Many industrial, food and personal care products contain foams, predominantly liquid foams. Common examples include meringue, ice cream, hair mousse, shaving foam and beer foam.
The characteristics of these foams, such as foam consistency and overall consumer acceptability, and functionality of final products, are greatly influenced by their rheological properties.
Foams behave like an elastic solid with a yield stress at low stresses and as a liquid at stresses above the yield stress (Figure 1). Their bubble rearrangements greatly affect their flow behavior. Nonlinear rearrangement events largely influence flow mechanics at stresses above the yield stress due to transformation of gas bubbles from one tightly packed configuration to another.
Figure 1. Foam image showing how individual gas cells are jammed together to form a solid-like structure at rest
The Herschel-Bulkley Model
Since geometrical packing considerations will affect the bubble rearrangements, the observed rheology will be largely affected by bubble characteristics, such as bubble size or gas volume fraction.
The flow viscosity can be correlated to the gas volume fraction using several models. However, suggesting an appropriate model is difficult because of assumptions in the models and experimental errors.
The Herschel-Bulkley model can be used to describe the flow behavior of foams because they are Yield stress fluids:
Where, K = consistency and n = shear thinning index, which defines the degree to which a material is shear thickening (n>1) or shear thinning (n<1).
Figure 2 presents a typical shear stress-shear rate profile for foam obeying this model. The steady state stress needs to be measured at a range of shear rates and the resulting data need to be fitted by a Herschel-Bulkley model in order to evaluate the foam consistency.
Figure 2. Typical shear stress-shear rate profile for a foam conforming to the Herschel-Bulkley model (linear scaling)
The above process can be replicated for various foam gas volume fractions, followed by plotting of the resulting yield stress and foam consistency values obtained from the Hershel Bulkley fit for each gas volume fraction as a function of the gas volume fraction.
The dynamic properties of foams, such as liquid flow through the foam, drainage, film rupture or collapse of the foam, and coarsening or growth of the gas bubbles through gas diffusion pose difficulties in obtaining reliable and accurate foam rheology measurements.
Ensuring the formation of a stable foam wherein each of these dynamic effects is reduced during the experiment and a consistent way of producing the foam is critical in acquiring valuable information about the rheology and structure of foams.
The effect of the gap size and the existence of liquid films close to the wall surface forming an effective slip layer are the other factors that need to be taken into account for obtaining accurate foam rheology measurements.
The measured rheological response will be greatly affected by the ratio of the size of the foam bubble to the size of the gap within which it will be measured. When the foam bubble diameter is much smaller than the gap size, it is possible to obtain only a continuum description of the bulk foam.
It is possible to use serrated or sandblasted parallel plate geometry or a vane tool to reduce the effect of wall slip caused by the presence of a liquid layer near the wall. The vane tool can be introduced into the test specimen with least disruption to the structure.
This experiment performed rotational rheometer measurements on a commercial shaving cream by means of a Kinexus rheometer, using standard pre-configured sequences in rSpace software.
The Kinexus rheometer was equipped with a Peltier plate cartridge and 40mm serrated parallel plates to prevent slipping of samples at the geometry surfaces.
The use of a standard loading sequence ensured the application of a consistent and controllable loading protocol on the sample. The sample was subjected to a range of shear rates, from 1 to 100s-1, to measure the data, which was then fitted with a Herschel-Bulkley model to determine yield stress and foam consistency. All rheology measurements were carried out at 25°C.
The shear stress-shear rate plot for the shaving foam fitted with a Herschel-Bulkley model is depicted in Figure 3. The fitting of the measured data by the model is very well with a correlation coefficient ≈ 1. The yield stress and the consistency index (K2) were found to be 52.23Pa and 12.44, respectively.
Figure 3. Flow curve for commercial shaving foam fitted with a Herschel-Bulkley model (logarithmic scaling)
Foams behave like an elastic solid and therefore exhibit yield stress behavior at low shear stresses and liquid like behavior beyond the yield stress.
A Herschel-Bulkley model can be used to describe the flow behavior by considering the yield stress and consistency as key fitting parameters.
This information has been sourced, reviewed and adapted from materials provided by Malvern Panalytical.
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