## 4 CFD Simulation of Mixing Processes
### CFD Modeling of Laminar and Turbulent Mixing  
CFD provides a powerful framework for analyzing mixing processes in food engineering, enabling detailed visualization and quantification of flow characteristics such as velocity fields, shear zones, vorticity, and RTDs. Whether operating in laminar, transitional, or turbulent regimes, CFD delivers insights into mixing performance that are often inaccessible through experimental methods, particularly when working with opaque, heterogeneous, or shear-sensitive food systems. Understanding flow behavior across different regimes is essential for designing efficient mixers, optimizing energy use, and ensuring consistent product quality [52]. In laminar mixing, flow is characterized by the dominance of viscous forces and an absence of turbulent fluctuations, typically occurring at Reynolds numbers below approximately 2000. This regime is common in high-viscosity food systems such as doughs, batters, emulsions, and pastes. Mixing in such systems is governed primarily by convective transport driven by impeller or screw rotation, shear-induced deformation of fluid layers, and limited molecular diffusion across interfaces. CFD models in the laminar regime can directly solve the Navier-Stokes equations without incorporating turbulence models, offering both computational efficiency and accuracy. For non-Newtonian fluids, shear-dependent viscosity models--such as the power-law or Herschel-Bulkley models--are implemented to accurately reflect the fluid's rheological behaviour [53]. CFD simulations under laminar conditions provide key outputs including detailed velocity and shear rate distributions, which are particularly important for evaluating structural transformations in protein-rich or viscoelastic systems. Additional metrics such as mixing indices and the intensity of segregation help quantify spatial homogeneity, while RTD analysis supports process monitoring and control, especially in continuous systems. Optimization efforts in laminar mixing often focus on refining impeller geometry, adjusting rotation speeds, and improving baffle placement to reduce dead zones and enhance fluid circulation [54]. Turbulent mixing, by contrast, occurs at Reynolds numbers typically above 4000, where inertial forces dominate and the flow becomes chaotic and time-dependent. This regime is encountered in low-viscosity systems, including slurries, thin emulsions, and liquid-liquid dispersions processed in high-speed mixers such as rotor-stator devices or impeller-based reactors. Turbulence enhances mixing through the rapid generation and dissipation of eddies, which stretch and fold fluid elements, resulting in high shear rates and efficient macro- and micro-scale blending. These conditions are favorable for droplet breakup, solid dispersion, and rapid emulsification [55]. Due to the inherent complexity and computational cost of resolving turbulent flows, DNS is rarely feasible for industrial-scale systems. Instead, CFD relies on turbulence models to approximate the effects of turbulent fluctuations. The RANS models are the most widely used, with variants such as the k-\(\varepsilon\) model providing robust performance for high-Reynolds-number flows, and the k-\(\omega\) model offering improved accuracy near walls and in confined geometries. The Reynolds Stress Model (RSM) allows for anisotropic turbulence modeling in swirling or complex flows. For more detailed resolution of transient mixing dynamics, LES is employed to capture large-scale turbulent structures while modeling the smaller eddies [56]. CFD simulations of turbulent mixing yield quantitative maps of turbulent kinetic energy (TKE), energy dissipation rates, and mixing time scales, all of which are essential for process optimization and scale-up. In multiphase systems, simulations also predict droplet or bubble size distributions and their evolution during mixing, supporting the design of emulsification or aeration processes.