710 Fermentation and Biochemical Engineering Handbook the equilibrium moisture content is essentially zero at all temperatures and humidities. Equilibrium moisture content is particularly important in drying because it represents the limiting moisture content for given conditions of humidity and temperature. The mechanisms of drying during this phase are not completely understood, but two ideas can be considered to explain the physical nature of this process one is the diffusion theory and the other the capillary theory Diffusion Mechanism. In relatively homogeneous solids, such as wood, starch, textiles, paper, glue, soap, gelatin and clay, the movement of moisture towards the surface is mainly governed by molecular diffusion and, therefore follows Ficks La Sherwood and Newman gave the solution of this equation in the hypothesis of an initial uniform moisture distribution and that the surface is dry; the following expression is derived ( for long drying times) Eq1.4 Bm两 where dw/dois the rate of drying during the falling rate period, D is the liquid diffusivity of the solid material, L is the total thickness of the solid layer thickness through which the liquid is diffusing, W is the moisture content of the material at time, o, and we is the equilibrium moisture content under the prevailing drying conditions. Equation 4 neglects capillary and gravitational Capillary Model. In substances with a large open-pore structure and in beds of particulate material, the liquid flows from regions of low concentration to those of high concentration by capillary action. based on this mechanism, the instantaneous drying rate is given dw h(ta-ts)(W-We Eq. 5 Do 2pL IWo-w where o is the density of the dry solid and wo is the moisture content when diffusion begins to control Most biological materials obey Eq 4, while coarse granular solids such as sand, minerals, pigments, paint, etc, obey Eq. 5 Shrinkage and Case Hardening. When bound moisture is removed from rigid, porous or nonporous solids they do not shrink appreciably, bur colloidal nonporous solids often undergo severe shrinkage during drying This may lead to serious product difficulties; when the surface shrinks against710 Fermentation and Biochemical Engineering Handbook For non-hygroscopic materials, the equilibrium moisture content is essentially zero at all temperatures and humidities. Equilibrium moisture content is particularly important in drying because it represents the limiting moisture content for given conditions of humidity and temperature. The mechanisms of drymg during this phase are not completely understood, but two ideas can be considered to explain the physical nature of this process￾one is the diffusion theory and the other the capillary theory. Diffusion Mechanism. In relatively homogeneous solids, such as wood, starch, textiles, paper, glue, soap, gelatin and clay, the movement of moisture towards the surface is mainly governed by molecular diffusion and, therefore, follows Ficks' Law. Sherwood and Newman gave the solution of this equation in the hypothesis of an initial uniform moisture distribution and that the surface is dry; the following expression is derived (for long drying times): Eq. 4 where dW/dq+is the rate ofdrying during the falling rate period, D is the liquid difisivity of the solid material, L is the total thickness of the solid layer thickness through which the liquid is diffusing, W is the moisture content of the material at time, 0, and We is the equilibrium moisture content under the prevailing drying conditions. Equation 4 neglects capillary and gravitational forces. Capillary Model. In substances with a large open-pore structure and in beds of particulate material, the liquid flows from regions of low concentration to those of high concentration by capillary action. Based on this mechanism, the instantaneous drying rate is given by: Eq. 5 dW h (ta- ts) (W- We) D0 2p L 1 (Wo- We) -- - where 9 is the density of the dry solid and Wo is the moisture content when diffusion begins to control. Most biological materials obey Eq. 4, while coarsegranular solids such as sand, minerals, pigments, paint, etc., obey Eq. 5. Shrinkage and Case Hardening. When bound moisture is removed from rigid, porous or nonporous solids they do not shrink appreciably, but colloidal nonporous solids often undergo severe shrinkage during drying. This may lead to serious product difficulties; when the surface shrinks against