Intertwining roles of the disperse phase properties during

Subscriber access provided by UNIV OF DURHAM

Interface Components: Nanoparticles, Colloids, Emulsions, Surfactants, Proteins, Polymers

Intertwining roles of the disperse phase properties during emulsification Nelmary Roas-Escalona, Yhan Williams, Eliandreina Cruz-Barrios, and Jhoan Toro-Mendoza Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b00396 • Publication Date (Web): 14 May 2018 Downloaded from http://pubs.acs.org on May 14, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Intertwining roles of the disperse phase properties during emulsication Nelmary Roas-Escalona, Yhan O'Neil Williams, Eliandreina Cruz-Barrios, and

∗

Jhoan Toro-Mendoza

Centro de Estudios Interdisciplinarios de la Fisica, Instituto Venezolano de Investigaciones Cienticas. Caracas, Venezuela. E-mail: [email protected]

Abstract The combined eect of viscosity ratio, interfacial tension, and disperse phase density on the process of droplet formation during emulsication was evaluated. For that aim, emulsication by ultrasonication of oil/water systems with viscosity ratios between 1 and 600, with and without surfactant were performed. The time evolution of the average droplet size was estimated by dynamic light scattering measurements. For viscosity ratios between 1 and 200 in presence of surfactant, our results partly reproduce those of the intriguing U -type reported in the literature. Beyond that range, the droplet size decreases, as the viscosity ratio rises. For surfactant-free systems, the size is slightly aected by the increase in viscosity. This complex scenario is analyzed in terms of both the individual and intertwined roles of interfacial tension, viscosity, and density ratios: (1) if the interfacial tension dominates, the droplet rupturing process is independent on its internal properties, and, inversely, (2) if the interfacial tension is low, the internal properties play a major role in the rupturing of the droplet. Finally, we identied a scenario where the retarded addition of surfactant leads to emulsions with a stability similar to those with the surfactant added at the beginning, saving energy and time. 1

ACS Paragon Plus Environment

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Introduction and background

Emulsions are systems formed by droplets suspended into another liquid medium. Their presence in our daily life is abundant in food, personal care, industrial, and pharmaceutical applications to name but a few examples. The common preparation of emulsions requires energy to disperse one phase into another, i.e. the system cannot be formed spontaneously and, therefore, is thermodynamically unstable. The emulsication process is frequently described in terms of the energy needed to create area and, therefore, the work is made against interfacial tension γ . 14 To reduce that energy requirement and favor emulsication,

γ is lowered by the addition of an amphiphilic surface active agent or surfactant. 5,6 Other parameters of the system are viscosity and mass density even though the thermodynamic description makes no mention to them. It is expected that viscosity dissipates energy during the droplet formation process, thus limiting the droplet formation to larger sizes. 7 It is also plausible to set the adequate viscosity ratio χ = ηd /ηc (disperse and continuous phases) and interfacial tension values such that the tendency of one of these parameters toward larger droplet sizes is oset by the second parameter. Here, our rst interest is to examine experimentally the evolution of the average size of oil/water emulsion formation by ultrasonication from low to high viscosity ratios for oils of dierent densities, and interfacial tensions in presence and absence of surfactant. Most reports on emulsication kinetics study the process in a viscosity ratio between 1 and 100. We broaden the range of χ to 0.85 - 602. Second, the results are aimed to be analyzed in terms of a hydrodynamic description of the droplet formation process which accounts for the forming uids responses in both the bulk and interface. In other words, if the energy cost is paid in creating area and/or internal dissipation. Finally, from these results we will try to identify a set of parameter values where the emulsication process can be improved, thus saving time and energy. The eect of viscosity on the deformation and breakup of droplets in a simple shear eld was outlined by Karam and Bellinger. 8 They reported that the rupture of droplets occurs 2


Page 2 of 28

Page 3 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

for a range of χ of 0.005- 4. Gaikwad and Pandit 9 observed that the size of droplets is almost constant for viscosity ratios in a range of 1 to 55. Later, Nazarzadeh and Sajjadi 10 extended the range of the viscosity ratio to 1-100 and studied its eect on the mean droplet size and the capillary number. Their experimental results show a signicant reduction in the droplet size with increasing ηd till the midrange viscosities, followed by a sharp increase at the higher viscosities, nding an intriguing U -type curve of size vs. χ. The results of Nazarzadeh and Sajjadi 10 agreed with theoretical estimations based on a previous work of Bentley and Leal 11 on the capillary number in the midrange values of the viscosity ratio only. A qualitative agreement for the size curve was found in the extreme values of χ. The droplet rupturing mechanism appeared to depend on viscosity ratio: droplets underwent stretching at low viscosity, but erosion at high-viscosity ranges. It is widely accepted that a higher surfactant concentration results in a lower droplet diameter due to the reduction in the work done against interfacial energy. 12,13 In his seminal work, Taylor 14,15 discussed the behaviour of a uid droplet under shear ow, and studied the case where interfacial tension eects were dominant over viscous ones. Taylor showed that the droplet size in such systems could be approximated by D ∝ 2γ/3ηc τ , where τ is the shear rate. This expression indicates that droplet breakup occurs when the applied shear is greater than the Laplace pressure of the droplets. 16,17 Nonetheless, the classical theoretic description of emulsication by Taylor rarely ts with experimental results and some authors have mentioned other possible mechanisms to describe the emulsication process, and even predict the size of droplets during sonication by empirical correlations. 18 In the case of a turbulent regime, Hinze 19 predicts that the droplet size during emulsication is given by

D = C(γ/ρc )3/5 −2/5 ,

(1)

where C is a constant of proportionality, ρc is the continuous phase density and is the power density applied (power input per unit mass). In obtaining Eq. (1), Hinze nondimensionalized

3


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 28

the shear stress σ that creates droplets using the Weber number W e = σD/γ . He assumed that there is a critical Weber number W ecrit = C2 [1+f (Oh)] below which droplets cannot be further split apart, and that W ecrit should be corrected by a function of the Ohnesorge num√ ber Oh = ηd / ρd γD. This latter nondimensional number quanties if the inserted energy converts into internal viscous dissipation or into surface tension energy. Hinze considered the case Oh 1 in which case f (Oh) vanishes, leading to Eq.(1). Davies also obtained an expression for the minimum droplet size under turbulent regime. 20 That model includes the turbulent velocity uctuation but the internal phase density and the external viscosity are dismissed. Taking into account these approaches, Gupta et al. 21 recently proposed a modication to the equations obtained by Hinze to predict the size of nanoemulsion droplets in a viscous turbulent regime. This regime refers to the fact that the continuous medium is turbulent (homogenizers, ultrasonicators) but the size of the eddies are above or close to the size of the droplets, which leads to a viscous behaviour of the uid at the droplet surface. Hence, the average size of the droplets obeys, according to Gupta et al., 21 the following equation 1/3

D=C

γ 5/6 ηd . (ρd γ)1/5 (ηc ρc )5/12

(2)

Besides, Gupta et al. 21 veried experimentally the scaling laws of the size given by Eq.(2) for nanoemulsion systems for a wide range of Oh (0-70) and ηd from 3 to 97 cP. With the results here reported, we are able to test to what extent the model of Gupta et

al. could be applied since our range of viscosity ratio and Ohnesorge number is above the range they claim their ndings are valid.

4


Page 5 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Materials and methods

Materials The oil phase in our experiments was analytical grade (≥ 99%) of hexadecane, sh, castor, silicone, soybean and mineral (molecular biology grade) all of which were obtained from Sigma Aldrich. In addition, decane (analytical grade ≥ 95%) was purchased from Merck. Ionic surfactant in the form of sodium dodecyl sulphate (SDS)(≥ 99% Sigma-Aldrich) were used for sample stabilization after purication.

Interfacial tension measurement The interfacial tension for systems with surfactant were measured by the spinning drop method (GDT 110 M3 Model). The droplet of the least dense phase was subjected to rapid rotation while placed in a capillar tube(which contains the other phase). The centrifugal force induces an axial elongation of the droplet which opposes the capillary forces. The , interfacial tension was calculated using the following relation γ(dina/cm) = 5.22 × 105 d3 ∆ρ P2 where d is the droplet diameter (nm), ∆ρ is the density dierence of the two phases (g/cm3 ) and P is the rotation period (ms/rev ). The interfacial tension of surfactant free systems were taken from literature (see gure 1).

Ultrasonic bath conguration for emulsication A cell lled with an emulsion volume of 5 mL was submerged at an immersion depth of 5 mm in the ultrasound bath (see discussion on the use of ultrasound bath in the Results section). The temperature was monitored throughout the sonication period and was kept around 25◦ C by by adding cold water to the bath.

5


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Emulsion preparation Oil/water emulsion were prepared with and without surfactant using 5% w/v oil, 5% w/v SDS (critical micellar concentration 0.2 % w/v), and deionized water (0.075 µS/cm, η =

0.9 cP). The emulsication process was carried out by sonication, performed at a frequency of 40 KHz using a Branson Digital Sonicator bath (Model 08895-43 Cole Parmer) where the temperature was kept around 25◦ C.

Kinetics of emulsication The average droplet size as a function of sonication time was determined by dynamic light scattering (DLS) measurements using a Brookhaven BI-200M autocorrelator goniometer with a Ne-He laser at a xed angle of 90◦ and a 633 nm wavelength, for a total study of 6 h . The rst aliquot was taken after complete emulsication was visually observed. The next aliquots were taken every 5 min during the rst hour and every 30 min for the next ve hours. Both tendencies and values here reported were corroborated by, at least, three rounds of experiments. All samples were diluted and placed on the vortex for 15 sec to eliminate possible aggregates before performing DLS measurements. Besides, the polydispersity index in all cases was below 0.4 for surfactant-free systems and below 0.27 for surfactant enriched systems. The DLS measurements for the droplet size corresponded to an averaging of six runs which last at least 1 minute. Q test with a 90% condence interval was used to assess the signicance of the results obtained.

Emulsion stability measurements After complete emulsication, three types of systems were studied: (1) systems in absence of surfactant, (2) surfactant added before emulsication, and (3)surfactant added after a time where a minimum droplet size is achieved τmds in any of the conditions of surfactant presence. To quantify the stability of the prepared emulsions, turbidity measurements were

6


Page 6 of 28

Page 7 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

performed using a TurbiscanT M during a 24 h lapse. Its operation principle consists in measuring the backscattering and transmission intensities versus the sample height in order to detect particle size change (coalescence, occulation) and phase separation (sedimentation, creaming). In parallel, the stability of emulsion was assessed also by measuring the droplet size as a function of the storage time using DLS.

Results and Discussion

Kinetics of emulsication. Figure 1 shows the properties of the oils used and their classication according to their viscosity, density, and interfacial tension with and without SDS. In absence of SDS we can identify the following: (1) low viscosity oils (decane and hexadecane), which show high interfacial tension, (2) intermediate viscosity oils (mineral and soybean oil) with high interfacial tension, and (3) high viscosity oil (silicone, castor, and sh) with intermediate values of interfacial tension. All systems, however, show low interfacial tensions (below 5.5 mN/m) in presence of surfactant, except silicon oil (10.8 mN/m). It is also noticeable that the oils with larger density are silicon (1040 kg/m3 ) and castor (960 kg/m3 ). Figure 1 suggests that there will be dierent possible behaviours, depending on the complex interplay between η and γ , i.e. depending on whether the dominant mechanism is viscous or elastic. The evolution of the average droplet size during sonication of the systems studied are shown in Fig.2. The lower viscosity oils systems (decane and hexadecane) rapidly reach an almost constant droplet size throughout the sonication time (Figs. 2a and 2b). After 90 min of sonication a droplet size of 124±4 and 208±7 nm was measured for decane and hexadecane with surfactant, respectively. It was observed that the systems with surfactant have lower average sizes than those without surfactant, obtaining 288±6 nm for decane and 291±5 nm for hexadecane. When interfacial tension is low and the dispersed phase viscosity is similar to the continuous phase, the shear force required to overcome the interfacial energy is lower 7


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 1: Interfacial tension and viscosity of the dierent oils used in this work. Numbers in parenthesis are the density of each oil in kg/m3 . 2226 and, therefore, a larger number of small droplets are formed. Systems composed of mineral oil (not shown in Fig. 2 for simplicity) and soybean oil (see Fig. 2c) present similar average droplet sizes when the system contains surfactant compared to decane and hexadecane systems. After 90 min of sonication, droplets of 154 ± 9 and

133 ± 7 nm were obtained for mineral and soybean oil with SDS, respectively, while for the systems without surfactant we report values of 340 ± 33 and 424 ± 109 nm, respectively. Figures 2d, 2e and 2f show the droplet size evolution of the more viscous oils. In principle, droplet formation of the more viscous oils is more taxing since the energy supplied by sonication is dissipated in the process of droplet breakup. Intriguingly, for silicone and castor oils, we see that the case with surfactants results in larger droplet sizes than without, suggesting that it have to be understood in terms beyond the eect of γ only-to be discussed soon. For the castor oil with SDS, we have the unusual increasing trend. However, according to the error bars the rst and last points are comparable, and the data dispersion indicated oscillation about a mean droplet size. 8


Page 8 of 28

Page 9 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 2: Process of emulsication by ultrasonication for systems with and without surfactant. Oils with increasing viscosity are displayed from (a) to ((f). All systems show a lower value of droplet size in presence of surfactant compared to SDS-free emulsions, except silicone (d) and castor (e) oil (grey background). Continuous lines are ttings of a power law model. The frequency of sonication was 40 KHz in all cases.

9


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

It is also noticeable that both uctuations and even some increase in the size of the droplets are mainly due to recombination (coalescence) and possible strong aggregation of droplets. The concentration of SDS above the CMC could aect the stability of the formed emulsions because of depletion interactions. However, during sonication, the eect of ultrasound waves should force the non adsorbed surfactant molecules to be homogeneously dispersed in the medium. The size of the eddies ( Kolmogorov length) formed during cavitation are around 300 nm 21 which is far above the size of the possible formed micelles thus generating a ow eld which prevents the accumulation of surfactant. Therefore, at the emulsication stage, it is expected that the eect of depletion to be negligible.

Figure 3: Π = γ/D values for systems (a) without and (b) with surfactant. The exponential index of a power law tting is shown. See text for details. We quantify the amount of energy which is converted into surface energy during the emulsication kinetics observed in (Fig. 2) by plotting γ/D vs. sonication time in Fig. 3. The quantity γ/D is proportional to Laplace pressure. Each curve is t to a power-law as 10


Page 10 of 28

Page 11 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

γ/D ∼ tbs , with the exponent b labeling each curve on the right side. The index b represents, as usual, how rapidly a plateau is reached. The idea is based on the fact that each droplet has surface energy γπD2 , and the number of droplets N of size D depends on the total volume of oil V . Thus the total energy required to form an emulsion is N γπD2 = 6V γ/D. Assuming a constant shear rate and no energy loss during sonication, it would be expected that 6V γ/D = Cts where C is the energy input rate, up to the maximum value. A recent report by Li et al. 27 shows that the droplet size decreases with the ultrasound radiation exhibiting two regions which follow a power-law dependence scaling with the power input as D ∼ P −1.4 τ −1.1 and D ∼ (P τ )−0.6 for fast and steady state transition regions, respectively. These power laws were tted by empirical relations which are independent of the physicochemical parameters of the system. Presumably, the scaling laws found by Li et

al. will deviate in systems with parameter ratios dierent to 1, as those reported here and represented in Fig. 2. Nevertheless, the regions identied by them are in agreement with the ones of gure 3. In Fig. 3a we observe that the systems with higher viscosity present the largest exponential index (0.28 − 0.61), and their respective curves are lower than the systems with smaller viscosity. The oils with higher interfacial tension employ most of the energy into making surface area, therefore the highest pressure corresponds to hexadecane oil and this value diminishes in descendent order of interfacial tension. In Fig. 3b the pressure drops in one order of magnitude in comparison with the systems without surfactant as expected. Contrary to the systems without surfactant the exponential index of systems enriched with surfactant are all in a similar range (0.22 − 0.30) except castor oil. This latter case can be understood in terms of the high coalescence occurrence observed in Fig. 2e. Contrary to Fig. 3a, the behaviour is not only dependent on interfacial tension but rather combined with viscosity. For example, the interfacial tension for silicone oil with surfactant is greater than other oils. As a consequence, one would expect that the high Laplace pressure corresponds to silicone but we noted that it is not fullled, in short, the ultrasonication energy is not fully 11


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

converted into surface energy. The same behaviour is observed for castor oil. Remarkably, the curves of decane, soybean, silicone, and castor oils show a particular uctuations in the surface pressure, which can be likely due to the recombination droplet process observed in their respective kinetics curves (see Figs. 2a, 2c, 2d, and 2e).

Hydrodynamic conditions, droplets formation, and surface and viscous energy considerations The results up to this point have suggested that emulsication with surfactant is more ecient in the low viscosity oil systems, i.e. the eect of η is insucient to be considered as the dominant factor of the emulsication process. However , there are also cases in which a far more complex scenario is expected .i.e. More than one disperse phase property is responsible for the behavior observed during the emulsication process. To account for the suggested interplay between the forces responsible for the emulsication of the oils studied √ , we use the Ohnesorge number (Oh = ηd / ρd γD). D is the droplet diameter taken as an average of the droplet size once an almost constant value was achieved. 9 Figure 4 summarizes some characteristics of the obtained emulsions and the associated Oh. High viscosity oils show high Oh values with an appreciable dierence for the systems in absence (Fig. 4a) and in presence of surfactant (Fig. 4b). In the case of small Oh( 1) less energy is converted into viscous dissipation. In principle, it means that most of the inserted energy converts into surface tension energy, i.e. a droplet can be easily formed. Oh >> 1 indicate that the internal viscous dissipation is more signicant, meaning that most of the inserted energy converts into internal viscous dissipation, i.e, droplet formation is dicult. 28 In order to determine if our results follow scaling laws, we use the denition of the critical √ Weber number as W ecrit = ρc ηc D/γ based on the nal droplet diameter. Figure 4 plots

W ecrit vs. Oh with a power law tting as proposed by Gupta et al. 21 Although the only parameter varied is γ , two distinct power law ts are found since the presence of surfactant allows the formation of stable droplets. The power law relation obtained for systems without 12


Page 12 of 28

Page 13 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

SDS was W ecrit ∼ 0.065Oh0.15 , while for systems with SDS we nd W ecrit ∼ 0.3Oh0.25 . In this sense, the stronger dependence on the Ohnesorge number for systems with surfactant gives evidence that the viscous dissipation dominates the droplet breakup process, suggesting that erosion instead of elongation takes place, being more pronounced as viscosity increases. Now, for low ηd /ηc the elongation mechanism should lead the process. Moreover, a mixed droplet breakup mechanism would be found when the energy requirement for droplet breakup is split up into viscous dissipation and work done against interfacial tension, as can be seen in Fig. 4b for mineral and soybean oils whose viscosity and interfacial tension values (see Fig. 1) describes this scenario. For all these considerations, Gupta et al. proposed a lament model leading to equation 2, suited to describe the aforementioned viscous behavior of the uid at the droplet surface. It is also important to consider that the eciency of the ultrasonic bath is below the found in experiments with ultrasonic probe. 2931 In the latter case, the time needed to achieve the smaller droplet size is about 20 min. and the reproducibility of the results is high. Another important aspect to consider is that the volume fraction of O/W is 5% which is much higher than most experimental reports, aecting thus the power-law behavior of the kinetics curves. Moreover, in our case, 200 min of sonication are needed to reach the designated minimum size in most cases. It also limits the proper statistics to determine a more precise value of the exponent, because more time-consuming experiments are needed. However, the mixed eects of interfacial tension and viscosity exhibited in Fig. 2 suggest that the value of the exponent of the scaling law should deviate from the value predicted by Gupta et al. of 0.4 for very high Oh. Besides, the high concentration of surfactant can also modify the viscoelastic properties of the medium. That could be responsible for the even larger deviation of the pre-exponential factor of the systems with surfactant compared to the absence of it Figure 5 shows the observed droplet size as a function of the viscosity ratio χ. As can be seen, droplet sizes for surfactant-free systems increase from the low viscosity oil region to that of intermediate value (mineral oil) after which the trend reverses. For the surfactant13


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 4: Relation between the critical Weber number and the Ohnesorge number, and also a representative power law t for systems: (a) without surfactant and (b) with surfactant.

14


Page 14 of 28

Page 15 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

rich systems, the droplet diameter is nearly constant for χ ≤ 24, but then sharply increases at χ ≈ 200 (Fig. 5) followed by a decrease in D with a further increase of χ. Here, we partly reproduced the intriguing behaviour reported in ref. 10 in the range of viscosity ratio 1 − 100, and we also found that the behaviour of systems with a viscosity ratio above 100 is even more complex, since the tendency to increase droplet size is not innite. If the latter was the case, the emulsication of high viscosity oils would be impossible. In fact, if we interpolate an approximate value for D from our experimental tendency, a value of ∼ 300 nm similar to that observed by Nazarzadeh and Sajjadi is found at χ = 100. Although our maximum droplet size corresponds to silicon oil, the size of castor oil droplets is also much greater than those of the observed for lower χ (Fig. 5), which indicates that it is possible to obtain similar peaks using other viscous oils. In this sense, the peak exhibited by silicon oil is precisely due to high values in γ , ρ, and η . Meanwhile, the density of castor oil is the responsible for its size. We notice that the reduction in interfacial tension in the silicone oil system with SDS is insucient to overcome the eect of the high dispersed phase viscosity since a value of 10.8 mN/m can be considered intermediate. On the contrary, although sh oil systems are the most viscous dispersed phase studied, when the surfactant is added the interfacial tension drops to 1 mN/m, a value lower than the value obtained in decane systems. Hence, in this case, interfacial tension appears to outweigh the eects due to the high disperse phase viscosity. It is worthy to mention that it has been reported the occurrence of depletion occulation in Silicon oil/W system in presence of SDS after emulsication 32 (see next section). In our case, the average size was measured during the emulsication process. The procedure followed here of diluting the sample and put it on the vortex for 15 seconds is intended to separate possible aggregates. In fact, some size measurements were performed with and without vortex agitation, nding that those agitated were lower and stable during the time measurements compared to those without agitation being an indicative of weak aggregation. Besides, the polydispersity observed in presence of surfactant is lower than in absence of it 15


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(0.20 to 0.32, respectively). As known, the use of DLS technique makes dicult to dierentiate droplets from aggregates and even the appearance of monodal distributions suggest, at least, a family of single droplets with a denite size. In order to test the real existence of the peak observed in Fig. 5, two similar experiments were performed using a lower amount of oil (1%) and 5% of SDS and 1% of oil and 1% of SDS, nding a nal average size around 600nm for sonication times larger than 450min. One can speculate that if the droplet size curve of Fig. 5 is extended to χ > 600 a non monotonous behaviour should be found. For example, crude oil emulsions can be formed with droplet sizes in the order of microns, 33 which indeed suggests that eventually there is, at least, another peak in which the droplet size increases. Interestingly, the experimental results shown in Fig. 5 which correspond to several oils of dierent nature with no correlation in their values of interfacial tension and density are described by the theoretical predictions mentioned. We would like to emphasize this point because if Eq.(1) or (2) are plotted varying one of the parameters χ, ρd or γ leaving the rest constant, a monotonous variation is observed. As Nazarzadeh et al. 10 reported, the tting of the theoretical results of Bentley and Leal requires the use of dierent tting values for each point, which introduces some misinterpretation of the results. Moreover, Nazarzadeh used a mixture of oils to vary viscosity leading to monotonous changes in both density and interfacial tension. Our proposal of a non monotonous curve of droplet size with χ would correspond to a scenario where ρd and

γ vary in a non-monotonous way as χ increases. In Fig. 5 we also compare our data to the scaling relations of Hinze (Eq.(1), ref. 19 ) and Gupta et al. (Eq.(2), ref. 21 ). Equation (1) only accounts for the eect of surface tension, outer phase density, and power density applied. Therefore, the new droplets are formed by scission mechanisms due to the fact that high interfacial tension acts as a "rigid" boundary where elongations are unlikely to occur. As seen, the size of the droplets is slightly dependent on the oil viscosity and density, which suggest that mechanisms of rupture only depends on the energy input and its eciency of creating new droplets. On the contrary, in the presence 16


Page 16 of 28

Page 17 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

of surfactant, the lowering of the interfacial tension diminishes the local dierences between the two liquids. It means that the internal properties of the droplets play a major role since the work to create a new droplet is made against the viscous friction, surface deformation, and the inertial eects represented by the oil density. For this case, Eq. (2) adequately reproduces the experimental data. However, the Gupta et al. approach fails in predicting the size for the surfactant-free systems. Hinze and Gupta's approaches do not consider any possible viscoelastic response of the interface, although previous works consider the eect of the frequency response of the droplets accounting for the surfactant diusion to the interface. 34,35 Unfortunately, it is not straightforward to determine the actual oscillation of the droplet surface, because part of the power input is dissipated in the medium by heating and/or viscous response. Furthermore, not all cavitation processes result in an eective rupture of droplets. Taking these considerations into account, we will assume that the droplets suer low-frequency oscillations, leading to a constant interfacial tension.

Emulsion stability:

comparison with retarded surfactant

addition.

From our observations of the emulsication kinetics plotted in Fig. 2, we identied cases in which smaller droplets sizes are reached more quickly without surfactant (castor and silicone). For that reason, our interest now lies in evaluating retarded surfactant incorporation and its eects on the emulsion stability. In this regard, we evaluate the possible destabilization mechanisms responsible for the droplet size evolution kinetics shown in Figure 6a,b,c. Each system selected was evaluated with surfactant, without surfactant, and surfactant added at the moment when an almost steady state in droplet size is achieved τmds .(see Fig. 2). We assessed three systems: decane, silicone, and sh oils, over 24 hrs using DLS to measure droplet size, and the stability of each prole was determined through turbidity 17


Langmuir

Hinze

D (nm)

1500

Gupta et al.

Experiments

(a)

f

1000

500

0

750

(b)

500

f

D (nm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 28

250

0 1

10

100

Viscosity ratio (

1000

)

Figure 5: Experimental results compared with theoretic predictions. 10,19,21 Relation between minimum droplet diameter and viscosity ratio (χ). The tting values used are C=0.35 (Hinze), C=0.008 (Gupta), and = 3.8 × 108 W/kg. 21

18


Page 19 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 6: Average radius R of droplets in a 24 h lapse: (a) Decane systems, (b) Silicon systems, (c) Fish systems. Emulsions with surfactant added from the beginning of the emulsication (open circles), with surfactant added at 180 min of sonication (open triangle) and oil/water emulsion without surfactant (open square). Backscattering proles in a 24 h lapse are at the bottom plots. (d) Decane systems, (e) Silicone systems, and (f) Fish systems. measurements. These oils were selected to examine emulsion stability in dierent illustrative cases of interfacial tension, viscosity, and density identied in gure 1. The droplet size evolution of decane over 24 hrs exhibits two clear tendencies (gure 6a). On one hand, both surfactant enriched systems present a slower growth rate than the decane system free of surfactant. Interestingly, the addition of surfactant after an initial emulsication period of 80 minutes generates little change in the droplet growth rate as both curves overlap. On the other hand, the delta backscattering (BS) prole (gure 6d) shows an initial increase for the surfactant enriched systems before 3hrs which is a signature of creaming. Backscattering for these systems gradually reduces to 10% after 24 hrs indicative of droplet aggregation. Furthermore, this behavior is in agreement with the approximate linear droplet growth observed in gure 6a. It is possible that both Ostwald ripening and 19


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

coalescence to proceed in surfactant-free oil in water emulsions. In fact, evidence of a linear growth between the cube of the droplet radius and time is a manifestation of Ostwald ripening. 3638 Notwithstanding the fact, Urbina-Villalba et al. 39 demonstrated that it is also possible to obtain a linear relation of R3 vs time due to occulation and coalescence, and not necessarily as a consequence of Ostwald ripening. We suggest that the behavior observed is due to Ostwald ripening as implied by Sakai et al. 40 They suggested the dominance of Ostwald ripening in the growth processes of droplets in oil/water emulsions with long chain hydrocarbons (C10-C16) rather than coalescence, but argued the dominance of coalescence in the growth processes of droplets in oil/water emulsions with short chain hydrocarbons (C6-C8). They concluded that this behavior was due to the fact that oils with a higher vapor pressure are considered to have a higher rate of molecular diusion because of the weaker interaction between their molecules. The mean droplet size evolution of silicone oil systems over the 24 hrs is presented in gure 6b. Interestingly, an almost invariant droplet diameter is maintained for the measurement period indicating that neither Ostwald ripening nor droplet coalescence plays an active role in the destabilization process. In fact, Bibette et al. 41 used emulsions comprised of initially monodisperse silicone oil droplets, enabling them to monitor the progress of coalescence quite precisely. Moreover, silicone oil was chosen owing to its extremely low diusivity in water, through which they discarded the occurrence of Ostwald ripening. The stability of silicone oil systems is attributed to the high density of surface-ionized hydroxyl groups. 42 Although the delta BS prole gives evidence that droplet aggregation is present along with droplet sedimentation in the 24 hrs, the observed aggregation is reversible, since after simple agitation the droplet size is restored. In addition, the proles illustrate that the system with surfactant added at 165 minutes of sonication was the most stable of the three systems. Initially, both surfactant enriched systems reduce their delta backscattering and values of 5-10% are estimated for the surfactant systems added after 165 min of sonication and from the onset, respectively. The prole indicates that sedimentation is probably the dominant 20


Page 20 of 28

Page 21 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

phase separation mechanism. In this case, the retarded incorporation of surfactant reduces not only the sonication time necessary for achieving a minimum desired size but moreover, there is a guarantee of emulsion stability. Figure 6c shows the average droplet size evolution of sh oil systems. We observe that the enriched surfactant systems of sh oil present almost no droplet growth over the 24 hrs. It is also noticeable that both the droplet sizes and droplet growth rate for these surfactant enriched systems are similar, making it is dicult to determine which system is more ecient. Thus, we consider that they possess comparable stability. In Fig. 6c, the surfactant-free system presents some droplet size uctuation but not to a great extent, indeed most droplet sizes are between 600-670 nm range. According to the backscattering prole for the sh oil systems (gure 6f), we detect creaming for the surfactant-free system and for the enriched surfactant system added after 180 min of sonication. No creaming was detected for the surfactant enriched system added from the onset of sonication as its delta backscattering remained xed at the reference value of 0%. In short, we propose that high viscosity and intermediate interfacial tension systems can be pre-emulsied without surfactant and at an adequate time at which the droplet size is minimum, the surfactant can be incorporated in order to guarantee the stability of the emulsion. Needless to say, the widely known complexity of formulation circumvents a general criterion for optimization and our proposition applies to, perhaps, some specic physicochemical conditions.

Conclusions

We summarize the main conclusions of this work as follows: The nal average droplet size in presence of SDS partly reproduce a U -type curve reported in the literature, exhibiting a peak at χ =200. After that value, a decrease in size is observed. Despite the complexity of these results, the recently proposed 21


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

model by Gupta et al. 21 adequately predicts the obtained sizes. The shape of the curve is likely due to the importance of surface tension as well as the viscosity ratio, so it is plausible that the behavior at even larger viscosity ratios could continue to be non-monotonic. Certainly, this assertion requires experimental verication. In absence of surfactant, the nal mean droplet size is slightly aected by the increase in viscosity. This behaviour is properly predicted by the theory developed by Hinze. 19 In that approach, the work made against the interfacial tension is the only mechanism responsible for droplet breakup. However, high values of γ indicate that large surface deformations are unlikely to occur. The previous results suggest that the lower the interfacial tension the more important the role of viscosity and density of the droplet. In other words, for high interfacial tension systems, most of the energy is paid on creating area. Therefore, the role of the internal dissipative mechanisms is not expressed. Hence, Hinze's theoretical description ts well with these results. On the contrary, for low interfacial tension systems, the energy for droplet breakup is made against the internal mechanisms determined by viscosity and density. In this sense Gupta's description, which takes into account the internal droplet properties, is adequate. For that reason , for low viscosity and low interfacial tension the results are qualitatively well predicted by both theories since the two mechanisms are comparable. The dependence of the critical Weber number on the Ohnesorge number is that of a power law. The exponent is lower than 0.4, predicted by Gupta et al. This deviation is probably due to the lower eciency of the ultrasonication process instead of the larger Ohnesorge number here reported. Our results convey a means to identify an adequate pre-emulsication protocol based on the physicochemical properties of oils: for systems with high oil viscosity and density, and intermediate interfacial tension pre-emulsication without surfactant is rec22


Page 22 of 28

Page 23 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

ommended. Then, at an optimum time at which the droplet size is minimum, the surfactant should be incorporated to guarantee the stability of the emulsion, reducing energy cost and time.

Acknowledgments

Thanks are given to Prof. Eric R. Weeks (Emory University) for fruitful discussions, suggestions, and criticisms. Thanks are also given to anonymous reviewer for suggesting experiments to give more support to our ndings and open new perspectives on the problem of mixed droplet breakup mechanisms. JT-M thanks to Juan C. Granadillos for his help in the preparation of the gures. This research was partly supported by IVIC Grant 1013.

References

(1) Urbina-Villalba, G.; Toro-Mendoza, J.; García-Sucre, M. Calculation of Flocculation and Coalescence Rates for Concentrated Dispersions Using Emulsion Stability Simulations. Langmuir 2005, 21, 17191728. (2) López-Montilla, J. C.; Herrera-Morales, P. E.; Pandey, S.; Shah, D. O. Spontaneous Emulsication: Mechanisms, Physicochemical Aspects, Modeling, and Applications. J.

Dispersion Sci. Technol. 2002, 23, 219268. (3) Israelachvili, J. The Science and Applications of Emulsions: An Overview. Colloids

Surf., A 1995, 4, 18. (4) Calabrese, R. V.; Chang, T.; Dang, P. Drop Breakup in Turbulent Stirred - Tank Contactors. Part I: Eect of Dispersed-Phase Viscosity. AIChE J. 1986, 32, 657666. (5) Delmas, T.; Piraux, H.; Coun, A.-C.; Texier, I.; Vinet, F.; Poulin, P.; Cates, M. E.;

23


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Bibette, J. How to Prepare and Stabilize Very Small Nanoemulsions. Langmuir 2011,

27, 16831692. (6) Naskar, M. K.; Patra, A.; Chatterjee, M. Understanding the Role of Surfactants on the Preparation of ZnS Nanocrystals. J. Colloid Interface Sci. 2006, 297, 271275. (7) Gupta, A.; Narsimhan, V.; Hatton, T. A.; Doyle, P. S. Kinetics of the Change in Droplet Size During Nanoemulsion Formation. Langmuir 2016, 32, 1155111559. (8) Karam, H. J.; Bellinger, J. C. Deformation and Breakup of Liquid Droplets in a Simple Shear Field. Ind. Eng. Chem. Fundam. 1968, 7, 576581. (9) Gaikwad, S. G.; Pandit, A. B. Ultrasound Emulsication: Eect of Ultrasonic and Physicochemical Properties on Dispersed Phase Volume and Droplet Size. Ultrason.

Sonochem. 2008, 15, 554563. (10) Nazarzadeh, E.; Sajjadi, S. Viscosity Eects in Miniemulsication via Ultrasound.

AIChE J. 2010, 56, 27512755. (11) Bentley, B.; Leal, L. An Experimental Investigation of Drop Deformation and Breakup in Steady, Two-Dimensional Linear Flows. J. Fluid Mech. 1986, 167, 241283. (12) McClements, D. J. Food Emulsions: Principles, Practices, and Techniques ; CRC press, 2015. (13) Tadros, T.; Izquierdo, P.; Esquena, J.; Solans, C. Formation and Stability of NanoEmulsions. Adv. Colloid Interface Sci. 2004, 108-109, 303318. (14) Taylor, G. I. The Formation of Emulsions in Denable Fields of Flow. Proc. R. Soc.

London, Ser. A 1934, 146, 501523. (15) Taylor, G. I. The Viscosity of a Fluid Containing Small Drops of Another Fluid. Proc.

R. Soc. London, Ser. A 1932, 138, 4148. 24


Page 24 of 28

Page 25 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

(16) Meleson, K.; Graves, S.; Mason, T. G. Formation of Concentrated Nanoemulsions by Extreme Shear. Soft Mater 2004, 2, 109123. (17) Mason, T. G.; Wilking, J. N.; Meleson, K.; Chang, C. B.; Graves, S. M. Nanoemulsions: Formation, Structure, and Physical Properties. J. Phys.: Condens. Matter 2006, 18, R635R666. (18) Torza, S.; Cox, R. G.; Mason, S. G. Particle Motions in Sheared Suspensions XXVII. Transient and Steady Deformation and Burst of Liquid Drops. J. Colloid Interface Sci.

1972, 38, 395411. (19) Hinze, J. O. Fundamentals of the Hydrodynamic Mechanism of Splitting in Dispersion Processes. AIChE J. 1955, 1, 289295. (20) Davies, J. Drop Sizes of Emulsions Related to Turbulent Energy Dissipation Rates.

Chem. Eng. Sci. 1985, 40, 839842. (21) Gupta, A.; Eral, H. B.; Hatton, T. A.; Doyle, P. Controlling and Predicting Droplet Size of Nanoemulsions: Scaling Relations with Experimental Validation. Soft Matter

2016, 12, 14521458. (22) Than, P.; Preziosi, L.; Josephl, D. D.; Arney, M. Measurement of Interfacial Tension Between Immiscible Liquids with the Spinning Rod Tensiometer. J. Colloid Interface

Sci. 1988, 124, 552559. (23) Goebel, A.; Lunkenheimer, K. Interfacial Tension of the Water/n-Alkane Interface.

Langmuir 1997, 13, 369372. (24) Dijke, K.-v.; Kobayashi, I.; Schroën, K.; Uemura, K.; Nakajima, M.; Boom, R. Effect of Viscosities of Dispersed and Continuous Phases in Microchannel Oil-in-Water Emulsication. Microuid. Nanouid. 2009, 9, 7785.

25


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(25) Neelamegam, P.; Krishnaraj, S. Estimation of Dynamic Viscosities of Vegetable Oils Using Articial Neural Networks. Indian J. Chem. Technol. 2011, 18, 463468. (26) White, G. F. A Study of the Viscosity of Fish Oils. J. Ind. Eng. Chem. 1912, 4, 106 110. (27) Li, W.; Leong, T. S. H.; Ashokkumar, M.; Martin, G. J. O. A Study of the Eectiveness and Energy Eciency of Ultrasonic Emulsication. Phys. Chem. Chem. Phys. 2018,

20, 8696. (28) Li, D. Encyclopedia of Microuidics and Nanouidics ; Springer, 2013; Vol. 53; p 1513. (29) McClements, D. J.; Jafari, S. M. Improving Emulsion Formation, Stability and Performance Using Mixed Emulsiers: A Review. Adv. Colloid Interface Sci. 2017, (30) Mahdi Jafari, S.; He, Y.; Bhandari, B. Optimization of Nano-Emulsions Production by Microuidization. Eur. Food Res. Technol. 2007, 225, 733741. (31) Mahdi Jafari, S.; He, Y.; Bhandari, B. Nano-emulsion Production by Sonication and Microuidization - A Comparison. Int. J. Food Properties 2006, 9, 475485. (32) Bibette, J.; Roux, D.; Nallet, F. Depletion interactions and uid-solid equilibrium in emulsions. Phys. Rev. Lett. 1990, 65, 24702473. (33) Schramm, L. L. Surfactants: Fundamentals and Applications in the Petroleum Industry ; Cambridge University Press, 2000. (34) Alexandrov, N.; Marinova, K. G.; Danov, K. D.; Ivanov, I. B. Surface Dilatational Rheology Measurements for Oil/Water Systems with Viscous Oils. J. Colloid Interface

Sci. 2009, 339, 545550. (35) Langevin, D. Inuence of Interfacial Rheology on Foam and Emulsion Properties. Adv.

Colloid Interface Sci. 2000, 88, 209222. 26


Page 26 of 28

Page 27 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

(36) Lifshitz, I. M.; Slyozov, V. V. The Kinetics of Precipitation from Supersaturated Solid Solutions. J. Phys. Chem. Solids 1961, 19, 3550. (37) Taylor, P. Ostwald Ripening in Emulsions. Colloids Surf., A 1995, 99, 175185. (38) Wooster, T. J.; Golding, M.; Sanguansri, P. Impact of Oil Type on Nanoemulsion Formation and Ostwald Ripening Stability. Langmuir 2008, 24, 1275812765. (39) Urbina-Villalba, G.; Forgiarini, A.; Rahn, K.; Lozsan, A. Inuence of Flocculation and Coalescence on the Evolution of the Average Radius of an O/W Emulsion. Is a Linear Slope of R3 vs. t an Unmistakable Signature of Ostwald Ripening? Phys. Chem. Chem.

Phys. 2009, 11, 1118411195. (40) Sakai, T.; Kamogawa, K.; Nishiyama, K.; Sakai, H.; Abe, M. Molecular Diusion of Oil / Water Emulsions in Surfactant-Free Conditions. Langmuir 2002, 132, 19851990. (41) Bibette, J.; Roux, D.; Nallet, F. Depletion Interactions and Fluid-Solid Equilibrium in Emulsions. Phys. Rev. Lett. 1990, 65, 24702475. (42) Obey, T. M.; Vincent, B. Novel Monodisperse Silicone Oil/Water Emulsions. J. Colloid

Interface Sci. 1994, 163, 454463.

27


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

85x47mm (296 x 296 DPI)


Page 28 of 28

Intertwining roles of the disperse phase properties during

Recommend Documents