Diffusing Wave Spectroscopy (DWS) is a method of analysis specifically suited to study the rheological properties of turbid samples. This powerful optical technique uses the fluctuations of coherent laser light that is scattered multiple times within a sample as the basis for measurement [1,2]. The DWS RheoLab from LS Instruments is a versatile tool that makes use of DWS to conduct such measurements.
To perform DWS properly there must be well-defined scattering objects embedded in the sample. These objects may be a natural feature of the sample or, in the case of transparent samples, they can be added for the purpose of enabling DWS measurements.
In both cases, these objects are termed tracer particles and ideally have high optical contrast with uniform dispersion across the sample. However, this uniformity may not be possible in emulsions such as lotions, creams, or milk, as the scattering objects are liquid droplets instead of solid particles, affecting the droplet size distribution.
This article has been written to demonstrate that, regardless of this polydispersity, emulsion droplets can act as natural tracers to probe the rheological properties of emulsions using DWS. This methodology is applied to a model system which is a 20 vol.% oil-in-water emulsion with xanthan in the continuous phase as a viscosity modifier. Later in the article, measurements of the viscoelastic properties of the emulsion obtained by DWS microrheology are compared to those gained through mechanical rheology.
In order to conduct the experiment a continuous phase is prepared by dissolving 0.55 wt.% xanthan and 0.3 wt.% Cosmocil as an antimicrobial agent in distilled water. This solution is heated for 3 hours to 85 °C to avoid sensitivity to thermal history  and subsequently stirred for 48 hours.
The emulsion is prepared by heating 164 g of the continuous phase to 50 °C and adding 2.1 g Tween 80. During homogenization, 34 g of almond oil (density: 0.91 g/mL) is added and then subsequently homogenized further for 12 minutes. All measurements are performed at a temperature of 25 °C and 14 days after preparation of the samples.
Characterization of the Emulsion
The first step is to investigate the emulsion by confocal microscopy to access the droplet size. Figure 1 shows an image of the emulsion. It has been stained using lipophilic Nile red to create a greater contrast in the droplets.
Figure 1. Confocal image of the emulsion stained with Nile red. The inset shows the corresponding droplet size distribution.
It can be clearly seen that the oil droplets are well dispersed and fully arrested in the xanthan matrix of the continuous phase. The corresponding droplet size distribution can be seen in the accompanying inset.
DWS on the emulsion is performed in cuvettes with thickness L=2 mm in transmission geometry. For calibration, a dispersion in water of 1.0 wt.% PS particles with a diameter of 980 nm is used. The measured value for the transport means free path l* of the emulsion is 226 µm. For the tracer particle diameter, a value of 1.2 µm is used, which corresponds to the main peak in the inset of Figure 1.
Mechanical rheology measurements used a Malvern Bohlin Gemini rheometer equipped with sand blasted plane-cone geometry (60 mm, 2°) and solvent trap. The storage G’ and loss moduli G’’ are measured in oscillation mode with a constant amplitude of 0.1, which is found to be in the linear viscoelastic range by performing an amplitude sweep at 1 Hz.
A comparison of the values for G’ and G’’ measured by DWS microrheology and mechanical rheology is seen in Figure 2. The data sets show good agreement for the overlapping frequency range.
Figure 2. Storage modulus (full symbols, full line) and loss modulus (open symbols, dashed line) of the emulsion. The data obtained from DWS (lines) agree well with the data obtained from the mechanical rheology (symbols).
There is a moderate volume fraction of the dispersed phase in the prepared emulsion, making the continuous phase the main contributor to the rheological properties. For the model system in this article, the continuous phase is a gel with 0.55 wt% xanthan and well known rheological properties [3, 4].
The continuous phase is measured separately by DWS microrheology and mechanical rheology. For mechanical rheology, the measurement parameters are the same as the ones used for measurements on the emulsion. DWS on the continuous phase was performed on a sample prepared by adding polystyrene (PS) particles with diameter 980 nm (dispersed in water) to a xanthan solution prepared as above but with 0.58 wt.% xanthan.
The resulting mixture contained 1.0 wt.% PS particles in a continuous phase with 0.3 wt.% Cosmocil and 0.55 wt.% xanthan. Therefore, the PS particles probe an environment corresponding to the continuous phase of the emulsion. DWS on the emulsion used cuvettes with thickness L=2 mm in transmission geometry. For calibration, a dispersion in water of 1.0 wt.% PS particles with a diameter of 980 nm is used. The measured value for the transport means free path l* of the emulsion is 398 µm.
The values for G’ and G’’ measured by DWS microrheology and mechanical rheology are compared in Figure 3. The data sets show excellent agreement in the overlapping frequency range, with the observed crossover frequency (where G’=G’’) of about 104 rad/s being in very close agreement with literature . When Figure 2 and Figure 3 are compared, it can be seen that the moduli of the emulsion are about 50% enhanced compared to the continuous phase whereas the overall shape of the curves is very similar. This confirms the previously stated hypothesis that for emulsions with moderate volume fraction the rheological properties are mainly determined by the continuous phase.
Figure 3. Storage modulus (full symbols, full line) and loss modulus (open symbols, dashed line) of the continuous phase only. The data obtained from DWS microrheology (lines) agree well with the data obtained from mechanical rheology (symbols).
In a crude approximation, the liquid droplets in an emulsion can be interpreted as suspended solid particles that increase the overall viscosity η with respect to the viscosity of the continuous phase η0 according to the Batchelor equation :
that yields, for a volume fraction φ = 0.2, an increase in G’’(ω) = ηω of 70%. The observed value of 50% is somewhat lower and might be explained by the polydispersity of the droplets that allows better packing.
DWS microrheology was applied to an oil-in-water emulsion and the results were compared to mechanical rheology, with very good agreement between the two techniques seen in the overlapping frequency range. As well as this, the continuous phase (xanthan solution) has been characterized separately by DWS microrheology and mechanical rheology and found in excellent agreement with each other and also with literature.
This shows how the droplets, i.e. the dispersed phase, may be used as tracer particles to probe the rheological properties of the emulsion. Moreover, as long as there is a known droplet size, it is demonstrated that DWS microrheology is well suited for the quantitative characterization of emulsions.
It is important that care is taken when the continuous phase of an emulsion is inhomogeneous on the length scale of the droplets. This makes a quantitative characterization of emulsions more difficult as the droplets probe a variety of different local environments . This was not the case in the investigated model system as the mesh size of the xanthan network at the chosen concentration was well below the droplet size, at around 40 nm .
Finally, the values obtained by DWS microrheology are highly reproducible and might thus allow the study of time-dependent properties of emulsions such as aging or stability.
 D.A. Weitz, and D.J. Pine, Diffusing-Wave Spectroscopy. In Dynamic Light Scattering; Brown, W., Ed.; Oxford University Press: New York, 652-720 (1993).
 D. Lopez-Diaz, and R. Castillo, Microrheology of solutions embedded with thread-like supramolecular structures, Soft Matter 7, 5926–5937 (2011).
 E. Choppe, F. Puaud, T. Nicolai, and L. Benyahia, Rheology of xanthan solutions as a function of temperature, concentration, and ionic strength, Carbohydrate Polymers 82 (2010).
 K.v Gruijthuijsen, H. Vishweshwara, R. Tuinier, P. Schurtenberger, and A. Stradner, Origin of suppressed demixing in casein/xanthan-mixtures, Soft Matter 8 (2011).
 S.R. Derkach, Rheology on the way from dilute to concentrated emulsions, Inter. Rev. Chem. Eng. 2 (2009).
 F.K. Oppong, L. Rubatat, B.J. Frisken, A.E. Bailey and J.R. de Bruyn, Microrheology and structure of a yield-stress polymer gel, Physical Review E 73 (2006).
This information has been sourced, reviewed and adapted from materials provided by LS Instruments.
For more information on this source, please visit LS Instruments.