## 6 CFD Analysis of Drying as a Mechanically Aided Process
### CFD Modeling of Particle-Fluid Interactions  
Particle-fluid interactions are central to numerous food processing operations, particularly those involving drying and mechanical transport, such as fluidized and spouted beds, spray drying, suspension mixing, and pneumatic conveying. These interactions critically influence heat and mass transfer efficiency, particle residence time, product uniformity, and final structural integrity. CFD provides a powerful framework for analyzing such multiphase systems, enabling detailed insights into flow behavior, particle dynamics, and coupled transport phenomena [117]. In food processing, particle-fluid systems exhibit diverse configurations. These include solid particles suspended in gas flows, as in fluidized beds; liquid droplets dispersed in air streams, as encountered in spray drying; gas-solid transport in pneumatic conveying; and solid-liquid suspensions such as starch or fiber dispersions in hydration tanks. The behavior of these systems is governed by a combination of particle characteristics (including size, shape, and density), fluid properties (such as viscosity, temperature, and velocity), and interfacial forces (e.g., drag, lift, and virtual mass effects). In dense particulate systems, particle-particle collisions and contact mechanics further complicate the flow regime and influence energy dissipation and mixing efficiency [112]. CFD offers several modeling strategies for particle-fluid interactions, selected based on the system's concentration, scale, and flow regime. In the EE or two-fluid model, both the fluid and particulate phases are treated as interpenetrating continua. This approach is particularly suited to dense flows, such as those in fluidized or spouted beds, and relies on momentum exchange terms and drag force correlations, including those proposed by [PERSON] or [PERSON], to describe interphase interactions [118]. The EL model adopts a different strategy, treating the fluid as a continuum while tracking individual particles using [PERSON]'s second law of motion:  
\[m_{p}\frac{dv_{p}}{dt}=\sum F\]  
where \(m_{p}\) is the particle mass, \(v_{p}\) is its velocity, and \(\sum F\) represents the sum of forces acting on the particle, including drag, buoyancy, gravity, and lift. This method is ideal for dilute systems and allows for detailed analysis of particle trajectories, deposition zones, and drying behavior--particularly relevant in spray drying and powder dispersion modelling [113]. In systems with intense particle-particle interactions--such as cohesive powders, vibrating beds, or granulation processes--CFD can be coupled with the DEM. DEM accounts for contact forces, friction, restitution, and cohesion during collisions, providing insight into mechanical stress distribution, agglomeration dynamics, and powder flowability [42]. Heat and mass transfer processes are tightly coupled with particle-fluid dynamics and are crucial for predicting product behavior during drying and transport. CFD models typically incorporate convective heat transfer using Nusselt number correlations, surface evaporation models for droplets or wet particles, and--in the case of porous or larger particles--intraparticle heat and moisture diffusion. In spray drying, models may also account for crust formation, which alters evaporation dynamics and affects particle morphology and product quality [119]. Practical applications of CFD in this context include predicting moisture front progression during fluidized grain drying, simulating droplet drying paths and wall deposition in spray dryers, and evaluating agglomeration risks under varying humidity and temperature conditions. Such models support optimization of process parameters, including air velocity, particle size distribution, inlet temperature, and chamber geometry [39]. CFD modeling of particle-fluid systems has been successfully employed across various food sectors.