# Sedimentation of microparticles in Highly Concentrated Non-Newtonian Emulsions
## 1 Introduction  
In many areas of industry, such as food [1], pharmaceuticals [2] or cosmetics [3], one can find many products consisting of an oil and an aqueous phase, which most often form dispersions called emulsions. Often, solid particles also appear in these systems. From the perspective of product quality, it is important that such three-phase systems remain stable [4], i.e., that no phase separation occurs over time, because such a product will not be uniform throughout its volume and may lose its properties [5]. Both emulsion-destabilization processes, such as droplet coalescence and creaminess, and solids-sedimentation processes can occur [6]. While emulsion stability can be maintained with various types of surfactants [7; 8; 9], the sedimentation process of solids is more difficult to control. Of course, there are stabilizers that, when added to a liquid, affect its rheological properties and thus indirectly ensure the stability of the system [10], but in many cases, their use is impossible or even disadvantageous. In addition, nowadays one strives for products with the simplest possible composition, which will be as free of artificial additives as possible since such products are the most preferred by consumers. Therefore, if it was possible to predict the intensity of the process of sedimentation of solids in such systems depending on the parameters of emulsions and particles, it would be possible to design such products in which stability depended on the properties of the medium itself withoutthe introduction of additives. However, this requires thorough knowledge of the mechanisms and phenomena occurring during this process, which requires detailed experimental studies, which was the motivation of this study. Sometimes, instead of maintaining stable three-phase systems, it becomes a matter of separating them. Such is the case when separating oil wastewater from solids, such as wastewater generated after a machining process [11; 12]. Such liquids are highly emulsified and have metal particles. Separation of such systems is not easy. Passing such substances through filters is connected with high energy expenditure, and using chemical methods causes the creation of toxic compounds [13]. All this also contributes to environmental poisoning and high disposal costs. Therefore, it seems to be the most economical but also ecological to subject such substances to spontaneous separation processes. While the separation process of the emulsion itself may be difficult to achieve in this way, the sedimentation of solids is possible. However, to be able to design such processes, it is also necessary to have a thorough knowledge of the mechanisms occurring during the sedimentation of solids in emulsions, which was another motivation for this work. The sedimentation process of solid particles in highly concentrated emulsions is a very complex issue and is poorly studied in the literature. An accurate theoretical description is known only for the sedimentation of single particles in an unconfined liquid with Newtonian properties, for which the flow resistance is described by the well-known Stokes' law [14]. In the case of multi-particle sedimentation in a confined liquid, the process becomes more complicated. In such a situation, the sedimenting particles displace the liquid; i.e., they fall in a liquid flowing in a countercurrent to the falling particles rather than in a stationary liquid, as in the case of single-particle fall [15]. This results in a lower sedimentation velocity. Equal correlations are known to account for this decrease in velocity, e.g., the Richardson-Zaki correlation [16]. The mechanism of solid particle fall is further complicated in the case of emulsions with concentrations above 50% that exhibit the properties of shear-thinning non-Newtonian liquids [17; 18]. There are papers [19; 20; 21; 22] devoted to modeling the falling of solid particles in a non-Newtonian fluid. However, these works refer to single particles and do not consider the interaction between a cluster of particles.