Effect of preparation temperature and wax concentration on bubble formation
We first optimised the temperature to which the suspension of wax microparticles in sunflower oil was heated prior to mixing and bubble formation. The concentration of wax was 2.5% w/v in all the experiments. After heating to the desired preparation temperature, each sample was shaken for 2 min on the vortex mixer. The temperature at the end of mixing was measured and was found to have decreased by ΔT ≈ 20 − 40 °C, corresponding to a cooling rate of 10 − 20 °C/min. The samples were allowed to cool down to room temperature after mixing and prior to imaging.
Figure 1a shows optical micrographs of samples prepared with different preparation temperatures in the range T = 50 − 120 °C. For preparation temperatures below T = 65 °C, which corresponds to the first melting peak of the wax, few or no bubbles are formed. A significant number of bubbles are formed in the range T = 80 − 115 °C. The bubbles formed in this temperature range are mostly non-spherical. At T = 120 °C, the number of bubbles is reduced again (SI Fig. 2). The bubbles formed for temperatures below T = 65 °C and at T = 120 °C tend to be spherical and to possess smooth interfaces. Micrographs with higher magnification in Fig. 1b show non-spherical shapes and buckled interfaces for T = (75 − 110) °C, which are characteristic of bubbles stabilised by elastic layers. Further, above 65 °C, fewer wax crystals were prominent in the bulk. The bulk appears like a network with fine material present in it.
The samples were stored at room temperature (SI Fig. 3a), and the stability of the bubbles was tested by optical microscopy after 1 week (SI Fig. 3b) and again after 4 months (SI Fig. 3c). Except for the bubbles prepared at temperatures between T = 80 − 110 °C, the bubbles in the other samples had shrunk significantly with respect to their initial size and many had disappeared at the locations where there were previously many bubbles.
We then tested the effect of wax concentration while keeping the preparation temperature and the mixing time the same for all the samples, T = 90 °C and 2 min, respectively. The wax concentration was varied in the range 0.5–7.5% w/v. Below a concentration of 2.5% w/v, the bubbles were few and they dissolved within minutes to hours (SI Fig. 4). Above 2.5% w/v, the sample became very viscous as it cooled during mixing, resulting in fewer bubbles and optically opaque samples which were difficult to image using optical microscopy.
Finally, keeping the wax concentration fixed at 2.5% w/v, the mixing times were varied from 30 s to 3 min for a narrower range of temperatures, T = 75 − 95 °C. The temperatures at the end of mixing were recorded and were found to have decreased by ΔT ≈ 30 − 40 °C for mixing times of 2–3 min. The number of bubbles increased with increasing mixing time up to 2 min. For longer mixing time, the number of bubbles did not increase significantly (SI Fig. 5).
Based on these results, we selected the parameters of the oleofoam preparation protocol to be used in the rest of the study: preparation temperature T = 90 °C, wax concentration of 2.5% w/v and mixing time of 2 min, followed by cooling to room temperature before use. All the results presented in Figs. 2, 3, 4, and 5 correspond to samples prepared with this protocol (see other details of protocol in “Results”).
Microscopic imaging of single bubble dissolution during heating
We studied the dynamic evolution of the size of single, isolated bubbles upon heating. We conducted three different experiments so as to gain insights into the roles of the bulk rheology of the oleogel network and of the interfacial rheology of the adsorbed crystal layer:
- 1.
Bare bubble in sunflower oil (control experiment).
- 2.
Wax-coated bubble: a bubble was extracted from the oleofoam and resuspended in sunflower oil; care was taken to ensure no bulk gel and crystals were left in the oil surrounding these bubbles. The interfacial layer was still present on the bubbles, as confirmed by their buckled interface.
- 3.
Bubble within oleofoam, i.e. a bubble in the sample as prepared. These bubbles were therefore coated with an interfacial layer of wax crystals and also embedded in the bulk gel network.
All bubbles considered had initial radii in the range R0 = 100 ± 20 μm. Care was taken to observe individual, isolated bubbles, in order to prevent unwanted Ostwald ripening effects from neighbouring bubbles, particularly important for bare bubbles and wax-coated bubbles. The samples were inserted in the temperature-controlled stage at an initial temperature T0 = 21 °C. The temperature was then increased to the desired final temperature at a heating rate of 5 °C/min. The temperature was then maintained constant while images were recorded every 10 s. The values of the final temperature were chosen below the melting range of the wax, T1 = 25 °C, and after the first melting peak, T2 = 74 °C.
The dissolution behaviour of the three types of samples at the two different final temperatures is shown in Fig. 2. The radius R has been normalised by the initial (effective) bubble radius, R0. Time has been normalised by t∗, the theoretical dissolution time of a bare bubble in oil, with the same initial radius R0, at a reference temperature T = T1 = 25 °C, and including a correction factor to account for the presence in the experiments of a gas impermeable wall next to the bubbles (see “Foam preparation”). This theoretical dissolution time is computed using the theory by Epstein and Plesset (1950) and is given by \( {t}_{\mathrm{th}}=\frac{R_0^2}{3D{k}_{\mathrm{H}}}\left(\frac{R_0\rho }{2{M}_{\mathrm{w}}\sigma }+\frac{1}{BT}\right) \). The gas diffusivity in the liquid, D; the liquid density, ρ; the gas-liquid surface tension, σ; and Henry’s constant, kH, are evaluated at the reference temperature T1. Mw is the molar mass of the gas, and B is the universal gas constant. The correction for confinement effects gives t∗ = tth/ ln 2 (Duncan and Needham 2004).
First, the control experiment with bare bubbles in sunflower oil, shown in Fig. 2a, provides qualitative information on the net effect of the change in physicochemical properties of the air-oil system with increasing temperature. A bare bubble heated to T2 = 74 °C dissolves approximately 5 times faster than a bare bubble held at a temperature T1 = 25 °C. For the wax-coated bubbles, it can be seen in Fig. 2b that also in this case, the rate of dissolution increases with increasing temperature. In Fig. 2c, it can be seen that a bubble within the oleogel at T1 = 25 °C barely changes radius over a timescale of several times the dissolution time of a bare bubble, t∗. Bubbles within the oleogel at T2 = 74 °C dissolve on a timescale that is only slightly slower than the case of wax-coated bubbles. Finally, in Fig. 2d, the dissolution behaviour of the three types of bubbles at T = 25 °C are compared directly: wax-coated bubbles dissolve on a much slower timescale than bare bubbles, while the dissolution of bubbles in the oleofoam is practically arrested. Additional data sets for wax-coated bubbles (n = 10) show a large variability in dissolution times, due to the variability in wax surface coverage between different bubbles. Nevertheless, the additional data (provided in Table 1 in the Supporting Information) confirm the qualitative trends shown in Fig. 2.
Figure 3 shows image sequences for three representative experiments at T1 = 25 °C, below the melting range of the wax. The bare bubble dissolves completely (Fig. 3a). For a wax-coated bubble, the interfacial layer remained solid, and in a few instances, it could be seen unfolding around the bubble (Fig. 3b). Over the same timescale, a bubble embedded in the oleogel remains stable (Fig. 3c).
Rheological measurements
In order to understand the increased bubble stability against dissolution in the oleofoam, we have characterized the bulk rheology of the pure sunflower oil, a suspension of undissolved wax particles in oil, the oleogel, and the oleofoam. Bulk elasticity, for instance, may stabilize bubbles of all sizes as reported by Kloek et al. (2001).
Flow rheology of wax suspensions, oleogels, and oleofoams
Figure 4a provides an overview of the influence of temperature on the four systems studied. The heating rate was dT/dt = 10 °C min−1. These measurements were performed using smooth boundary conditions; we therefore applied a shear rate of 50 s−1 to suppress wall slip. The viscosity of the pure sunflower oil follows an Arrhenius-like behaviour (see Esteban et al. (2012)). For temperatures above 70 °C, the viscosity of all four systems is similar, confirming that most solid content has melted. For lower temperatures, the viscosity of the oleogel and oleofoam deviate significantly from the wax suspension. Repeat experiments show a sample variability of around ±30% for the oleogel and the oleofoam, confirming that the preparation protocol and rheological characterization are sufficiently controlled. Comparison with the literature on waxy crude oils (Lorge et al. 1997; Dimitriou and McKinley 2014; Geri et al. 2017) suggests that, in our system, T = 70 °C roughly corresponds to the rheological wax appearance temperature below which wax crystals nucleate and grow in the oil to a sufficient extent as to form a percolating network. The presence of bubbles in the oleogel—producing the oleofoam—does not result in a dramatic change in rheology, most probably due to the small bubble volume fraction (Ducloué et al. 2015), or possibly because the foam releases the bubbles under strong shear.
Figure 4b offers a more in-depth understanding of the rheology of the oleogel at T = 25 °C using rough boundary conditions. The flow curve has been obtained for decreasing shear rates after a 20-s pre-shear step performed at 1000 s−1. Its shape is identical to the waxy crude oils below wax appearance temperature presented in Mendes et al. (2015) and Geri et al. (2017). The presence of a local stress minimum around \( \dot{\gamma}=0.1 \) s−1 is a signature of thixotropic behaviour below which the oleogel experiences ageing. Additional experiments with smooth boundary conditions (data not shown) confirm this flow curve shape down to the local minimum, below which wall slip significantly affects the measurements. The stress minimum of 0.35 Pa can be used as an estimate of the oleogel yield stress just after being stirred.
Oscillatory rheology of the oleofoam
Figure 4c shows an amplitude sweep of the oleogel at T = 25 °C using a rough geometry. Two runs have been performed, first for increasing strain amplitudes up to γ = 1000%, then—immediately afterwards—for decreasing amplitudes. We observe that the gel is initially stiff with a shear modulus around 16 kPa and a limited linear viscoelastic plateau, up to 0.2% in deformation. Experiments conducted with smooth boundary conditions yield G′ = 9 kPa in the linear plateau, which is most likely due to a combination of limited slip in the linear elastic regime and sample variability.
For strain amplitudes above γ = 1%, the gel quickly yields: the storage modulus G′ decreases so steeply (with an exponent below − 1) that the applied stress amplitude decreases with increasing deformation, indicative of the oleogel failure. The stress amplitude maximum reached before failure, τ = 43 Pa, is an upper bound of the yield stress for an initially undisturbed sample. More classical estimates—for instance, the G′ = G′′ crossover point (Dinkgreve et al. 2016)—result in a yield stress around 21 Pa. We finally note that the data obtained for decreasing strain amplitude are not superposed to the data for increasing amplitude: after failure, the oleogel remains softer for all applied deformations. This is further evidence of thixotropic behaviour.
Finally, Fig. 4d shows the evolution of the storage and loss moduli of the oleogel during heating for an applied frequency of 1 Hz and with a smooth geometry. We set the strain to 0.05%—in the linear viscoelastic regime—to limit slip and damage to the microstructure. The temperature ramp is measured to be dT/dt = 7 °C/min. The shear modulus at T = 25 °C is slightly lower than in Fig. 4c, indicating moderate wall slip. The measured shear modulus then decreases sharply and reaches values as low as 100 Pa for T ≥ 40 °C. At this point, the instrument torque falls below 0.5 μN m, which severely limits our measurement precision.
Dilatational rheology of wax-coated air-oil interface
Interfacial rheological effects due to the wax layer (see Fig. 3b) can also contribute to bubble stability against dissolution (Kloek et al. 2001). Since such effects cannot be investigated directly on the oleofoam bubbles, we used a pendant drop geometry as model system for a wax-coated air-oil interface.
To produce a wax-coated air-oil interface on a pendant drop, we deposited a layer of hot oleogel on the surface of a clean oil drop as described in “Dilatational interfacial rheology.” After deposition of the oleogel, the drop was first expanded to facilitate spreading of the wax over the interface. The drop volume was then decreased to compress the interface, mimicking the conditions relevant to bubble dissolution. Figure 5a shows an image sequence during drop compression. The drop area, A, is normalised by the area corresponding to the maximum volume, A0. In the experiment shown in Fig. 5, it is A0 = 31.25 mm2. Compression below A/A0 = 0.82 led to drop shapes characteristic of elastic interfaces (Knoche et al. 2013; Hegemann et al. 2018). As shown in Fig. 5a, the effect is more pronounced for A/A0 = 0.46. Magnified images of the drop surface reveal an interfacial layer of wax crystals, but it is not possible to assess whether it is a multi-layer or a single layer, and to confirm that it reproduces the microstructure of the layer on bubbles in an oleofoam (see Fig. 8 in Supporting Information).
The transition from liquid- to solid-like behaviour of the interfacial layer can be identified quantitatively by plotting the meridional curvature profile of the drop, κ(z). For a fluid interface, the curvature varies linearly with height, obeying the Young-Laplace equation. For an elastic interface, the profile is no longer linear (Nagel et al. 2017). Figure 5b shows that the deviation from linearity increases for decreasing A/A0.
The interfacial compression modulus, Ed, can be estimated as the Gibbs modulus, EGibbs, in the range where the interfacial layer is fluid-like, and can be determined from the drop shape fitting elastometry (DSFE) in the elastic regime as \( {E}_{\mathrm{d}}^{\mathrm{DSFE}} \) (see “Dilatational interfacial rheology” for details). In the DSFE, the strains are defined with respect to an elastically relaxed reference shape profile, in which the surface stress is isotropic. Compression below this state gives rise to elastic extra-stresses. We selected the reference state as A/A0 = 0.82 based on the curvature profiles (Fig. 5b). Both the Gibbs modulus, EGibbs, and the compression modulus obtained from the DSFE, \( {E}_{\mathrm{d}}^{\mathrm{DSFE}} \), are plotted as a function of area in Fig. 5c. Drop shape fitting elastometry, strictly applicable for purely elastic interfaces, is expected to give better estimates of Ed for compressed states below the reference state (grey shaded region) while EGibbs is expected to be a more reliable measure for fluid interfaces (outside shaded region). For reference, EGibbs is shown also in the elastic regime (empty symbols). Within the elastic regime, we find an approximate value of the compression modulus Ed ≈ 40 mN/m, to be used for testing the Gibbs criterion. The interfacial shear modulus, also found by the DSFE, was small compared with Ed, in the range 0.02 mN/m ≤G2D≤ 0.12 mN/m.