Mayonnaise is a stable liquid-liquid, oil-in-water, emulsion with high content of the disperse phase. The production of mayonnaise is a typical mixing process, in which the ingredients (i.e. egg yolk, vinegar, oil and water) are first mixed together in large stirred vessels at moderate rotational speed. Then the formed emulsion is finally fluxed into a high-shear mixer, where the oil droplets undergo breakage until the final size distribution is reached. This last step is crucial to fine tune the droplet size distribution, in order to determine the properties of the final product, such as structure, stability over time, taste and colour. In this work, we aim to model the last step of the production process by means of a Computational Fluid Dynamics approach coupled with a Population Balance Model (CFD-PBM) and with a Dissipative Particle Dynamics (DPD) model. A schematic representation of the investigated apparatus, so called cone mill mixer (1), is reported in Figure 1. It is constituted of a solid conical frustum rotor inside a slightly larger stator of the same shape, forming a small gap in which the emulsion flows (as it can be seen in Figure 1) and experiences high-shear rates, due to the high rotational speed of the rotor. To properly describe the non-Newtonian dynamics of the emulsion, the fluid is considered as a shear thinning pseudo single phase. In order to describe the evolution of the droplet size distribution, the Population Balance Equation is employed (2), in which coalescence and breakage of oil droplets are taken into account by appropriate coalescence and breakage kernels, which depend on local flow conditions. These kernels are also function of the local concentration of the surface active molecules contained in mayonnaise, namely phospholipids and apoproteins. In order to understand the role of these molecules in stabilizing the oil-water interface and with the final objective of improving the coalescence and breakage kernels currently employed in CFD-PBM simulations, a molecular modelling technique is used here for the first time in this context. Molecular Dynamics (MD) is employed to build a coarse-grained engineering model, based on DPD, to describe the molecular interactions between phospholipids and apoproteins and the oil-water interface and extract useful information, that can be in turn used in the development of coalescence and breakage kernels. MD simulations are run with the software GROMACS, whereas DPD simulations are run with the commercial software CULGI-Siemens. CFD-PBM simulations are performed with the open-source code OpenFOAM (version 6.0).
The flow field show particular patterns in agreement with experimental data and other numerical simulations (3). CFD-PBM results are reported in terms of the mean oil droplets diameter in Figure 2, along a longitudinal section of the cone mill. As expected, the mean droplets size decreases along the flow direction, since droplets undergo breakage induced by the high-shear rates inside the mixer.
This effort is carried out in the context of the VIMMP project (www.vimmp.eu), where the entire workflow will serve to devise a marketplace for generic multiscale and multiphysics simulations. The VIMMP project has received funding from the European Union’s Horizon 2020 Research Innovation Programme under Grant Agreement n. 760907.
References
(1) A. Dubbelboer, J. J. M. Janssen, H. Hoogland, E. Zondervan, J. Meuldijk, Chem. Eng. Sci. 148 (2016) 32–43.
(2) D. Li, Z. Gao, A. Buffo, W. Podgorska, D. L. Marchisio, AIChE J. 63 (2017) 2293–2311.
(3) X. Li, J. Zhang, L. Xu, J. Hydrodyn. 26 (2014) 431–435.
