Gas–liquid–solid (G-L-S) mechanically agitated reactors are commonly used in chemical, pharmaceutical and bioprocessing applications due to their low operating costs and controlled and effective mixing. Computational Fluid Dynamics (CFD) is a powerful tool that enhances the understanding of flow dynamics, phase interactions and reactor performance. However, the CFD modeling of G-L-S mechanically agitated reactors is not extensively studied in the literature due to complex multiphase interactions, along with reactor design variations. This paper provides a critical synthesis of the literature, offering an overview not only of G-L-S stirred tank CFD modeling approaches but also of practical guidance on their selection and validation. Emerging high-resolution experimental techniques such as Electrical Resistance Tomography (ERT) coupled with pressure transducers, and Machine Learning (ML) models combined with experimental data, look promising to overcome current three-phase validation limitations. Future work to enhance predictive capabilities and reactor design and operation includes developing real-time digital twins, physics-based ML models and/or hybrid CFD-ML models.

Rheology is central to the design and industrial manufacture of cosmetic products, which are multicomponent soft materials whose performance depends on formulation, microstructure, processing history, temperature, shear, and time. Although apparent viscosity is widely used for quality control, a single-point measurement cannot fully describe yield behavior, viscoelasticity, thixotropic recovery, wall slip, extensional response, crystallization, or sensory performance. This review presents an industrial framework for applying rheology across the cosmetic-product lifecycle, from formulation and raw-material selection to scale-up, manufacturing, filling, release, stability, quality assurance, and consumer experience. Steady-shear, oscillatory, transient, nonlinear, extensional, tribological, powder-flow, and slurry measurements are discussed together with key methodological limitations. Particular attention is given to emulsification, polymer hydration, pigment and powder incorporation, deaeration, cooling, crystallization, and scale-up criteria, including tip speed, power input, circulation, heat transfer, and energy history. Rheological fingerprints are also examined for batch comparability, process analytical technology, statistical process control, computational fluid dynamics, machine learning, and digital twins. The review highlights links among formulation, microstructure, rheology, processing, stability, package performance, sensory response, and consumer outcomes and proposes a stage-based testing framework and research priorities for more robust cosmetic manufacturing.