Table 6

Comparison of dispersion for varying dimensionless dispersant concentrations.

ΘD (×103)	FT (μl/min)	u (×10-2 m/s)	τ (min)	σθ2	D*/uL	D* (×10-5m2/s)	(×10-10m2/s)	Bo
0	10.00	0.940	2.51±0.04	0.0060	0.0030	1.57	6.68	2120
4	10.00	0.940	2.17±0.03	0.0071	0.0035	1.83	5.73	2480
10	10.00	0.940	2.04±0.03	0.0080	0.0040	2.09	5.02	2830