7.3 Emulsions stabilized by cationic surfactants
7.3.2 Effect of the addition of salt on sheet perforation
As for the emulsions stabilized by anionic surfactants (section 7.2.2.1), we investigate the influence of the addition of salt on the perforation of liquid sheets produced with the single-tear experimental set-up. Here, the emulsion aqueous phase is a solution of CpCl at 0.9 mM with increasing concentration of salt. The experimental impact parameters are the same as the ones reported in section7.2.2.1. The perforation process is quantified by the value of the total number of perforation events Ntot.
7.3.2.1 Monovalent salt
In Figure 7.16are shown images of the sheets obtained for different concentrations of NaCl in the emulsion aqueous phase. As for the emulsions stabilized by SDS (Figure7.4), we observe that without salt there is almost no perforation of the sheet (Figure7.16(a)).
The addition of salt at 1 g/L triggers the perforation (Figure7.16(b)), a further increase of the NaCl concentration entails an increase of the number of perforation events (Figure 7.16(c,d)).
a 3 mm b c d
Figure 7.16: Images of liquid sheets made of emulsions stabilized by CpCl for different concentrations of NaCl in the aqueous phase. The images are taken 3.6 ms after the impact of the tear. a). CNaCl=0 g/L b). CNaCl=1 g/L c). CNaCl=2.5 g/L and d).
CNaCl=10 g/L.
The evolution of the total number of perforation events, Ntot, as a function of the NaCl concentration is plotted in Figure 7.17. On the bottom x-axis, the NaCl concentrations are expressed in g/L and on the top x-axis in mol/L. We find that an increase of the salt concentration from 0 g/L to 20 g/L entails an increase of the total number of perforation events from 15 to 137.
For the emulsions stabilized by anionic surfactants, we have shown that the total number of perforation events, Ntot, decreases with the Debye length, κ−1, i.e. with the
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Chapter 7. Playing with emulsion formulation to tune the perforation of liquid sheet
0 5 10 15 20
0 20 40 60 80 100 120 140 160
Ntot
CNaCl (g/L)
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
CNaCl (mol/L)
Figure 7.17: Evolution of the total number of perforation events, Ntot, as a function of the NaCl concentration in the aqueous phase of emulsions stabilized by CpCl.
range of the electrostatic repulsive forces. The Debye length is an inverse function of the ionic strength (I) (Equation 7.3) that strongly depends on the charge number of ions (Equation 7.4). For a same molar concentration, the ionic strength, I, of a divalent salt in solution will be larger than for a monovalent salt and so the Debye length shorter.
To further investigate the influence of the Debye length on the sheet perforation, we add divalent salt in the emulsion aqueous phase and compare the results to those obtained with monovalent salt.
7.3.2.2 Divalent salt
We use sodium sulfate, Na2SO4, as divalent salt. In Figure 7.18 is shown the evolu-tion of the total number of perforaevolu-tion events as a funcevolu-tion the Na2SO4 concentration in the emulsion aqueous phase. As expected, we observe that without salt the sheet is not perforated. An increase of the divalent salt concentration entails a continuous in-crease of the total number of perforation events, from 23 for CNa2SO4=0.07 g/L to 126 for CNa2SO4=2.8 g/L. Hence, the same influence is observed for the divalent salt (Na2SO4) as for the monovalent salt (NaCl). We will now compare the influence of these two salts on the sheet perforation.
7.3. Emulsions stabilized by cationic surfactants 179
0 1 2 3
0 20 40 60 80 100 120 140
Ntot
CNa
2SO4(g/L)
0.000 0.005 0.010 0.015 0.020
CNa
2SO4(mol/L)
Figure 7.18: Evolution of the total number of perforation events, Ntot, as a function of the Na2SO4 concentration in the aqueous phase of emulsions stabilized by CpCl.
7.3.2.3 Comparison of the influence of monovalent and divalent salts
In Figure 7.19(a) is plotted the evolution of the total number of perforation events as a function of the salt molar concentration in the emulsion aqueous phase for monovalent salt (NaCl, orange circle symbols) and for divalent salt (Na2SO4, green diamond symbols).
As previously observed, for both salts, Ntot increases with salt concentration. However, the curve is shifted to larger salt concentrations for the monovalent salt compared to the divalent one. Hence, at the same molar concentration, the divalent salt is more efficient to promote the sheet perforation. In Figure 7.19(b) is plotted the evolution of the total number of perforation events as a function of the Debye length of the emulsion aqueous phase for the two salts. Ntot decreases with the Debye length for both salts. An increase of the range of the electrostatic repulsion forces (the Debye length) prevents the perforation of liquid sheets. Compared to Figure 7.19(a), we observe a better collapse of the data points for the two salts once plotted as a function of the Debye length. This collapse highlights that the perforation of liquid sheets is controlled by the range of the electrostatic repulsion forces. The collapse is however not perfect and for a given Debye length, κ−1, the divalent salt is slightly more efficient to promote the sheet perforation.
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Chapter 7. Playing with emulsion formulation to tune the perforation of liquid sheet
Figure 7.19: a). Evolution of the total number of perforation events, Ntot, as a func-tion of the salt concentrafunc-tion in the aqueous phase of emulsions stabilized by CpCl, for monovalent salt (NaCl) and divalent salt (Na2SO4). b). Evolution of the total number of perforation events, Ntot, as a function of the Debye length, κ−1, of the aqueous phase of emulsions stabilized by CpCl, for monovalent salt (NaCl) and divalent salt (Na2SO4).
7.3.3 Effect of the addition of amphiphilic copolymer on sheet perforation
Amphiphilic triblocks copolymer (Pluronic F108) is added to the aqueous phase of the emulsion. We investigate the influence of the Pluronic F108 concentration on the sheet perforation for different sodium chloride concentrations. Figure 7.20 shows images of the sheets for different concentrations of Pluronic F108 in the aqueous phase of the emulsion taken at the same time after the tear impact. Here the NaCl concentration in the emulsion aqueous phase is set at 20 g/L. As observed previously, without Pluronic F108 and at high salt concentration (20 g/L), a high number of perforation events are observed in the liquid sheet (Figure7.20(a)). Then, the addition of Pluronic F108 entails a continuous decrease of the number of perforation events observed in the liquid sheets (Figure 7.20(b,c)). For a concentration in Pluronic F108 equal to 7.5 g/L, we do not observe any perforation of the liquid film (Figure 7.20(d)). The pictures presented in Figure 7.20 correspond to a salt concentration of 20 g/L but the same phenomenon is observed for the different NaCl concentrations investigated.
In Figure 7.21(a) is plotted the evolution of the total number of perforation events, Ntot, with the Pluronic F108 concentration in the emulsion aqueous phase for different NaCl concentrations. For a given salt concentration, we observe that an increase of the copolymer concentration entails a large decrease of Ntot. For CNaCl=20 g/L, Ntot is equal to 146 for CF108=1 g/L and to 3 for CF108=7.5 g/L. The addition of Pluronic F108 permits to completely inhibit the perforation process. The same phenomenon is observed for the different salt concentrations, but a decrease of the salt concentration entails a
7.3. Emulsions stabilized by cationic surfactants 181
a 3 mm b c d
Figure 7.20: Images of liquid sheets made of emulsions stabilized by CpCl for different concentrations of Pluronic F108 in the aqueous phase. Images are taken 3.6 ms after the impact of the tear. a). CF108=0 g/L b). CF108=2.5 g/L c). CF108=4 g/L and d).
CF108=7.5 g/L. Here the NaCl concentration in the emulsion aqueous phase is set at 20 g/L.
shift of the curve towards smaller values of Ntot. For example, at CF108=2.5 g/L, 113 perforation events are counted for a salt concentration of 20 g/L and only 22 without salt. The influence of the concentration of sodium chloride on the sheet perforation is highlighted in Figure 7.21(b), where the same data as in Figure 7.21(a) are plotted as a function of the salt concentration for the different Pluronic F108 concentrations. This representation emphasizes that an increase of the salt concentration entails an increase of the total number of perforation events and that this effect is stronger as the Pluronic F108 concentration is lower.
7.3.4 Effect of the addition of salt and amphiphilic copolymer on the perforation mechanism
We have seen that for monovalent and divalent salts, the addition of salt in the emulsion aqueous phase triggers the perforation process. Then, a further increase of the salt concentration entails a continuous increase of the total number of perforation events.
We have shown that the addition of amphiphilic copolymer (Pluronic F108) entails a decrease of the total number of perforation events. The addition of an adequate copolymer amount permits to completely inhibit the sheet perforation process. To understand the origin of these phenomena, we investigate the influence of the different parameters (salt and copolymer concentrations) on the two steps of the perforation mechanism: (i) the entering of oil droplet at air/aqueous phase interface and (ii) the spreading of oil droplet at the interface.
7.3.4.1 Pre-hole widening dynamics
In this section we investigate the localized thinning of the liquid film (pre-hole) due to the spreading of oil droplets at the air/aqueous phase interface. We perform these
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Figure 7.21: a). Evolution of the total number of perforation events, Ntot, as a function of the Pluronic F108 concentration in the aqueous phase of emulsions stabilized by CpCl for different NaCl concentrations as indicated in the legend. b). Evolution of the total number of perforation events, Ntot, as a function of the NaCl concentration in the aqueous phase of emulsions stabilized by CpCl for different concentrations of Pluronic F108 as indicated in the legend.
experiments for three different compositions of the emulsion aqueous phase : 1. CCpCl=0.9 mM,
2. CCpCl=0.9 mM and CNaCl=20 g/L,
3. CCpCl=0.9 mM, CNaCl=20 g/L and CF108=5 g/L.
For the first emulsion aqueous phase composition (CCpCl=0.9 mM), very few perfo-ration events were observed (around 15), on the contrary for the second composition (CCpCl=0.9 mM and CNaCl=20 g/L) a large number of perforation events were observed (around 137). For the third composition (CCpCl=0.9 mM, CNaCl=20 g/L and CF108=5 g/L), very few perforation events were again observed (around 16). The objective is to investigate if those discrepancies are due to a difference of spreading behavior of oil droplets at the interface and so to a difference in the pre-hole widening dynamics.
In Figure 7.22 is plotted the evolution of the pre-hole radius, Rph, as a function of the time elapsed since its formation, T = t− tph, for the different compositions of the emulsion aqueous phase. We find that, for the three aqueous phases investigated, Rph increases with T as a power-law with an exponent 3/4: Rph = kT3/4. Once again, these results are in agreement with the ones obtained for model emulsions in Chapter6and so confirm a widening dynamics of pre-hole in agreement with the dynamics of Marangoni spreading.
In Figure 7.22, we observe a very good collapse of the curves obtained for the three different compositions of the emulsion aqueous phase. Hence, the widening dynamics
7.3. Emulsions stabilized by cationic surfactants 183
3/4
10-4 10-3
10-4 10-3
R ph (m)
T (s) CCpCl=0.9 mM
CCpCl=0.9 mM, CNaCl=20 g/L
CCpCl=0.9 mM, CNaCl=20 g/L, CF108=5 g/L
Figure 7.22: Evolution of the radius of the pre-hole, Rph, as a function of T , the time elapsed since the pre-hole formation for emulsions stabilized by CpCl with different con-centrations of NaCl and Pluronic F108 in the emulsion aqueous phase. The exact com-positions of the emulsions aqueous phase are indicated in the legend. Different symbols correspond to different experiments. The lines are the best fits of the experimental data of the form: Rph = kT3/4.
of the pre-hole and so the spreading dynamics of oil droplet at the air/aqueous phase interface are the same for the different compositions. Therefore, the differences observed in the perforation of liquid sheets for the different emulsion compositions do not arise from a different spreading behavior of the oil droplets at the air/aqueous phase interface.
As explained in section7.2.3.1, we can extract from the fit of the experimental curves Rph vs T , a value of the spreading parameter Sfit. These values are summarized in Table 7.2. We remark that the values obtained for Sfit are really close for the three compositions of the emulsion aqueous phase (Sfit = (9.5 ± 0.8) mN/m averaged over the three compositions), as expected from the superimposition of the Rph vs T curves (Figure 7.22). The values of Sfit can be directly compared to macroscopic measurement of the spreading parameter. The relevant surface tensions are presented in Table 7.2.
The value of γair/oil is measured with a Wilhelmy plate tensiometer and is equal to 29.6 mN/m. The surface tension of the aqueous phases of different compositions, γair/aq, are also measured with a Wilhelmy plate tensiometer and are reported in Table 7.2. The interfacial tension between the oil and aqueous phases, γaq/oil, is measured thanks to a spinning drop tensiometer (see Appendix A.2). The values are reported in the second column of Table 7.2. From these surface tension measurements, one can estimate the
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Chapter 7. Playing with emulsion formulation to tune the perforation of liquid sheet values of the spreading coefficient denoted Smeasured and reported in the third column of Table 7.2.
For the three aqueous phase compositions Smeasured >0, which is a prerequisite for Marangoni spreading. The values measured for Smeasured for the three compositions of the emulsion aqueous phase are comparable (Smeasured = (6.2± 2.9) mN averaged over the three compositions) highlighting a similar tendency of oil droplets to spread over the aqueous phase of different compositions. The values of Smeasured are in quantitative agreement with the values of the spreading coefficient deduced from the fits, Sfit. We remark that the values of Sfit are systematically larger than the values of Smeasured, which suggest that the relevant air/aqueous phase surface tension for the pre-hole widening dynamics is not the equilibrium one, as explained in details for emulsions stabilized by SDS (section 7.2.3.1).
emulsion aqueous γair/aq γaq/oil Smeasured Sfit
phase composition (mN/m) (mN/m) (mN/m) (mN/m)
CCpCl=0.9 mM 42.7 3.8 9.3 10.1
CCpCl=0.9 mM and CNaCl=20 g/L 35.4 0.7 5.1 9.8
CCpCl=0.9 mM, 34.3 0.6 4.1 8.6
CNaCl=20 g/L and CF108=5 g/L
Table 7.2: Values of γair/aq and γaq/oil for the three different compositions of the emul-sion aqueous phase and values of Smeasured calculated from these values with γair/oil=29.6 mN/m. The values of Sfit extracted from the fit of the evolution of Rph vs T are also reported.
In conclusion, we have seen that the addition of salt and amphiphilic copolymer in the emulsion aqueous phase do not modify the widening dynamics of pre-holes and so the spreading of oil droplets at the air/aqueous phase interface. As the spreading behavior is the same for the different compositions of the emulsion aqueous phase, we will now investigate the influence of the compositions on the first step of the perforation mechanism, i.e. the entering of oil droplets at the air/aqueous phaser interface.
7.3.4.2 Entering of emulsion oil droplets at the air/aqueous phase interface We investigate the entering properties of emulsion oil droplets at the air/aqueous phase interface thanks to the entering experimental set-up described in section 7.2.3.2.
In Figure7.23 is plotted the evolution of the surface tension measured at the air/aqueous phase interface during the entering of emulsion oil droplets. Three emulsion aqueous phase compositions are investigated (the same as for the study of the pre-hole widening dynamics):
1. CCpCl=0.9 mM,
7.3. Emulsions stabilized by cationic surfactants 185
2. CCpCl=0.9 mM and CNaCl=20 g/L,
3. CCpCl=0.9 mM, CNaCl=20 g/L and CF108=5 g/L.
For each curve, we observe at short time a plateau value corresponding to the equilibrium surface tension of the emulsion aqueous phase. The black arrows indicate the time of injection of emulsion oil droplets in the Petri dish. For the emulsions with aqueous phase composed of CCpCl=0.9 mM and CCpCl=0.9 mM, CNaCl=20 g/L and CF108=5 g/L, we observe a plateau value of the surface tension during the whole experiment (1000 s, i.e. 650 s after the injection of emulsion below the interface). For the emulsion with the aqueous phase composed of CCpCl=0.9 mM and CNaCl=20 g/L, we observe a sharp decrease of the surface tension around 100 s after the injection. The decrease of the surface tension corresponds to the entering and spreading of oil droplets at the interface.
300 400 500 600 700 800 900 1000
26 28 30 32 34 36 38 40 42 44
surface tension (mN/m)
t (s)
CCpCl=0.9 mM
CCpCl=0.9 mM, CNaCl=20 g/L
CCpCl=0.9 mM, CNaCl=20 g/L, CF108=5 g/L
Figure 7.23: Time evolution of the surface tension of the aqueous phase solutions to monitor the entering of emulsion oil droplets at the air/aqueous phase interface for emul-sions stabilized by CpCl with different concentrations of NaCl and Plutonic F108 in the aqueous phase. The exact compositions of the emulsion aqueous phase are indicated in the legend. Black arrows indicate the injection time of the emulsion.
In conclusion, for the emulsion stabilized by CpCl with a high concentration of NaCl (20 g/L) in the aqueous phase, the emulsion oil droplets enter the air/aqueous phase in-terface relatively rapidly (tentering = (94±14) s) after the injection of the emulsion whereas for the emulsions stabilized by CpCl and by CpCl with high concentrations of NaCl (20 g/L) and Pluronic F108 (5 g/L), emulsion oil droplets never enter the air/aqueous phase interface during the experiment time (i.e. tentering > 650 s). Hence, the addition of NaCl
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Chapter 7. Playing with emulsion formulation to tune the perforation of liquid sheet in the aqueous phase of emulsion stabilized by CpCl promotes the entering of oil droplets at the air/aqueous phase interface. On the contrary, the addition of an amphiphilic copolymer (Pluronic F108) in the aqueous phase of emulsion stabilized by CpCl and NaCl hinders the entering. The physical origin of the influence of the salt and copolymer concentrations on the entering of oil droplets at the air/aqueous phase interface will be discussed in the next section.
7.4 Discussion
We have seen that the addition of salts or amphiphilic copolymers on emulsions sta-bilized by ionic surfactants can trigger or inhibit the perforation process. We have shown that these two parameters do not modify the spreading properties of emulsion oil droplets at the air/aqueous phase interface but strongly alter the entering of oil droplets at the in-terface. In this section, we rationalize the influence of the salt and amphiphilic copolymer concentrations on the entering of oil droplets at the air/aqueous phase interface.
The entering and spreading of oil droplets at the air/aqueous phase interface are thermodynamically described by the entering, E, and spreading, S, coefficients. Those parameters have been previously defined (Equation7.1 and 7.2). Positive values of these coefficients indicate that it is thermodynamically favorable for an oil droplet to enter and spread at the interface. In Table 7.3 are summarized the values of the entering and spreading coefficients for the different compositions of the aqueous phase of the emulsions that we have investigated. The values reported are the ones calculated from the macroscopic measurement of the various surface tensions. In Table 7.3 are gathered data for emulsions stabilized by anionic surfactants (SDS) and by cationic surfactants (CpCl).
As already highlighted, all the values of E and S are positive indicating that for all the investigated systems, it is thermodynamically favorable for an oil droplet to enter and spread at the air/aqueous phase interface. Hence, the two necessary conditions for the perforation mechanism are fulfilled. However, these two conditions are necessary but not sufficient. As highlighted by our experimental data, for some compositions of the emulsion aqueous phase (CSDS=2.5 g/L, CNaCl=10 g/L; CCpCl=0.9 mM; CCpCl=0.9 mM, CNaCl=20 g/L, CF108=5 g/L ), very few perforation events are observed, whereas for other compositions (CSDS=0.1 g/L, CNaCl=10 g/L; CSDS=2.5 g/L, CNaCl=20 g/; CCpCl=0.9 mM, CNaCl=20 g/L), a large number of perforation events are observed (see Table 7.3), although E and S are positive for all emulsion compositions. An important feature to keep in mind is that positive values of E and S only indicate that it is thermodynamically favorable for oil droplets to enter and spread at the air/aqueous phase interfaces. However such thermodynamic approach does not consider the energy barriers that can kinetically
As already highlighted, all the values of E and S are positive indicating that for all the investigated systems, it is thermodynamically favorable for an oil droplet to enter and spread at the air/aqueous phase interface. Hence, the two necessary conditions for the perforation mechanism are fulfilled. However, these two conditions are necessary but not sufficient. As highlighted by our experimental data, for some compositions of the emulsion aqueous phase (CSDS=2.5 g/L, CNaCl=10 g/L; CCpCl=0.9 mM; CCpCl=0.9 mM, CNaCl=20 g/L, CF108=5 g/L ), very few perforation events are observed, whereas for other compositions (CSDS=0.1 g/L, CNaCl=10 g/L; CSDS=2.5 g/L, CNaCl=20 g/; CCpCl=0.9 mM, CNaCl=20 g/L), a large number of perforation events are observed (see Table 7.3), although E and S are positive for all emulsion compositions. An important feature to keep in mind is that positive values of E and S only indicate that it is thermodynamically favorable for oil droplets to enter and spread at the air/aqueous phase interfaces. However such thermodynamic approach does not consider the energy barriers that can kinetically