Stability Analysis of Pure Oil-Water Emulsion in Gravity-Based Separators¹

An emulsion is simply the mixture of, at least, two immiscible liquids that under natural circumstances do not mix [1–7]. The formation process of such a mixture is commonly known as mixing or emulsification [8,9]. The formation of oil-water emulsion is desirable in many applications, such as cosmetics, pharmaceuticals, energy, petroleum, petrochemicals, and food industry. It is well known in the scientific community [1,2,4] that the presence of stabilizers (i.e., surfactants, solid particles, and natural emulsifiers) boosts the stability of oil-water emulsions to several months or sometimes years, depending on the performance of the stabilizer at the liquid-liquid interface. However, before introducing stabilizers, it is crucial that we understand the fundamental aspects of oil-water mixtures, such as the significance of initial mixing speed, water concentration, and temperature.

Surprisingly, although mixing speed and the volume concentration of water are the main reasons for the formation of an oil-water emulsion in gravity-based separators, their effects were never addressed in a systematic way. In addition, available models [10–14] that predict the free phase separation were never validated at mixing speeds more than 1500 rpm and water concentrations above 75%. A chronological review of previous research on pure oil-water emulsion carried out by Berger [15] in 1987, Nadiv and Semiat [16] in 1995, Jeelani and Hartland [10] in 1998, May et al. [17] in 1998, Yau and Mao [13] in 2004, and Gavrielatos et al. [4] in 2018 were all found to be emulsified at speeds <1000 rpm. Further, there was no mention of the effect of high-water concentration, only concentrations that are ≤75%. Even though the shear speed varied significantly between 1158 and 1458 rpm in the work of Hartland and Jeelani [18], the water concentration of all oil-water emulsions in their study did not exceed 65%. As a result of the minor variations in speeds and the low concentrations of water, the full separation time of all emulsions in the above-mentioned studies was within a few minutes.

Indeed, when an oil-water emulsion inverts from W/O to O/W, the lifetime of the emulsion will be greatly impacted by the impeller speed given initially to the properties of its liquid in the dispersed phase. In other words, O/W emulsion is more sensitive to mixing speed than W/O emulsion. This is also supported by many studies carried out in the past. For example, in one study by Kochick [19] in 2019, data from water-continuous emulsion showed smaller oil droplets as compared to water droplets (although mixed at the same speeds). In addition, in another study by Chen and Tao [20] in 2005, it was concluded that the increase in initial mixing speed to 2500 rpm increases the volume of surfactant-stabilized O/W emulsion.

In addition to mixing speed and the concentration of water, an oil-water emulsion is also impacted by temperature [21–25], as it changes the interfacial tension between oil and water. Indeed, temperature influences almost all physical properties of liquids, including the interfacial tension, density, and viscosity [26]. Hence, when temperature modifies the physical properties of the oil and water phase, the whole separation process of their emulsions will be impacted. For example, an increase in temperature decreases the viscosity of the continuous phase of the emulsion, which in turn, speeds up the film drainage and improves coalescence rate of dispersed droplets [27]. Also, the drop in viscosity leads to easier fragmentation of the dispersed phase due to reduced cohesive force between the molecules of dispersed droplets, which in turn increases stability. In addition to that, an increase in temperature increases the gap in density between the internal and external liquid phases, which in turn increases the probability of faster droplets sedimentation.

As far as the interfacial tension is concerned, there is currently disagreement in the literature regarding the effect of temperature on interfacial tension of oil and water. For example, Cabrerizo-Vilchez et al. [25] and Jennings [22] state that by increasing the temperature, the interfacial tension will decrease, whereas Gaonkar [23] and Lutton et al. [24] disputed this claim. Therefore, until this time, it is still poorly understood how temperature influences the interfacial tension of oil and water when the two phases are emulsified. If in case an increase in temperature decreases the interfacial tension between oil and water then deformation of droplets will be enhanced, which in turn improves the stability of the emulsion. However, this is currently not well understood.

The main goal of the present research is to investigate the effects of initial mixing speed (between 600 rpm and 2500 rpm) on the stability of pure O/W and W/O emulsion. The overall stability is assessed in terms of the separation kinetics (profiles) of the free liquid phase, oil/water emulsion volume, and the initial time of free phase separation. No emulsifier was used, and only pure fluids (Exxsol^TM D110 and distilled water) were considered. For each emulsion type, two volume water concentrations (WCs) were considered (i.e., 75% and 90% WC for O/W emulsion and 25% and 50% WC for W/O emulsion). In addition to 25 °C, the study investigated effects of temperature at 60 °C and 80 °C (on O/W emulsions only). In the first part of the paper, the study explains the research method followed to collect data. Next, it shows the results of the effect of mixing speed on pure O/W and W/O emulsions; followed by discussion of the effect of temperature on O/W emulsions and also some error analysis of the research facility.

Distilled water and mineral oil were used as the two immiscible liquids in this research. The water portion of the emulsion was supplied from Premium Waters Inc. in Quincy, IL. whereas oil was acquired from ExxonMobil in Spring, TX. The mineral oil phase (Exxsol^TM D110) is a de-aromatized hydrocarbon solvent made from petroleum-based raw materials that have been treated with hydrogen in the presence of a catalyst to create a low-odor, low-aromatic hydrocarbon solvent [28].

Figure 1(a) depicts the measured viscosity (μ) of both liquids versus the shear rate (⁠$γ˙)$⁠. Viscosity data were collected from the same rheometer, Anton Paar MCR72. The working principle of this rheometer is briefly discussed in Sec. 2.3. As illustrated in Fig. 1(a), the μ of Exxsol™ D110 is about three times the μ of water. However, they both exhibit Newtonian behavior (viscosity approximately remains constant with shear rate). The dynamic surface tension (σ) of both liquids is also shown in Fig. 1(b). Exxsol™ D110 showed a surface tension of only 30 mN/m for a time (t) of 443 s. The procedure that was followed to collect surface tension data is briefly discussed in Sec. 2.3 below.

The densities of distilled water (⁠$ρw$⁠) and Exxsol™ D110 (⁠$ρo$⁠) (shown in Table 1) were both measured from a glass pycnometer having a usable volume of 24.298 ± 0.050 ml. To determine the density of each liquid, the mass of the pycnometer and the liquid sample were measured first, and then, the net mass of the liquid sample was divided by the nominal volume of the liquid sample in the pycnometer (which was roughly around 24.3 mm in each density test). In order to minimize the error when measuring the mass of the liquid in the pycnometer, an accurate digital mass balance (AC100) of resolution 0.10 mg and maximum capacity of 100 g was used.

At each WC, the stirrer speed (N) varied significantly whereas the mixing time was kept constant, 5 min. Emulsions of 90% WC were mixed at speeds ranging between 800 rpm and 2500 rpm. Whereas the mixing speed of 75% WC varied between 600 rpm and 2500 rpm. The additional 600 rpm for 75% WC emulsion was to confirm behaviors seen at speeds < 1000 rpm. Unlike O/W, W/O emulsions of 25% and 50% WC were mixed at four speeds only (i.e., 1000, 1500, 2000, and 2500 rpm). The reason the speed range for W/O emulsion differed from O/W emulsion is because W/O emulsions separated immediately after formation even when speeds reached 2500 rpm. Therefore, it was un-necessary to go below 1000 rpm. When considering the effect of temperature on emulsion stability, the temperature of the oil and water phase was adjusted between 25 °C, 60 °C, and 80 °C. This occurred before mixing the liquids in the separator.

The viscosity of pure oil and water was measured from “Anton Paar MCR72” rheometer. In this rheometer, a liquid sample is bounded between two concentric cylinders with a 1 mm gap. The equipment operates as follows: the inner cylinder moves while the outer cylinder remains stationary. As the rotational speed of the inner cylinder increases so does the shear rate (velocity gradient) of the liquid between the two cylinders. As a result, the liquid sample exerts different values of shear stress on the inner (moving) cylinder, which is then interpreted by the software as viscosity data versus shear rate, giving rise to the concepts of shear-thinning, shear-thickening, and Newtonian flow-behavior.

Surface tension data of both liquids (oil and water) used in this research were collected from a pendant-drop tensiometer. In this tensiometer, a drop of liquid is allowed to form with the help of a drop dispenser, and its shape is then analyzed based on the pressure difference between the inner and outer surfaces of the drop (using the Young-Laplace equation).

Unlike most research provided in literature, this work used a state-of-the-art portable dispersion characterization rig (P-DCR) to form, control the initial conditions, and study the separation kinetics of oil-water emulsions. The specific details of the facility are shown in Fig. 2. Important parts of the facility include camera, light source, the stirrer, stirrer speed controller, batch separator, thermal jacket, and color spec tool as part of the computer. In the beginning, after fully closing the “liquid discharge port,” liquids are poured into a 60 mm diameter “batch separator” with an operational volume of 200 ml. After that, a thermal jacket insulator is placed around the separator (as shown in Fig. 2). Once this step is completed, the speed of a 163 mm long and 4 flat radial blade (35 mm diameter each) stirrer is adjusted via the “stirrer speed controller.” This step can only be done while the “stirrer electric switch” is on. After mixing the liquids to the required time, the oil and water separation profiles (as well as the remaining oil/water mixture volume) are monitored live during the entire time of the experiment, using a high-resolution camera. Then, after stopping the experiment, a color-spec sophisticated tool is used to scan the video of the separation. More details of this facility can also be found in the studies [29–31]. The facility is also equipped with heating and pressure controls to adjust the temperature and pressure of liquids before they are mixed. It can elevate the temperature and pressure of liquids to 200 °C and 34 bar, respectively. However, in this research, it was only used for up to 80 °C and 1 bar.

The working principle of the P-DCR facility is summarized in three main stages shown in Fig. 3. First, at stage 1 (when t < 0), both oil and water are introduced into the separator (see Fig. 2). Then (at stage 2) the impeller of the stirrer is placed halfway of the separator (at E_o/2; WC = 50%) and rotated at the required rotational speed “N.” Due to this rotation, shear energy will then be transferred to the oil and water phases to disperse one liquid in the other (according to the initial WC of the dispersion). For example, if an oil-water emulsion is prepared at WCs < 75%, then the type of emulsion will be W/O. But if it was prepared at WCs ≥ 75%, then it would be O/W. Thus, the initial volumes of the water and oil phase (Eq. 1) are the main determinant of emulsion type. Once reaching the desired mixing time (at t = 0), an oil-water mixture with an initial volume (E_o) of 200 ml will form as shown by stage 2 in Fig. 3. Since emulsions of immiscible fluids (without stabilizing agents) always tend to separate, three regions will evolve in stage 3 (at t ≫ 0), one is the emulsion layer, and others are the regions of the separated water and oil.

The physical phenomenon of stage 2 and 3 is further illustrated in Fig. 4. Initially, at t = 0, the volume (E_V) of the oil/water emulsion is equal to its initial volume E_O, which in this study is always 200 ml. In other words, E_V initially equals the total volume of the oil and water phase, as shown in Eq. (1). However, as time passes by, E_V reduces. This is because emulsions of immiscible fluids (without stabilizing agents) always tend to separate. E_V reduces due to the separation of free oil and free water from the emulsion layer, which starts at an initial time of t_o and t_w, as shown in Fig. 4. Since the oil phase is lighter than the water phase, the separation profile of the free oil starts at V = 200 ml and moves downward in the batch separator with time (if there is oil separation) whereas the separation profile of the free water does the opposite, it begins at V = 0 ml and progresses upward in the separator with the separation of free water from emulsion region. Having said that, the vertical (inner) distance between the water and oil separation profiles always represents the change of E_V with time, as shown in Fig. 4. If the two separation profiles touch each other, then the whole emulsion volume has collapsed by that time, indicating E_V = 0. At that instant, one can read the full separation time (t_f) from the horizontal (time) axis directly.

The effect of mixing speed on the separation kinetics of 90% WC and 75% WC pure O/W emulsions are shown in Figs. 5 and 6, respectively. As shown in these figures, at each mixing speed, there are two profiles (upper and lower) of the same color. As mentioned earlier in Sec. 2.4, since the oil phase is lighter than the water phase, the upper profile is used to represent the separation of the dispersed (oil) phase from the emulsion layer whereas the lower profile is used to represent the separation of the continuous (water) phase. In other words, the vertical distance between V = 0 and the lower (water) separation profile always represents the volume of free (separated) water with time (V versus t). Likewise, the vertical distance between V = 200 ml and the upper (oil) separation profile always represents the volume of free oil from the emulsion layer. Having said that, the vertical (inner) distance between the upper and lower profile represents the decay in the volume of the oil/water mixture with time (E_V vs t). Obviously, since emulsions of immiscible fluids (without stabilizing agents) always tend to separate, this inner distance reduces with time until the two profiles touch each other at the original location of the interface, which was 150 ml for 75% WC and 180 ml for 90% WC emulsion. When they do, the time of the full separation of the oil/water mixture can be read directly from the horizontal (time) axis of Figs. 5 and 6.

In Figs. 5(a) and 6(a), the effect of mixing speed on pure O/W emulsion is shown for the whole duration of the experiment, which lasted for around 4 h. However, it is also important to show the first few minutes of the separation, especially at low speeds. Therefore, for both WCs, the details of the initial separation are also shown in Figs. 5(b) and 6(b). As shown in Fig. 5(b), at 90% WC, speeds of 800 rpm and 1000 rpm were not capable of keeping the continuous (water) phase emulsified for even two minutes. However, although mixed at 800 and 1000 rpm, the dispersed (oil) phase remained stable for around 4 h. Unlike 90% WC, however, 75% WC emulsions showed immediate oil separation (Fig. 6(b)) at low speeds. The reason why this occurs for 90% WC but not for 75% WC emulsion is owing to the increased probability of dispersion coalescence. At high WCs (like 90%), drop-drop coalescence is hindered due to lower collision frequencies between dispersed oil droplets. Apparently, when the volume fraction of the dispersed phase is less, the chance of droplet-droplet coalescence is lowered since droplets have less time to stay in contact so that the film of the continuous phase can be ruptured.

Increasing the mixing speed of pure O/W emulsion beyond 1000 rpm has drastically boosted its stability. Indeed, the change in O/W emulsion stability due to mixing speed was impressive. Figures 5(a) and 6(a) (respectively) illustrate this significant and sudden change in stability of both 90% and 75% WCs. The consistent decrease in water sedimentation rate with mixing speed is another intriguing observation. Although the WC of pure O/W emulsion decreased from 90% to 75%, the change in the water sedimentation rate against mixing speed remained consistent- the higher the mixing speed lower the water separation rate. However, unlike 90% WC emulsion (Fig. 5(a)), the increase in mixing speed from 2000 rpm to 2500 rpm barely affected the water separation rate of 75% WC emulsion (Fig. 6(a)). However, the oil separation rate of this WC was greatly impacted by mixing speed. Whereas emulsions of 90% WCs showed no sign of oil separation for about 4 h although speeds varied between 800 and 2500 rpm. Obviously, the higher the mixing speed the finer the oil droplets are of both 75% WC and 90% WC emulsions. Therefore, the coalescence time of dispersed droplets increases with smaller droplets [32,33], which in turns delays the rate of dispersed (oil) phase separation. Also, since the 90% WC showed no oil separation even at low speeds of 800 rpm due to the decreased probability of drop-drop collision, this behavior should also be expected at high speeds as shown in Fig. 5(a).

Photographs of O/W emulsion at t = 0 and at various times were also acquired (see Figs. 7 and 8). In Fig. 7, the pictures show 75% WC emulsion formed at t = 0 and various speeds whereas Fig. 8 shows the effect of mixing speed on 75% WC emulsion at various times after the formation. It is clear from Fig. 7 that the change in mixing speed between 600 rpm and 2000 rpm showed substantial effects on the appearance of the emulsion, with oil droplets being almost visible to the naked eye at speeds ≤ 800 rpm. Increasing the speed to more than 1000 rpm not only inhibited the visibility of oil droplets but also changed the color of the emulsion from opaque to whitish (Fig. 7), which is characteristics of very small dispersed phase droplets. The significant change in emulsion volume (Fig. 8) is also another evidence of the effect of mixing speed. For example, despite the fact that the 75% WC O/W emulsions are emulsifier-free, a significant portion of their volume remained stable for over 3 h at 2000 rpm, whereas at 800 rpm, the whole emulsion separated quickly after only 5 min.

The decrease in the volume concentration of water to ranges below 75% was very impressive to look at. This is because 50% (Fig. 9) and 25% (Fig. 10) WC W/O emulsions showed fast separation regardless of mixing speed. Furthermore, the increase in mixing speed barely affected the rate of separation of both phases, oil (upper profile) and water (lower profile), as shown in Figs. 9 and 10. The significant gap in the response of O/W and W/O emulsion to mixing speed is owing to the repulsive and attractive forces between polar (water) and nonpolar (oil) droplets, as illustrated in Fig. 11.

At 25% and 50% WCs, emulsions consist of water droplets where each molecule in the droplet has two pairs of unequally shared electrons between oxygen and hydrogen atoms. The presence of unshared electrons on the oxygen's shell strongly attracts positive hydrogen ions from neighboring water molecules, which leads to the creation of a permanent dipole force (Fig. 11). Therefore, during mixing, a water droplet does not split into smaller droplets, even when increasing the speed to 2500 rpm. Exxsol™ D110, on the other hand, is a hydrocarbon solvent consisting of nonpolar molecules. Therefore, the atoms in every single oil molecule are evenly distributed, resulting in a temporary dipole force between the molecules (Fig. 11). This temporary dipole force causes the molecules to exert both repulsive and attractive forces on each other, which randomly vary based on the molecules' orientation and distance. Consequently, there is a weakened affinity between oil droplets when an O/W emulsion is mixed, which results in the significant fragmentation of oil droplets in the water phase.

To clearly show the effect of water concentration, WC on the stability of both O/W and W/O pure emulsions, the study considered additional empirical parameters of the separation process. The parameters are the initiating time of water separation (t_w), initiating time of oil separation (t_o), emulsion volume (E_V), and the full separation time (t_f). As shown in Fig. 4, the initiating time of separation is the time required before oil or water just starts separating from the emulsion layer. The parameters were directly acquired from experimental data, as shown in Fig. 4. Because oil is less dense than water, the initiating time of water separation was measured from the “separated water profile” shown by the solid blue line in Fig. 4. Whereas for oil it was measured from the “separated oil profile” shown by the dashed red profile. The full separation time (t_f), however, was taken as the time when the two profiles meet at one point. But if the duration of the experiment ends before this time, then the volume of the emulsion (E_V) was used to evaluate the overall stability of the emulsion.

At higher mixing speeds (N > 1000 rpm), the increase of WC from 50% to 75% severely impacted the initiating time of water separation (t_w) as shown in Fig. 12, whereas at speeds ≤ 1000 rpm, all WCs showed a comparable time. However, at modest speeds such as 1500 rpm, the variation of WC from 25% and 50% to 75% and 90% delayed the initiating time of water separation by not more than 16 min. But once the stirrer speed increases to 2000 rpm it can be seen from Fig. 12 that the effect of WC becomes very significant on t_w. (It may be noted that the Y-axis of Figs. 12–14 are in log-scale.)

Like the initiating time of water separation, at speeds >1000 rpm, the increase of WC from 50% to 75% severely impacted the initiating time of oil separation (t_o) as shown in Fig. 13. At speeds of around 1000 rpm, however, the initiating time of oil separation was slightly affected by the WC. But, once increasing the speed to more than 1000 rpm, it becomes very sensitive to WC. For example, when mixed at 2000 rpm, the difference between the t_o of 25% and 75% WC emulsions became at least one hour. The difference also continued to increase at 2000 rpm and 2500 rpm. Overall, one can conclude from Figs. 12 and 13 that the stability of oil-water emulsion is greatly impacted by the WC if emulsions are mixed at speeds >1000 rpm.

After 4 h of forming the 90% WC emulsion, however, the change in speed between 800 rpm and 1000 rpm shows no visible effects on the emulsion volume (E_V), as Fig. 14 shows. In other words, at 800 rpm and 1000 rpm mixing speeds, the volume of pure 90% WC O/W emulsion remains constant (≈ 25 ml) for 4 h. Even at 2000 rpm, the difference in E_V between the first and the last three hours of the separation is insignificant, as it only dropped from around 47 ml to 29 ml. However, with the further increase in mixing speed from 2000 rpm to 2500 rpm, a remarkable difference in E_V can be seen, as it (between the first and fourth hour) dropped from around 197 ml to only 25 ml. In the case of 75% WC, however, emulsion volumes dropped gradually with time regardless of mixing speed (see Fig. 15). For example, at 1500 rpm, volumes of the O/W emulsion between the first and third hour dropped from 20 ml to 12 ml. Likewise, with the increase of mixing speed from 1500 rpm to 2000 rpm, the drop in volumes of 75% WC emulsion was much more, from 68 ml to 33 ml.

The inversion of emulsion from O/W to W/O was quite surprising in terms of its response to variations in mixing speed. Not only because it was affected very little by mixing speeds as Figs. 9 and 10 show, but also because of the drastic drop in its stability as compared to O/W emulsion. Indeed, emulsions formed at 25% and 50% WC fully separated within a few minutes even though mixing speed reached 2500 rpm. Once the WC drops below 75% WC it is no longer several hours of separation. Instead, full separation time (t_f) takes place within a few seconds or minutes, regardless of speed, as shown in Fig. 16. Full separation time in this work represents the time when the entire emulsion layer vanishes (e.g., when E_V = 0), as shown in Fig. 4. In other words, it is the time required for the “water separation profile” and the “oil separation profile” to touch one another as pictured in Fig. 4. As compared to 50% WC, the variation in the full separation time of 25% WC, due to mixing speed, was less as it only changed between 50 and 229 s. However, both WCs were about the same at low speeds (i.e., 1000 rpm).

In the previous sections, experimental data were presented to show the effect of mixing speed on pure O/W and W/O emulsion. It was shown that the effect of mixing speed on O/W emulsion is significant, as the stability of pure O/W emulsion at 2000 rpm and 2500 rpm were several hours more than the stability of W/O emulsion. Having said that, it is the goal of this section to examine the effects of temperature on pure O/W emulsions. In addition to 25 °C, they were tested at 60 °C and 80 °C. The investigation of temperature will be carried out at 75% and 90% WC (each will be tested at two speeds: 2000 rpm and 2500 rpm).

At 75% WC, the increase in temperature showed some remarkable effects on both water and oil separation profiles (Figs. 17(b) and 18(b)). For example, at 60 °C and 80 °C, the rate of oil separation was greatly accelerated. However, the increase in temperature delayed the initiating time of water separation. In other words, temperature was found to facilitate the separation of more oil but delay water separation. As time of separation passed by, however, it accelerated the water separation rate also as shown in Figs. 17(b) and 18(b). Nonetheless, the effect is insignificant since full separation did not take place for several hours although there was no emulsifier introduced to either phase.

To further emphasize the effect of temperature on O/W emulsion, another water concentration was considered (WC = 90%). At this WC, the effect of temperature was also examined at 2500 and 2000 rpm as shown in Figs. 17(a) and 18(a), respectively. Like 75% WC, the increase in temperature delayed the initiating time of water separation of 90% WC emulsion. However, the delay was not significant as compared to 75% WC. Further, the rate of oil separation was barely impacted by temperature as compared to 75% WC emulsion. Overall, the change in temperature between 25 °C and 80 °C could not separate the whole volume of pure O/W emulsion, even though it accelerated the separation of oil.

The reason why temperature accelerated the separation kinetic of the dispersed (oil) phase is owing to the increased frequency of oil droplets collision, which improved the coalescence rate of oil droplets [27] and, hence, oil phase separation. However, another possible reason is the lowered density of the continuous (water) phase as this also affects the driving force of the thin, water film between oil droplets [26]. It is also evident that the 90% WC oil separation profiles (see Figs. 17(a) and 18(a)) were less impacted by the increased coalescence rate due to temperature, as lowering the volume fraction of the dispersed oil phase from 25% to 10%, increases the mobility of droplets, and hence, diminishes the contact time of droplets. However, it is still unclear what has contributed to the less water separation rates with temperature. The low interfacial tension with temperature could be a reason since temperature may improve the solubility of the two phases, and thus, high temperatures result in delays in the water separation due to lessened immiscibility. However, such discussions are beyond the scope of this work, and future work is recommended to study this behavior.

Even though the P-DCR facility is more accurate than other conventional methods, such as the bottle test, there is always some relative uncertainty in the data. The source of error in the facility used by this research could have been a result of inaccurate preparations of the initial liquid volume, small fluctuations in the mixing speed (±10 rpm), inaccurate control of mixing time (±5 s), improper scanning of emulsion videos, or inefficient cleaning of the batch separator between one experiment and another. All these factors can affect the reproducibility of the experiment. Therefore, to quantitatively measure the error in the oil and water separation profiles obtained by this study, a minimum of three trials were considered of three different initial conditions, as shown in Table 2.

where $Vmax$ and $Vmin$ are the maximum and minimum volumes of the freed liquid phase of each trial shown in Table 3, and $Vavg$ is the average of all trials. The average of all trials of experiments 1–3 and the change in $ε (%)$ is reported in Table 3 at different times following the formation of the emulsion. In addition, the separation profiles of all three experiments are shown in Fig. 19.

It is interesting to see the decrease in $ε (%)$ of all three experiments with time. The error of experiments 1, 2, and 3 (respectively) starts at 3.06, 8.05, and 1.85% and then decreases to 0.96, 3.69, and 0.90%. Therefore, based on observations seen in Fig. 19, the error could be higher at the beginning of the experiment but then decrease as the time of separation passes by. Overall, however, the results are reproducible (as shown in Fig. 19) and carry a small magnitude of errors that could be minimized by carefully preparing the initial volume of oil and water with an accurate vessel of at most ± 1 mm uncertainty. Also, it can be minimized by keeping accurate mixing time and speed. Most importantly, the scanning procedure of emulsion separation videos should be done properly through accurate calibration of the canty vision software to avoid overprediction/underprediction of free phase separation. In addition, efficient cleaning of the batch separator should be implemented properly before beginning any emulsion testing.

The main goal of this work was to examine the stability of pure (emulsifier-free) mineral oil-distilled emulsion due to variations in mixing speed, water volume concentration, and temperature. According to the results of this study, the stability of pure oil-in-water (O/W) emulsion is greatly affected by mixing speed. For example, by changing the initial speed between 600 rpm and 2500 rpm, the full separation time of 75% WC O/W emulsions increase from a few seconds to over 4 h. Unlike 75% WC, oil separation of 90% WC O/W emulsions did not occur for over 4 h even though mixing speed was lowered from 2500 rpm to 800 rpm. This is owing to the decreased probability of droplet-droplet collision at lower dispersed oil volume fractions. 25% and 50% WC W/O emulsions were not affected by variations of initial mixing speed and were fully separating in a few seconds due to the strong dipole-dipole interaction of water molecules during mixing, which hinders droplet breakup. The increase in temperature accelerated the oil separation rate due to increased kinetic energy of droplets and thin film drainage of the continuous (water) phase. However, it delayed the water separation rate and was overall ineffective in the separation due to a possibly reduced interfacial tension between oil and water.

The author is grateful to the Tulsa University Separation Technology Projects (TUSTP) consortium for their excellent research resources and assistance in conducting this experiment.

The authors attest that all data for this study are included in the paper.

V  =

volume (ml)

$Vmax$ =

maximum volume of separated liquid phase (ml)

$Vmin$ =

minimum volume of separated liquid phase (ml)

$Vavg$ =

average volume of separated liquid phase (ml)

$ε$ =

error (relative uncertainty) in measured liquid volume (%)

N =

initial mixing speed of oil-water emulsion (rpm)

$Vtw$ =

total volume of water (ml)

$Vto$ =

total volume of oil (ml)

E_o =

initial volume of emulsion (ml)

E_v =

oil-water emulsion volume at time t (ml)

T =

time, second; minute; hour

t_w =

Initiating time of water separation, minute

t_o =

initiating time of oil separation, minute

t_f =

time of full separation, second

T =

temperature (°C)

$ρo$ =

density of oil phase (kg/m³)

$ρw$ =

density of water phase (kg/m³)

μ =

viscosity (mPa·s)

σ =

average surface tension (mN/m)

$γ˙$ =

shear rate (1/s)

rpm =

revolutions per minute

WC =

water concentration (⁠$Vtw$ divided by E_o), %

W/O =

water-in-oil

O/W =

oil-in-water

P-DCR =

portable dispersion characterization rig