Rheological behavior of high internal phase water-in-oil emulsions: Effects of droplet size, phase mass fractions, salt concentration and aging

Accepted Manuscript Rheological behavior of high internal phase water-in-oil emulsions: Effects of droplet size, phase mass fractions, salt concentration and aging Sumit Tripathi, Amitabh Bhattacharya, Ramesh Singh, Rico F. Tabor PII: DOI: Reference:

S0009-2509(17)30570-5 http://dx.doi.org/10.1016/j.ces.2017.09.016 CES 13793

To appear in:

Chemical Engineering Science

Received Date: Revised Date: Accepted Date:

20 May 2017 1 September 2017 8 September 2017

Please cite this article as: S. Tripathi, A. Bhattacharya, R. Singh, R.F. Tabor, Rheological behavior of high internal phase water-in-oil emulsions: Effects of droplet size, phase mass fractions, salt concentration and aging, Chemical Engineering Science (2017), doi: http://dx.doi.org/10.1016/j.ces.2017.09.016

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Rheological behavior of high internal phase water-in-oil emulsions: Effects of droplet size, phase mass fractions, salt concentration and aging Sumit Tripathia , Amitabh Bhattacharyab , Ramesh Singhb , Rico F. Taborc,∗ a IITB-Monash

Research Academy, Mumbai-400076, India Engineering Department, IIT Bombay, Mumbai-400076, India c School of Chemistry, Monash University, Clayton 3800, Australia

b Mechanical

Abstract The rheological properties of high internal phase emulsions (HIPEs), comprising polydisperse aqueous droplets in oil, have been characterized as a function of emulsification time, salt concentration, phase mass fractions and aging. The droplet size distribution and structural details of the emulsion samples were obtained using cryogenic-scanning electron microscopy (cryo-SEM) and optical microscopy. For rheological characterisation, amplitude sweep tests performed on HIPE samples with a high mass fraction of dispersed phase (93.5 wt%) show that the strain behavior, especially the yield strain (εy ) and crossover strain (εc ), are almost independent of the droplet size and polydispersity. However, emulsions with smaller droplets have higher yield stress (τy ) and storage moduli (G0 ) values; explanations for these observations, based on the physical properties of the systems are suggested. Furthermore, it is observed that, for constant mass fractions of oil and aqueous phases, the strain behavior is also independent of the salt concentration in the dispersed phase. Our findings indicate that, independently of the salt concentration, the energy requirement for the emulsion to start flowing is greater when smaller droplets are present. Aging studies, performed over a period of 6 months, show no significant change in the ∗ Corresponding

author, T: +61 3 9905 4558 Email addresses: [email protected] (Sumit Tripathi), [email protected] (Amitabh Bhattacharya), [email protected] (Ramesh Singh), [email protected] (Rico F. Tabor)

Preprint submitted to Chemical Engineering Science

September 9, 2017

rheological properties of the HIPEs. Experimental rheology data is compared to the Princen and Kiss model, and with modified Mougel model (Ind. Eng. Chem. Res. 2011, 50, 10359–10365), giving insight into the critical effects of non-ideality induced by polydispersity in thickened emulsions. Keywords: High internal phase emulsion, Rheology, Viscoelastic, Dynamic mechanical analysis, Polydispersity

1. Introduction Emulsions that have a dispersed (internal) phase volume fraction (φdv ) above the critical volume fraction for closely packed spheres (φcr ) are defined as ‘high internal phase emulsions’ (HIPEs). In these materials, φdv can be as high as 965

99% [1–3], significantly changing their yielding and flow properties when compared to conventional emulsions. The critical volume fraction (φcr ) of closely packed monodisperse spherical droplets of dispersed phase in an emulsion is 74%, assuming hexagonal close packing, and is slightly higher for the case of polydisperse spherical droplets that can pack more efficiently in a given volume

10

[1–6]. High internal phase emulsions (HIPEs) are typical viscoelastic fluids, displaying a yield transition and complex rheology. The dispersed phase droplets of HIPEs are deformed by the proximity of their neighboring droplets, and assume a polyhedral shape, with a narrow layer of continuous phase separating them [1, 5]. HIPEs are widely used in cosmetics, food industry, liquid explo-

15

sives, petroleum, paints, pharmaceuticals, and leatherworking [7, 8], where the presence of two immiscible phases is essential. The rheology of these materials is central to their preparation, handling and use, and depends on the method of formulation, the measuring system used, temperature, and other parameters. The rheological properties of HIPEs are primarily sensitive to the type of emul-

20

sifiers [1], droplet size distribution [9–11], relative proportions of internal and external phases [12, 13] and aging [14, 15].

One particularly exciting and commercially relevant application of HIPEs is

2

their use as emulsion explosives, primarily in mining industries [9, 16, 17]. Typi25

cally, such highly concentrated emulsions are formulated as water-in-oil systems, wherein the dispersed phase, having volume fraction > 90%, is a supersaturated solution of oxidizing salts, whereas the continuous phase is a mixture of oils and emulsifiers [9, 16]. Commonly used emulsifiers include high molecular weight derivatives of poly(isobutenyl) succinic anhydride (PiBSA) or lower molecular

30

weight simple surfactants such as sorbitan monooleate (SMO) [1, 6, 8]. These emulsifiers tend to take the form of long chain, oil soluble compounds with HLB (hydrophilic-lipophilic balance) values of 2–4 and molecular mass of 900– 1300 g/mol [4, 8]. The nature of the emulsifier may influence the interfacial and rheological properties of HIPEs, as the different head groups of emulsifiers may

35

interact differently with the salt present in the internal phase [1, 6].

The droplet size distribution (DSD) within an emulsion sample plays an important role in determining the rheological properties of HIPEs [9–11, 16, 18]. Emulsion refining, to decrease droplet size, can be achieved by intensive shear40

ing in a suitable mixer. The underlying physical mechanism of HIPE formation depends on the critical capillary number (Cacr ), which must be exceeded for the larger droplets to rupture and form smaller droplets [19]. The tendency toward these capillary-limited smaller droplets also reduces the degree of polydispersity, and there are methods to produce nearly monodisperse emulsion samples [20].

45

The DSD of HIPE samples can be described either by Gauss equation [17], or by the log–normal equation [16]. The rheological investigation of HIPEs indicates that, for a given composition and volume ratio of internal and external phases, the reduction in droplet size significantly changes the emulsion’s rheological behavior, and properties such as the viscosity, yield stress and storage

50

modulus drastically increase [11, 18]. Detailed reviews of different rheological aspects of emulsions as a function of their structural parameters are available in the literature [21, 22].

The presence of salts in the aqueous phase of an emulsion plays a key role in 3

55

emulsion stability, as it affects the interfacial film rigidity and the degree of ionization for ionic stabilisers [23–26]. The interfacial tension may increase or decrease, depending on the emulsifier type (ionic or nonionic) and its interaction with the salt at the droplet interface [25]. Typically for an ionic emulsifier, the interfacial tension decreases when salt is added, whereas it may increase for an

60

nonionic emulsifier [24]. The addition of salt also affects the interfacial rheology and the rigidity of the interfacial film, modulated by the complex set of interactions between the emulsifier(s) and salts present [25, 27]. Most of the studies on the effects of salt concentration on emulsion stability and interfacial rheology are reported for dilute emulsions, and little is known about the effects of salts

65

on HIPE rheology. However, the literature suggests that in most cases only a small amount of salt in the aqueous phase (typically < 1 wt%) contributes significantly toward the emulsion stability and interfacial rheology [24–26]. The HIPEs used in mining applications, as ‘liquid explosives’, are typically prepared with supersaturated salt solutions [4, 10], and thus the change in their rheolog-

70

ical properties with moderate and high concentrations of salts is of interest.

The effects of aging on explosive HIPEs have also been reported in the literature [14, 15]. These studies typically focus on the formation of crystalline structures in the dispersed phase of the supersaturated salt solutions – forming 75

solidified salt crystals over time, referring to this mechanism as an emulsionto-suspension transition [14, 15]. Typically, this phenomenon is expected to increase the yield stress, storage modulus and the overall viscoelasticity of the aged HIPE samples [14, 15]. However, it should be noted that smaller droplets may have a lower probability of containing a nucleation site for crystallisation

80

to begin, and thus are less prone to becoming solidified. Further, the stability of HIPEs towards aging depends on the emulsifier type and the specific concentration and identity of salts present in the aqueous phase.

In this work, we report the rheological characterization of highly concentrated 85

water-in-oil emulsions through dynamic mechanical analysis and shear sweep 4

tests. We perform parametric studies of HIPEs and explore their rheological properties for i) droplet size differences caused by varying mixing time (tm ), ii) different salt concentrations in the aqueous phase (Csalt ), and iii) different mass fractions of the continuous and dispersed phases (φcm and φdm ). Pri90

marily, the amplitude and frequency sweep tests were performed to study the elastic behavior of the emulsions in terms of the yield stress (τy ) and storage modulus (G0 ), whereas flow curves were obtained from shear sweep tests, showing the viscous behavior of the emulsions. The structural details of the HIPE samples were obtained using cryogenic scanning electron microscopy and

95

optical microscopy. The present study is focused on the detailed rheological characterization of the HIPEs, by which we seek to understand the relationship between the main control parameters and the rheological properties obtained from the resultant emulsions. A separate study on the effects of aging of HIPE samples over a period of six months was also performed, and the results are

100

compared with those of the fresh samples. Using our experimental values of G0 , and with the estimation of the average droplet size of the dispersed phase, we also present a comparison of our experimental data with the modified Mougel model [28], and the Princen and Kiss model [29]. These models are expected to give insights from the comparison of predicted values of storage modulus (G0 )

105

with experimental measurements. The Mougel model considers van der Waals interactions between droplets as dominant, whereas the Princen and Kiss model is based on surface energy considerations; the comparison of these two models therefore offers insight into the main factors behind the rheological behaviour of concentrated emulsions.

110

2. Materials and Methods 2.1. Sample preparation The preparation of HIPE samples requires intimate mixing of an aqueous phase and an oil phase, achieved by addition of a suitable emulsifier and significant shear energy. In our samples, the oil component (continuous phase) was a mix-

5

115

ture of emulsifier and oil blend. The emulsifier was a poly(isobutylene) succinic anhydride (PiBSA)-based derivative, produced by reacting a 1:1 molar ratio of PiBSA and diethanolamine [30]. The oil blend was a mixture of methylated canola oil and ExxolTM D130 (de-aromatized hydrocarbon) oil, mixed in the mass ratio 9:7. Methylated canola oil refers to the methyl ester of canola oil de-

120

rived fatty acids. In all the samples, the oil-blend and emulsifier were mixed in the mass ratio 16:9. The aqueous component (dispersed phase) was a solution of two salts: ammonium sulphate and ammonium chloride, in water. The samples were prepared with different mass fractions of the two phases and with different concentrations of salts in the aqueous phase, as detailed in the following sec-

125

tions. Prior to mixing, the oil and water components were separately heated to 50–60◦ C and 75–85◦ C, respectively. Heating of the aqueous phase is required to fully dissolve the salts, and the temperature should be higher than the ‘fudge point’ (or the salt crystallization temperature). However, once the emulsion is formed, the number of internal phase droplets typically exceeds the number of

130

heterogeneous nuclei present, preventing the solidification of the droplets even in instances where the salt solution is supersaturated [31]. To a first approximation (assuming ideal mixing, and values for the solubilities of the two ammonium salts from literature), the total solubility of the salts at laboratory temperature (23◦ C) is 40 wt%, and as such, only the most concentrated salt solution used

135

here (45 wt%) is technically supersaturated; other samples are below the salt saturation concentration. A high torque mixer (Caframo BDC 1850) with a high shear Jiffy impeller (LM, SS304) was used to prepare the HIPE samples. To facilitate homogeneous mixing, the water component was added slowly into the oil component, with typical pouring time of 1 min at 700 rpm. The samples

140

were then mixed at 1400 rpm for the mixing (emulsification) time tm , depending on the sample studied. Similar composition ratios and methods of HIPE sample preparation have been used in previous studies [1, 8, 10, 18]. In almost all of these reported HIPE preparation methods, the samples were prepared with a Hobart mixer and the salt used was ammonium nitrate, typically used in ‘liq-

145

uid explosive’ emulsions. We have used a mixture of ammonium sulphate and 6

ammonium chloride as a model system for this type of emulsion (although our samples lack the oxidising salt to make them explosive). However, based on the composition and mass fractions of the phases, and also due to the presence of industrial emulsifier and oil components, our samples possess the same rheologi150

cal behavior as those of true ‘liquid explosives’. All of the constituents of the oil component (oils and emulsifier) were supplied by Orica Limited, Australia. The following sections describe the the details of samples and parameters of these studies. 2.2. Effects of control parameters on HIPE rheology

155

The complex rheological behavior of HIPE samples was explored through parametric studies. Measurements were performed by varying three key parameters: mixing time of oil and aqueous phases, mass fraction of the two phases, and the salt concentration in the aqueous phase. A separate study on aging is also reported.

160

2.2.1. Controlling the mixing time of oil and aqueous phases The size distribution of dispersed phase droplets was achieved by controlling the initial mixing time (tm ) over which shear was applied to the oil/aqueous mixture, at the conditions specified above. Four samples were subsequently taken from a batch of 200 g of emulsion, corresponding to tm = 4, 8 12 and 16 min-

165

utes, respectively. The HIPE samples were imaged using optical microscopy and cryogenic scanning electron microscopy (cryo-SEM). In cryo-SEM, the freezefracture method was used, whereby the sample was frozen in liquid nitrogen, and physically fractured before analysis in the electron microscope for the size and packing details of the emulsion droplets. The droplet size and their distri-

170

bution were measured from optical microscopy images through image analysis using the ImageJ software [32]. The droplet size was presented in terms of Dd , which represents the diameter of a circle with equivalent droplet area. For these samples, the ratio of mass fractions of the dispersed (φdm ) and continuous (φcm ) phases was fixed at 93.5:6.5 w/w, while the salt concentration in the dispersed

7

175

aqueous phase was fixed at 45 wt%. 2.2.2. Internal phase mass fraction studies In this study, four samples were prepared with continuous (external) phase mass fractions (φcm ) of 6.5%, 10%, 15% and 20%, respectively. The composition of both the phases (internal and external) and the mixing time (tm = 8 min) were

180

kept the same for all samples, and all the samples were prepared in batches of 200 g each. The concentration of salt in the aqueous phase was also kept the same, at 45 wt%. The prepared samples were analyzed using optical microscopy, and the droplet size distribution was obtained through image analysis using ImageJ [32]. Of the four samples, we could not perform rheology of the

185

sample with 20% continuous phase, as the sample viscosity was too low for the parallel plate geometry; the rheological properties of this sample are therefore not reported in this work. 2.2.3. Salt concentration studies To study the effects of salt concentration (Csalt ) on the rheological properties

190

of the formulated HIPEs, four samples were prepared with aqueous phase salt concentrations of 5%, 15%, 30% and 45 wt%, respectively. Salts used in the aqueous phase were ammonium sulfate and ammonium chloride in the ratio of 4:1 w/w, while the mass fractions of the internal (solution) and external (oil+emulsifier) phases was 93.5:6.5 w/w. Both of these ratios were maintained

195

during preparation of samples for this study. All of the samples were prepared by mixing for the same time of 8 minutes, and the composition of the oil phase was also kept the same. A change in Csalt changes the mass ratios of the oil and water components, and so a proportional amount of water in the salt solution was added to keep this ratio the same. It was ensured that the final aqueous

200

phase has the desired salt concentration as well as the mass ratio of both the phases. An attempt was also made to prepare HIPE samples without any salts present in the aqueous phase. However, this resulted in an inhomogeneous and dilute sample, with only partial emulsification, therefore the sample without

8

salt was not studied further. 205

2.2.4. Aging studies Aging studies were performed by storing the HIPE samples at an ambient lab temperature, maintained at 23◦ C. All of the rheological properties were again measured after 3 and 6 months, and compared with those of fresh samples. The fomulation parameters of the stored sample were: φcm = 6.5 wt%, Csalt =45

210

wt% and tm =8 minutes. This study was performed to determine whether any changes were seen in the rheological properties of the emulsion over a period of 6 months. 2.3. Rheology studies: instrumentation and parameter ranges Rheological measurements of the HIPE samples were performed using an Anton Paar Rheometer (model: Physica MCR501) with a parallel plate measuring system (PPMS) at 25◦ C. Flow curves were obtained using rotary shear sweep tests, while the dynamic behavior was studied through oscillatory tests. In amplitude sweep tests, both the small and large amplitude behavior (linear and non-linear regimes) were investigated, while the frequency sweep was performed only with a small amplitude (linear regime) oscillatory test. In all of the tests, initial relaxation of the samples was performed by running the instrument at constant (lower) values of the studied property (i.e. shear or strain). All of the measurements were performed in the forward mode by logarithmically increasing the parametric values from low to high. The following three deformation modes were studied:

Shear dependence: The shear rate (ε) ˙ was varied from 0.001 to 10 s−1 . The obtained flow curves are presented in terms of viscosity (η) and shear stress (τ ).

Amplitude dependence: The percentage-strain (%ε) was varied from 0.01 to 300% at a constant frequency of 1 Hz. This oscillatory test gives a measure of the storage and loss modulii (G0 and G00 ), respectively, and also shows a linear

9

viscoelastic (LVE) region, if present, for the material being studied. The above strain range gave a fair measurement of linear and non-linear viscoelastic behavior. Hyun et al. have presented a detailed review of small and large amplitude oscillatory tests, and have also discussed the prediction of material behavior with the analysis of storage and loss moduli (G0 and G00 ) [33].

Frequency dependence: The angular frequency was varied from 0.5 to 300 rad s−1 at a constant small strain of 0.5%. The strain value was decided after analysing the amplitude dependence test, to ensure it was located within the LVE regime. The frequency dependence test is a measure of the stability and elastic behavior of samples over the range of angular frequencies studied. The dynamic behavior, incorporating the elastic and viscous responses, is represented in terms of complex viscosity (|η ∗ |), the magnitude of which is given as [34]: " 2  0 2 #1/2  1/2 G00 G 1 ∗ 02 002 |η | = η + η = + = |G∗ | ω ω ω

(1)

where η 0 is the dynamic viscosity, η 00 is the elastic (imaginary) part of the 215

complex viscosity, G0 is the elastic storage modulus, G00 is the viscous (loss) modulus and ω is the frequency. 2.4. Experimental data fitting of storage modulus (G’) The interfacial tension (γ0 ) between pure water and the oil blend (oil+emulsifier) was measured using pendant drop tensiometry [35], and we obtained a limiting

220

value of about 2 mN m−1 , which is close to that reported in literature for a similar system [36]. Using this, we compare our experimental values of G0 with that predicted by the Princen and Kiss model, and Modified Mougel model. The details of these models and the fitting methods are presented in section 3.5. 3. Results and Discussion

225

3.1. Imaging and droplet size distributions The first set of emulsion samples were obtained by mixing the oil and water phases for different times (tm ), at a constant stirring rate. The optical mi10

croscopy images of the samples with mixing (emulsification) time, tm , of 4, 8, 12 and 16 minutes respectively are shown in Figure 1. The corresponding size 230

distributions of droplets with average droplet diameter (Dd,avg ) are shown in Figure 2. The bin size in these distributions were optimized using Sturges’ equation: k = log2 (nd ) + 1, where k is the number of bins, and nd is the number of data points. The wide distribution of droplet size at lower mixing times indicates a higher degree of polydispersity, and such distributions are close to being

235

log-normal. It can be clearly seen that, in line with expectation, increased mixing times result in a smaller average droplet size and lower polydispersity. It is evident from Figure 2 that the droplet size distribution appears to converge at high mixing time. This may be explained by the concept of limiting droplet size, based on the critical capillary number. The sizing parameters obtained from

240

these measurements of emulsion samples with different mixing times (tm ) are shown in Table 1, where Nd is the number of droplets and Dd is the diameter of an equivalent circle representing the droplet size (in the case of polyhedral droplets). A cryo-SEM image of a representative HIPE sample is shown in Figure 3. The image represents typical structures of the droplets in a HIPE sample.

Table 1: Droplet size measurements of samples with different mixing times (tm ), showing the total number of droplets (Nd,total ), the average droplet diameter (Dd,avg ) and the diameter range in the measured sample (Dd,range ). Here, Csalt = 45 wt% and φcm = 6.5 wt% for all samples.

tm (min)

Nd,total

Dd,avg (µm)

Dd,range (µm)

4

700

4.21

1.58- 12.48

8

1100

3.58

1.20- 9.94

12

1725

2.63

0.93- 8.10

16

3130

2.00

0.34 - 4.89

245

The second set of emulsion samples were obtained by keeping tm constant,

11

(a)

(b)

8 min

4 min

(c)

(d)

16 min

12 min

Figure 1: Optical microscope images showing the droplet size reduction with increasing mixing time. In all the samples, the aqueous phase salt concentration (Csalt ) is 45 wt%, and the mass fraction of the continuous phase is (φcm ) is 6.5 wt%

1000

ϕ

6

= 6.5 (wt%) 16 min

600

4000

Dd, avg Nd, total

5

Nd, total

800

Dd, avg / µm

cm

4 2000

3 2

Nd

1

0 4

400

12

16

tm / min

12 min

200

8

Dd, avg (µm) 4.21 3.58 2.63 2.00

8 min

4 min

0 0

2

4

6

8

10

12

Dd / µm Figure 2: Droplet size distribution and average droplet diameters (Dd,avg ) of the samples prepared using different mixing times (tm ); the inset shows the total number of droplets (Nd,total ) measured in the sample and the corresponding decrease in the average droplet diameter (Dd,avg ); dashed lines are to guide the eye.

12

Figure 3: Cryogenic scanning electron microscope image of a representative HIPE sample, prepared with Csalt =45 wt%, φcm = 6.5 wt%.

while varying the mass fractions of the two phases. Optical micrographs and the corresponding size distributions of samples with different mass fractions of 250

the two phases, are shown in Figures 4 and 5, respectively. These images indicate that for the same tm , the droplets of samples with a higher φcm , have higher polydisperisty, and larger average size, even though all of the samples fall within the HIPE regime. The obtained droplet size parameters with different mass fractions of phases, are shown in Table 2. Again, these observations can

255

be rationalised qualitatively using simple concepts: in this case, the intervening continuous phase film thickness. For samples with larger continuous phase fractions, the intervening film of oil between droplets is thicker and droplet deformation is lower; the droplets flow more easily past one another, resulting in a ‘thinner’ consistency (i.e. lower emulsion viscosity). This also means that

260

shearing is less effective in breaking up the droplets. Indeed, the sample with φcm of 20 wt%, showed a very wide distribution of droplet sizes and noticeably different consistency, compared to the samples with lower φcm ; due to its low viscosity, this sample was not studied further. For quantitative characterization

13

of the remaining samples, however, rheology is required.

Figure 4: Optical microscope images of the samples with different mass fractions of the continuous phase (φcm ). In all of these samples, the Csalt = 45 wt% and tm = 8 min and the composition of the two phases are kept constant.

Table 2: Droplet size measurement results for samples with different mass fractions of continuous phase (φcm ). Here, Csalt = 45 wt% and tm = 8 min for all samples.

265

φcm (wt%)

Nd,total

Dd,mean (µm)

Dd,range (µm)

6.5

1100

3.58

1.20–9.94

10

395

5.70

2.26–14.04

15

215

7.67

2.56–19.99

20

155

7.89

2.31–30.47

3.2. Oscillatory tests: amplitude sweep testing The results of the amplitude sweep tests performed on the HIPE samples in terms of dynamic storage and loss modulii (G0 and G00 ) variation with shear strain (ε) and shear stress (τ ), are shown in Figures 6 and 7, respectively. These results indicate that at low strain values, the HIPE samples show a typical linear 14

8

300

ϕ

= 6.5 wt%

6

Dd, avg Nd, total

500

4

cm

Nd

200

1000

20

ϕ 15 / %wt10

5

cm

ϕ

100

= 10 wt%

cm

ϕ

= 15 wt%

ϕ

cm

0 0

Nd, total

Dd, avg / µm

tm = 8 min

5

10

15

20

Dd, avg (µm) 3.58 5.70 7.67 7.89

= 20 wt%

cm

25

30

Dd / µm Figure 5: Droplet size distribution and average droplet diameters (Dd,avg ) of samples with different mass fractions of the internal and external phases; the inset shows the total number of droplets (Nd,total ) measured in the sample and the corresponding decrease in the average droplet diameter (Dd,avg ); dashed lines are to guide the eye.

270

viscoelastic (LVE) behavior, while at medium to high strain values (non-linear regimes), the behavior is followed by a yield point and a well defined crossover point. The stress values shown in Figure 7 represent the total stress, which is the sum of elastic and viscous contributions. The amplitude sweep performed on samples prepared with different mixing times (with constant φcm = 6.5%

275

and Csalt = 45%) show that strain behavior of these samples, particularly the yield strain (εy ) and crossover strain (εc ), are almost independent of the droplet size and polydispersity, as shown in Figure 6(a).

We observe almost the same value of crossover strain (εc ≈ 55%) in all of the 280

samples prepared with different mixing times, although the dynamic storage modulus (G0 ) increases significantly with higher tm . The constant value for εc follows from the value of εy , since both quantities essentially indicate a transi-

15

10−2 104

10−1

ε/% 100

101

16 min

G', G'' / Pa

101

φ

cm

103

5 15 30 45

4 min

tm= varied, Csalt = 45%,

103

102

tm= 8 min, Csalt = varied,

= 6.5%

φ

102 cm

G', G'' / Pa

= 6.5%

(c)

(d)

10 (wt%)

103 fresh 3 months 6 months

102

– –

f = 1Hz G' solid G'' open tm= 8 min, Csalt = 45%,

100 10−2

10−1

100

φ

ε/%

cm

= varied

101

102

tm= 8 min, Csalt = 45%,

103 10−2

10−1

100

φ

ε/%

G', G'' / Pa

G', G'' / Pa

100

(b)

15 (wt%)

101

ε/%

Csalt (wt%)

c

6.5 (wt%)

103

10−1

(a)

8 min

102

103 10−2

ε ~ 55%

12 min

103

102

102 cm

= 6.5 %

101

102

103

Figure 6: Amplitude sweep results in terms of the variation of storage and loss moduli (G0 and G00 ) with shear strain (ε), performed by varying ε from 0.01% to 300% at a constant frequency of 1 Hz on samples with: (a) different mixing times (tm ) with the same Csalt and φcm ; (b) different salt concentrations (Csalt ) with the same tm and φcm ; (c) different mass fractions of the continuous phase (φcm ) with the same tm and Csalt ; (d) aging studies of one sample over 3 and 6 months of storage at constant room temperature (23 ◦ C).

tion from elastic to viscous behavior. The stress behavior of the same samples, shown in Figure 7(a), shows a considerable increase in the yield stress (τy ) with 285

smaller droplets. This is consistent with the qualitative observations from the microscopy observations above, and again indicates that a smaller intervening continuous phase layer thickness (that must be present if the same internal phase volume is dispersed as smaller droplets) results in a thicker emulsion that is more elastic, and can store more interfacial energy per unit volume.

16

10−1

103

τ / Pa 101

102

103

16 min 12 min

φ

cm

103

(b) 103

tm= 8 min, Csalt = varied,

= 6.5%

6.5 (wt%)

φ

102 cm

= 6.5%

(c)

(d)

10 (wt%)

103

15 (wt%)

fresh 3 months 6 months

102

– –

f = 1Hz G' solid G'' open tm= 8 min, Csalt = 45%,

100 10−2

10−1

100

φ

cm

= varied

101

102

τ / Pa

tm= 8 min, Csalt = 45%,

103

100

101

φ

τ / Pa

G', G'' / Pa

10

10

102

5 15 30 45

102

1

1

Csalt (wt%)

8 min 4 min

3

τ 10/ Pa

(a)

tm= varied, Csalt = 45%,

G', G'' / Pa

100

G', G'' / Pa

G', G'' / Pa

104

100

102 cm

= 6.5 %

102

103

Figure 7: Amplitude sweep results in terms of the variation of storage and loss moduli (G0 and G00 ) with shear stress (τ ), performed by varying ε from 0.01% to 300% at a constant frequency of 1 Hz on samples with: (a) different mixing times (tm ) with the same Csalt and φcm ; (b) different salt concentrations (Csalt ) with the same tm and φcm ; (c) different mass fractions of the continuous phase (φcm ) with the same tm and Csalt ; (d) aging studies of one sample over 3 and 6 months of storage at constant room temperature (23 ◦ C).

290

Further, as shown in Figures 6(b) and 7(b), the stress and strain behavior are quite independent of the salt concentration present in the aqueous (internal) phase, and no significant changes in the G0 values over the studied range of salt concentration is seen. Thus, the flow of such highly concentrated emulsions 295

appears to commence at the same strain value, regardless of salt concentration, droplet size and polydispersity. However, independent of the salt concentration,

17

the energy requirements for the emulsion to start flowing will increase due to the presence of smaller droplets and tighter overall droplet packing.

300

The most compelling demonstration of these effects is apparent in the data for emulsions with different mass fractions of the dispersed and continuous phases. The strain and stress behavior of the samples, prepared with different mass fractions of the continuous phase (φcm =6.5, 10 and 15wt%), are shown in Figures 6(c) and 7(c), respectively. The yield and crossover strains reduce with

305

increasing the continuous phase fractions, perhaps because of increased film thickness. The higher fraction of continuous phase results in looser droplet packing, as the droplets essentially have an interstitial lubricating layer, and can easily flow. Further, samples with higher φcm have lower values of τy and G0 , implying that they require less energy in order to flow. In fact, as discussed

310

earlier, the sample with φcm of 20 wt% easily flowed under gravity, and thus had too low a viscosity for accurate measurement using parallel plate geometry.

The amplitude sweep results of the HIPE samples aged over a period of 3 and 6 months at ambient lab temperature (maintained at 23 ◦ C) are shown in Fig315

ures 6(d) and 7(d), respectively. These results show that the strain behavior (εy , and εc ) of these samples does not change significantly over time. However, a modest reduction in the G0 and τy are noticed with aged samples. A possible reason could be the reorganization of droplets resulting in softening of the packing structure over time, thereby storing less energy. In the aged samples,

320

microscopy indicated no evidence of the supersaturated aqueous droplets forming solid crystals of salt, which may increase the storage modulus, as observed by Masalova et al. [14, 15].

The stress-strain behavior of all of the samples are shown in Figure 8, where the 325

change in slope indicates the start of yielding. Further, the stress behavior tends toward constant values beyond the yield point, which shows the transition from elastic to viscous regimes. For the studied range of salt concentrations, and the 18

aging studies over the period of 6 months, neither parameter has a significant effect on τ –ε behavior. 10−2 103

10−1

ε/% 100

101

102

103 10−2

(a)

(b)

10−1

ε/% 100

101

103 103

f = 1Hz

102 tm (min)

Csalt (wt%)

4 8 12 16

5 15 30 45

101 100

10−1

φ

tm= varied, Csalt = 45%,

cm

tm= 8 min, Csalt = varied,

= 6.5%

(c)

φ

cm

τ / Pa

τ / Pa

102

103

102

101 100

10−1

= 6.5%

103

(d)

102

φ

1

10

cm

100

10−2

(wt%)

tm= 8 min, Csalt = 45%,

10−2

10−1

100

φ

ε/%

cm

= varied

101

102

101

fresh 3 months 6 months

6.5 10 15

10−1

τ / Pa

τ / Pa

102

tm= 8 min, Csalt = 45%,

103 10−2

10−1

100

ε/%

φ

cm

100 10−1

= 6.5 %

101

102

103

Figure 8: Amplitude sweep results in terms of stress (τ ) vs strain (ε), performed by varying the ε from 0.01% to 300% at a constant frequency of 1 Hz on samples having: (a) different mixing times (tm ) with the same Csalt and φcm ; (b) different salt concentrations (Csalt ) with the same tm and φcm ; (c) different mass fractions of the continuous phase (φcm ) having the same tm and Csalt ; (d) aging studies of one sample over 3 and 6 months of storage at constant room temperature (23 ◦ C).

330

3.3. Small amplitude oscillatory tests: frequency sweep testing The frequency sweep results indicate the material stability over the measured frequencies at a constant amplitude (strain). The strain (ε) should typically be in the linear regime, where the material was found stable during the amplitude sweep testing. In our samples, the small amplitude frequency sweep was 19

335

performed by varying the angular frequency (ω) from 0.5 to 300 rad s−1 at a constant amplitude (ε) of 0.5%, which was well within the linear viscoelastic regime, as determined from the amplitude sweep tests described above. The results of the frequency sweep tests of all the samples, prepared with different tm , Csalt and aging, are presented in Figure 9, which show variation of storage

340

modulus (G0 ) and complex viscosity (|η ∗ |) with angular frequency (ω). It is seen that the HIPE samples are reasonably stable over the measured frequencies, as the G0 values are practically constant within the low to moderate frequency range, shown in Figures 9(a), (c) and (d). This suggests that the droplets are strongly associated with each other, resulting in G0 values almost independent

345

of the frequency. Further, at low frequencies, the bulk response of the sample is expected to dominate, as the time-scales are larger, and thus droplet packing maintains the stiffness and elasticity. However, at higher angular frequencies, such behavior is not directly associated with the stiffness of the droplet packing, as the sample responds only locally because of the shorter time scales, thereby

350

increasing the G0 values as shown in Figure 9(a). In our rheological measurements, it was noticed that at ε = 0.5%, the storage modulus (G0 ) dominated over loss modulus (G00 ) throughout the measured frequencies, which ensured that only the elastic response of the HIPE samples was studied.

355

The dynamic behavior, incorporating the elastic and viscous responses of different polydisperse samples in terms of their complex viscosity, is shown in Figure 9(b). These data represent the total resistance of the HIPE to flow, and arise from a combination of viscous and elastic resistances. The decrease of |η ∗ | with higher frequencies is primarily governed by the increased dissipation of

360

energy within the HIPE samples, thereby decreasing the resistance to flow. It is further noted that the behavior of G0 and |η ∗ | remain essentially unchanged with changes in the aqueous phase salt concentration and aging over a period of 6 months, as shown in Figures 9(c) and 9(d), respectively.

20

0

10

10

-1

2

10

3

10

0

1

10

102

10

(a)

8 min

102

φ

(c)

100

φ

101

ω / rad.s

mp

lex

vis co si

ty,

fresh 3 months 6 months

tm= 8 min, Csalt = 45%,

103

100

-1

104 103

Co

= 6.5% cm

102

(d)

φ

η*

102 101

= 6.5 % cm

101

102

ω / rad.s

η* / Pa.s

tm= 8 min, Csalt = varied,

101 = 6.5% cm

Storage modulus, G'

Csalt (wt%) 5 15 30 45

ε = 0.5% G' – solid η* – open

φ

G' / Pa,

η* / Pa.s

tm= varied, Csalt = 45%,

= 6.5% cm

103

101

104 103

4 min

104

102

(b)

4 8 12 16

12 min

103

103

tm (min)

16 min

tm= varied, Csalt = 45%,

G' / Pa,

ω / rad.s

-1

1

η* / Pa.s

G' / Pa

104

ω / rad.s

103

-1

Figure 9: Frequency sweep results, performed by varying the angular frequency (ω) from 0.5 to 300 rad/s at an constant amplitude of 0.5%, showing the behavior of storage modulus (G0 ) and complex viscosity (|η ∗ |) showing; (a) the G0 behavior with different mixing times (tm ) with the same Csalt and φcm ; (b) the |η ∗ | behavior of the different tm ; (c) the behavior of G0 and |η ∗ | for different salt concentrations having same tm and φcm ; (d) the aging studies of one sample when stored at constant room temperature.

3.4. Flow curves with rotary tests: shear sweep of HIPE samples 365

The deformation behavior of HIPE samples with respect to strain rate (ε) ˙ represented by the viscosity (η) is shown in Figures 10. These data demonstrate a typical shear thinning behavior, even at very low shear rates. The viscous behavior depends on the droplet size, polydispersity and the mass fractions of the two phases. For a given mass fraction of the continuous phase (φcm ), the

370

emulsion samples with smaller droplets show higher viscosity, while an increase

21

in φcm considerably reduces the viscosity as shown in Figures 10(a) and 10(c), respectively. This corroborates the data in previous sections, again pointing

ε. / s

-1

10−3 105

10−2

-1

10−1

100

(a)

101

10−3

10−2

10−1

100

(b)

tm (min)

105 104

η / Pa.s

10

101

Csalt (wt%) 5 15 30 45

4 8 12 16

4

η / Pa.s

ε. / s

103

103

102

102

φ

tm= varied, Csalt = 45%, 5

10

cm

= 6.5%

φ

(c)

cm

tm= 8 min, Csalt = varied,

φ

cm

= 6.5%

101

(d)

(wt%)

fresh 3 months 6 months

η / Pa.s

103

104

η / Pa.s

6.5 10 15

104

105

103

102 101 tm= 8 min, Csalt = 45%,

100 −3

10

10

−2

φ

cm

−1

10

ε/s .

= varied

10

0

tm= 8 min, Csalt = 45%, 1

−3

10

10

-1

−2

10

−1

10

ε/s .

φ

102 cm

= 6.5 %

101 0

10

1

10

-1

Figure 10: Flow curves of HIPE samples obtained through shear sweep by varying the strain rate (ε) ˙ from 0.001 to 10 s−1 for samples prepared with (a) different mixing time (tm ), with the same Csalt and φcm ; (b) different salt concentrations (Csalt ) with the same tm and φcm ; (c) different φcm having the same tm and Csalt ; (d) aging studies of one sample when stored at constant room temperature.

to the thickness of continuous phase layers between droplets as being central to the overall viscosity and consistency of HIPEs. Thinner intervening liquid layers 375

between the droplets result in tighter packing, reducing the emulsion’s ability to flow and resulting in higher effective viscosity. It is further seen that the viscous behavior practically remains constant as a function of aqueous phase salt concentration and aging over a period of six months as shown in Figures 10(b)

22

and 10(d), respectively. It should be noted that the viscosity of the aqueous 380

phase changes with the addition of salt. However, being the internal phase, the aqueous phase viscosity does not significantly affect the overall viscosity of the HIPEs. 3.5. Experimental G0 data fitting with Princen and Kiss, and modified Mougel models At low stress values, HIPEs typically behave as elastic solids, whereas at stresses above their yield stress, they show a shear thinning viscous behavior [19]. The elasticity present in the HIPEs is the result of the compressed nature of droplets that arises from the large volume fraction of the internal phase, thus storing the interfacial shear energy through deformation of their interfaces [37]. Princen and Kiss developed theoretical expressions relating different rheological properties in order to give approximations for real, polydisperse emulsion droplets [29, 38]. They presented the following expressions for storage modulus (G0 ): G0 = 1.769

γ0 1/3 φ [φev − 0.712] ; R32 ev

for φev > 0.712

(2)

where, γ0 is the interfacial tension, φev represents the equivalent volume fraction of the dispersed phase, while R32 is the Sauter mean radius estimated using the equivalent volume to surface area ratio. The expressions for φev and R32 are given as [29]: −1/3

φ−1/3 = φdv ev

− 1.105

h 2R32

(3)

and R32 385

P ni ri3 = Pi 2 i ni ri

(4)

where ni is the number of droplets with equivalent radius ri , h is the finite film thickness between the droplets, and φdv represents the dispersed phase volume fraction.

Paruta-Tuarez et al. have presented an extensive analysis of the Princen and Kiss equations and other approaches that are available in literature to model

23

the storage modulus (G0 ) of concentrated emulsions [28]. Their experimental data is best described by the model equation of Mougel et al., which is based on dominant van der Waals interactions between droplets [28, 39]. They presented a modified Mougel model as [28]: G0 =

2πγ0 Havg φdv R2 (φmax − φdv )

(5)

where R is the average droplet radius, φmax is the maximum volume fraction of 390

internal phase, and Havg represents an average distance based on the different interactions between droplets. As noted by Paruta-Tuarez et al., Havg can be estimated by adjusting Eq. 5 to experimental data [28].

The rheological properties of highly concentrated emulsions are expected to 395

depend not only on average droplet size and mass fractions of the two phases, but also on the polydispersity, droplet packing, interfacial dynamics, inter-droplet interaction potential, and the methods of preparation and measurement. For such emulsions, the consistency is affected by the presence of smaller droplets filling the space between larger droplets. We have compared our experimental

400

G0 values with those predicted by the Princen and Kiss model (Eq. 2) [29], and modified Mougel et al. model (Eq. 5) [28, 39]. The experimental values of G0 and the estimated values of R32 , for the samples with different tm and φdm , are shown in Tables 3 and 4, respectively. The values of R32 were estimated from droplet size measurements using Eq. 4. The comparison of experimental values

405

with the above discussed models, for samples having different mixing times, are shown in Figures 11(a) and (b), while those of samples with different mass fractions of the two phases are shown in Figures 11(c) and (d) respectively.

As noted by Paruta-Tuarez et al. and Pal, the applicability of the Princen and 410

Kiss model is not universal and it typically underpredicts the storage modulus [5, 28]. It can be seen (Figure 11) that the Princen and Kiss model consistently under-predicts the G0 values, and thus is not suitable for the complex HIPEs presented in this work. It should be noted that, while estimating the 24

tm / min 4

16

1

1.5

2

2.5

3

3.5

Experimental data Princen and Kiss model Modified Mougel model

104

G' / Pa

103

103 tm= varied,

φ

cm

= 6.5%

tm= varied,

(a)

φ

cm

Experimental data Princen and Kiss model Modified Mougel model

= 6.5%

(b)

Experimental data Princen and Kiss model Modified Mougel model

103

103

tm= 8 min,

102 0.8

φ

0.84 dv

φ

cm

= varied

0.88

tm= 8 min,

(c) 0.92 2

/ vol%

3

φ

cm

= varied

4

(d) 5

G' / Pa

G' / Pa

R32 / µm

12

Experimental data Princen and Kiss model Modified Mougel model

104

G' / Pa

8

102

6

R32 / µm

Figure 11: Comparison of experimental values of G0 with Princen and Kiss (1986), and modified Mougel et al. (2006) models, as per Eqs. 2 and 5; (a) and (b) show the comparison of samples prepared with different tm but fixed φcm ; while (c) and (d) show those with different φcm and same tm . The fitting parameters in Eq. 5 are: Havg = 70 nm and φmax = 0.98. All other values are shown in Tables 3 and 4.

G0 values from Princen and Kiss model, we have taken φev =φdv , and thus the 415

film thickness is not considered here (Eq. 3). However, if we calculate the φev values from actual values of G0 , we get φev > 1, which is clearly unphysical. Further, we cannot simply use a universal value of film thickness that would be applicable to all our samples having different droplet sizes and polydispersity. On the other hand the modified Mougel model, which is based on dominant

420

van der Waals interactions, predicts the G0 values of samples reasonably well at different mixing times, and also for higher values of φdv . However, a slight

25

mismatch is seen in the G0 values for low values of φdv , which could possibly be the effect of higher polydispersity. It should be noted that the modified Mougel model does not explicitly consider the effects of polydispersity present in the 425

HIPE samples. We would also like to highlight the fact that the comparison of these two models is not entirely fair as the modified Mougel model has a fitting parameter, while the Princen and Kiss model does not. However, one of the more pleasing factors that arises from the modified Mougel model is that our complete series of measurements can be fit using a single, consistent value of

430

Havg of 70 nm.

Table 3: Experimental values of G0 for samples with different tm , and thus different polydispersity. The values of R32 were estimated using Eq. 4. φdv was estimated by measuring the densities of the dispersed and continuous phases as ρd = 1.23 Kg.m−3 and ρc = 0.91 Kg.m−3 , respectively.

G0exp (Pa)

R32 (µm)

6830

1.17

4170

1.81

8

2260

2.38

4

1060

3.10

tm (min)

φdm (wt%)

φdv (vol%)

16 12 93.50

91.41

Table 4: Experimental values of G0 for different φdv samples, ρd = 1.23 Kg·m−3 and ρc = 0.91 Kg·m−3 . The values of R32 were estimated using Eq. 4

tm (min)

8

φdm (wt%)

φdv (vol%)

G0exp (Pa)

R32 (µm)

93.50

91.41

2260

2.38

90.0

86.94

633

3.88

85.0

80.74

213

5.48

Further, the average droplet radius (R32 or even R), are strong functions of droplet size distribution, polydispersity and the volume fractions of the two phases, and can be different for different combinations of these variables. How435

ever, for the case of φcm = 6.5%, if the fitting parameter (Havg ) is carefully 26

determined, the modified Mougel model can accurately predict the G0 values of HIPE samples, irrespective of the polydispersity. The physical meaning of Havg is not immediately clear, as it is neither directly the film thickness between droplets nor the intermolecular distance. In the original work of Mougel, 440

the authors found that their rheology data for emulsions stabilised by a small molecular nonionic surfactant (sorbitan monooleate) were best fit assuming a D0 value (contact separation) of 30 nm, clearly larger than the range of intermolecular or steric interactions. However, as discussed therein, in complex emulsion systems of deformable droplets, the exact value, and indeed the mean-

445

ing of D0 , may not be clearly defined. Thus the average distance Havg proposed by Paruta-Tuarez [28] provides a basis for internal comparison for these complex, polydisperse systems. Given the much larger molecular dimensions of the stabilisers used here, a film thickness on the order of 70 nm does therefore not seem unreasonable within the context of the literature and experiment. An in-

450

dependent verification of the actual film thickness within such droplet systems, such as could be accomplished using thin film interferometry [40], would be a valuable addition.

4. Conclusions We have explored the rheological properties of an industrially and scientifically 455

relevant series of high internal phase emulsions (HIPEs), having real, polydisperse droplets with different size distributions. This study shows a range of notable features. Firstly, we note that the storage modulus G0 has a complex relationship with the droplet size and mass fraction of the two phases, most likely due to the variation in polydispersity in the emulsion. For a given vol-

460

ume fraction of internal phase, G0 increases with higher mixing times, as the smaller droplets pack more tightly compared to larger ones. On the other hand, G0 typically decreases with a decrease in volume fraction of internal phase, as there would be thicker layer of continuous phase between droplets, resulting in relaxed packing of droplets. Secondly, it appears that, for high mass fraction

27

465

(φdm = 93.5%) of the dispersed phase, the strain behavior is almost independent of the droplet size, polydispersity and the aqueous phase salt concentration. On the other hand, the strain behavior does depend very strongly on the phase volume fractions, and G0 reduces dramatically for lower values of φdv . Further, the yield stress dramatically increases with smaller droplets as well as with higher

470

mass fraction of dispersed phase. This result is consistent with prior experimental results [12, 41], where a dramatic increase in yield stress is reported for high values of φdv . Thirdly, it is noticed that the effects of medium to high concentrations (> 5 wt%) of salts in the aqueous (dispersed) phase, do not have any significant effects on any of the rheological properties. Finally, the aging

475

studies of the emulsion samples, stored at ambient lab temperature (maintained at 23 ◦ C), show that the samples are quite stable over a period of six months, with no significant change in their rheological properties. However, a slight decrease in the G0 was observed in aged samples, interpreted as softening of the structure associated with relaxation of the droplet packing over time.

480

An attempt is also made to fit the experimental data of G0 with two key models available in literature. For the G0 values of samples prepared with different mixing times and higher dispersed phase mass fractions, we noticed a good agreement with the modified Mougel model. The Mougel model is based on the 485

van der Waals interactions between droplets, which are expected to dominate in the case of an oil-continuous emulsion stabilised by a non-ionic emulsifier [39]. Another important aspect of this model is that it takes into account the divergence of G0 when the φdv approaches φmax [28]. We also noticed a consistent disagreement of our measurements of G0 with the Princen and Kiss model. It

490

should be noted that, because of the complex nature of the HIPE and the dependence of its rheological properties on several variables – such as droplet size distribution, droplet packing, polydispersity, method of formulation and the measurement technique used – a simple set of equations cannot be applicable to all possible cases. Overall, the under-prediction of G0 by the Princen and Kiss

495

model suggests that that the surface energy of the droplets does not completely 28

account for the value of storage modulus in HIPEs. On the other hand, the reasonable agreement of Mougel model with our data on G0 suggests that van der Waals interaction forces may be playing a critical role in increasing the stiffness of HIPEs. 500

Thus, for a given volume fraction of internal phase, the rheological behavior of HIPEs is primarily governed by the droplet polydispersity as well as drop size, as samples with smaller droplets will have higher viscoelasticity. Crucially, the effective film thickness of the continuous phase between the droplets can 505

be considered as the central parameter for controlling the overall viscoelasticity of the HIPE samples. In a polydisperse HIPE sample, this film thickness is difficult to measure as it will change locally within the sample, and cannot be considered a constant as in the case of monodisperse droplets. However, for a given dispersed phase fraction, the average film thickness must decrease with

510

smaller droplets. In addition, for a given droplet size distribution, the film thickness must decrease with a decrease in the continuous phase fraction. In both the cases, we see an increase in the viscoelasticity of the HIPE samples, demonstrating greater structural stability.

Acknowledgments 515

The authors are thankful to Orica Limited (Australia) for the financial support, supplying materials (oils, emulsifiers), and permission to publish the outcomes of this work. This work was supported in part by a Discovery Project (DP140100677) and a Future Fellowship (FT160100191) from the Australian Research Council. We are also grateful for use of the cryo-SEM facility at IIT

520

Bombay and rheometer facility at Monash University.

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34

104

Cross-over strain ~ 55%

(d)

(a)

(b)

G', G'' / Pa

(c) (b) (a) 3

10

– –

f = 1Hz G' solid G'' open

4 min

8 min

(c)

(d)

12 min

16 min

102

10−2

10−1

ε/% 100

101

102

103



-

Rheological properties of industrially relevant, highly concentrated emulsions are explored.

-

Emulsion strain behavior is almost independent of the droplet size and polydispersity.

-

HIPEs is quite insensitive to medium to high concentrations of salts (>5 wt%) present in the internal phase.

-

A modified Mougel model can be used to predict the rheology with high accuracy.