Function Of Phase Volume Research Articles

Interpreting rheological behaviour of sugar-fat mixtures as a function of solids phase volume

Abstract Many confectionary items and food components are based on complex suspensions of hydrophilic sugar particles in a hydrophobic fat phase. We hypothesise that the rheology of these suspensions is defined by either the Maron-Pierce-Quemada (MPQ) model, which theoretically predicts the viscosity of hard spheres, or by the percolation model describing a network of attractive particles (gel). The rheology of two sugar-fat mixtures, sugar-shortening based biscuit-creams and chocolate, are characterised as a function of phase volume, particle size distribution (PSD) and emulsifier concentration. It is found that their rheological behaviour shows the formation of a network gel structure at sufficient concentration of sugar particles. We find that, upon addition of sufficient emulsifier, the suspension viscosity follows the MPQ hard sphere model, which only depends on phase volume and particle size distribution. Combining the use of the theoretical model and emulsifiers, we are able to decouple the effects of phase volume and particle size distribution from that of particle interactions. The results provide a theoretical basis for identifying levers to control the rheological behaviour of molten chocolate, biscuit-creams, and other sugar-fat based systems, which is relevant to food processing and sensory perception during consumption.

Analytically predicting the viscosity of hard sphere suspensions from the particle size distribution

Suspension rheology is of widespread importance to industry and research. Hard spheres represent a benchmark by which to compare other particle suspensions, and there are a variety of analytical and numerical models available to describe their rheology. However, it is experimentally challenging to produce ideal hard spheres, where surface forces are negligible between particles, and where phase volume is precisely defined. Beyond the dilute regime, the model by Maron and Pierce [1] and Quemada [2], which we refer to as the MPQ model, is commonly used analytically to describe the relative viscosity of hard sphere suspensions as a function of phase volume and a maximum packing fraction (ϕm). We show that obtaining ϕm from empirical fits can lead to misinterpretation of experimental data. We reveal that reasonable prediction of the viscosity is obtained using the MPQ model when ϕm is set to the geometric random close packing fraction ϕrcp, which is independently defined from the particle size distribution using the packing model of Farr and Groot [3]. This ‘theoretical’ approach is tested using a wide variety of experimental data on colloidal and non-colloidal hard spheres without need for any fitting parameters or empiricisms. In addition, plotting the inverse of the square-root of viscosity as a function of phase volume, which linearises the MPQ model, provides a convenient means by which to clearly see where suspensions deviate from the model due to such effects as particle aggregation, particle softness and measurement errors. We also demonstrate the necessity of this approach by accurately predicting the viscosity of microgel suspensions up to ϕrcp; empirical fits across the full data set are erroneous because particle deformation and viscoelasticity lead to values of ϕ>ϕrcp. This approach provides a suitable unambiguous theoretical baseline for comparison to experimental studies on suspension rheology involving polydisperse size distributions.

Experimental validation of the modified Avrami model for non-isothermal crystallization conditions

The modified Avrami model was found to accurately predict the induction time, maximum phase volume and dimensionality of crystal growth for stearic acid containing molecules when the experimental method employed measures as a function of phase volume. Four methods were examined to validate the model including: Fourier transformed infrared spectroscopy (FT-IR), differential scanning calorimetry (DSC), small deformation rheology and polarized light microscopy (PLM). PLM and FT-IR were able to detect the nucleation event prior to DSC and rheology. FT-IR and PLM provided the most accurate data due to the similarities between the experimental and fitted induction times (x0), maximal phase change (ymax) and the Avrami exponent (n). Further, the Avrami exponent, obtained from FT-IR, was sensitive to both the mode of nucleation and the dimensionality of crystal growth. Therefore, the apparent rate constants (kapp) obtained by FT-IR and PLM are useful in providing further insights into the kinetics of non-isothermal crystallization. The calculated apparent rate constants suggest a diffusion limited crystallization at slow cooling rates (i.e., below 5–7 °C min−1) and at cooling rates greater than 5–7 °C min−1, the incorporation of the gelator molecules onto the crystal lattice becomes limited by the reaction rate constant.