# Kinetic Models of Wood Biomass Drying in Hot Airflow Systems
On the other hand, a significant group of researchers have tried to model drying on the basis of mass transfer phenomena. In this respect, there are two trends in the scientific literature: on the one hand, those who model drying based on diffusivity by Fick's Law (Equation (1)) and mass convection (Equation (2)) [4; 12]; on the other hand, those who consider a simplified mass transfer model where the drying speed is proportional to the difference between the moisture of the material at each instant and the moisture of the material at equilibrium (Equation (3)) [12; 13; 14; 15; 16; 17]. \[\dot{m}_{w}=D_{w}\cdot\rho_{air}\frac{(\omega_{sat}-\omega_{air})}{L} \tag{1}\]  
\[\dot{m}_{w}=h_{m}\cdot\rho_{air}\cdot(\omega_{sat}-\omega_{air}) \tag{2}\]  
\[\dot{m}_{w}=K\cdot(x-x_{e}) \tag{3}\]  
where \(\dot{m}_{w}\) is the mass flow rate of water particles in the drying process (g water m\({}^{-2}\) s\({}^{-1}\)), \(D_{w}\) is the mass diffusivity (m\({}^{2}\) s\({}^{-1}\)), \(L\) is the distance where the difference in humidity in the air occurs (m), \(h_{m}\) is the convective mass transfer coefficient (m s\({}^{-1}\)), \(\rho_{air}\) is the density of the air at the average process temperature (g\(\cdot\)m\({}^{-3}\)), \(\omega_{air}\) is the absolute humidity of the air and \(\omega_{sat}\) is the humidity of the saturated air at the material surface (g water\(\cdot\)g\({}^{-1}\) air), \(K\) is the overall mass transfer resistance (g solid m\({}^{-2}\) s\({}^{-1}\)), \(x\) is the humidity of the material at a given instant, and \(x_{e}\) is the humidity of the material at equilibrium. However, these models do not work accurately due to a number of influencing factors, such as material porosity, pore size distribution, capillarity, and electrostatic forces. These factors mean that the diffusivity within the material is not constant, and hence neither is the transfer at the solid-air interface [18]. Various mass transfer models attempt to predict the value of \(h_{m}\) from the Sherwood number, which in turn depends on the [PERSON] number and the Schmidt number following correlations analogous to those used in the heat transfer model, where [PERSON]'s number is replaced by [PERSON]'s number, and [PERSON]'s number is replaced by [PERSON]'s number. However, one of the most important limitations of these models is that these numbers depend mainly on the properties of the air flow used in the drying process, but they also depend on the diffusivity, which in most materials is not well determined, since it is not constant but variable with humidity for a given porous structure [19; 20]. This represents a scientific challenge that has not yet been addressed in sufficient depth. An interesting study for determining this variability of diffusivity is the one presented by [21]. They present a patented prototype for this purpose. Table 1 shows a set of works that report the variability of diffusivity with humidity. However, they do not provide equations but rather graphs for their determination. A key aspect in modelling the drying process is the value of the _Biot_ number in mass transfer (4), where \(h_{m}\) is the coefficient of mass transfer by convection, \(D_{w}\) is the diffusivity, and \(L_{c}\) is the characteristic length. This number relates the rate of mass transfer by diffusion within the material and mass transfer by convection at the surface. \[Biot=\frac{h_{m}\cdot L_{c}}{D_{w}} \tag{4}\]