## 4 CFD Simulation of Mixing Processes  
### Types of Mixers and Their Working Principles  
Mixing is a fundamental mechanical operation in food processing, serving to homogenize ingredients, disperse particulates, form emulsions or foams, and induce targeted microstructural transformations. The effectiveness of mixing depends not only on the operational parameters but also on the type of mixer and the rheological characteristics of the food material. The diversity of materials handled in the food industry--ranging from powders and slurries to viscous doughs and multiphase emulsions--has led to the development of a wide array of mixing technologies, each adapted to specific process requirements and physical states of the ingredients [44]. Mixers are commonly classified based on the phase composition of the processed material and the dominant mixing mechanism they employ. In solid-solid systems, ribbon blenders and paddle mixers are widely used. Ribbon blenders feature a horizontal trough with helical ribbons that rotate to create counter-current flows, whereas paddle mixers use flat or curved blades to move material in multiple directions. Both designs rely primarily on convective mixing and are well suited for fragile, dusty, or hygroscopic powders [46; 47]. For high-viscosity and viscoelastic systems such as doughs and batters, planetary and spiral mixers are preferred. Planetary mixers utilize an agitator that rotates on its axis while orbiting around a central shaft, ensuring effective mixing throughout the bowl. Spiral mixers, characterized by a rotating spiral agitator and stationary bowl, are optimized for gluten development and hydration uniformity in bread doughs. These systems are widely adopted in bakery operations. High-shear mixers, including rotor-stator systems, are applied in processes requiring emulsification, dispersion, and droplet size reduction. The rotor rotates rapidly within a stationary stator, generating intense shear and turbulence that disrupt droplet structures and facilitate mixing of immiscible phases. These systems are common in the production of sauces, dairy emulsions, and mayonnaise [48]. In continuous operations, static mixers play a vital role. These devices contain stationary internal elements that divide and recombine flow streams, inducing mixing through flow redirection rather than mechanical agitation. Static mixers are energy-efficient and well suited for blending miscible liquids or introducing additives into flowing systems [49]. Tumbling mixers, such as V-blenders and double-cone mixers, operate by rotating a container filled with the material. Mixing is achieved by gravitational motion, making them ideal for gentle handling of delicate or abrasive solids. Although mixing rates are relatively low, these devices are advantageous in pharmaceutical and nutritional powder processing where minimal shear is desirable. Extruder-mixers, including single- and twin-screw configurations, integrate transport, mixing, and thermal processing in a continuous format. The geometry of the screw--defined by pitch, length, and mixing element design--determines the level of shear and residence time, which are critical parameters in thermomechanical applications such as snack production or plant-based meat extrusion. Finally, fluid and pneumatic mixers rely on gas flow (typically air or steam) to agitate solid or liquid systems. These are found in fluidized beds and bubble column reactors, where mixing is induced by the motion of gas bubbles through the material. Such systems are prevalent in drying and coating processes for snacks and cereals. The mechanisms underlying mixing can be broadly categorized as convective, diffusive, shear-induced, or turbulence-driven. Convective mixing involves the bulk movement of material from one location to another and dominates in systems such as ribbon and paddle mixers. Diffusive mixing arises from random particle motion and is particularly relevant in dry powder blending.