Drying second falling rate period

As drying proceeds, the point is reached where the evaporating surface is unsaturated. The point of evaporation moves into the solid, and the dry process enters the second falling-rate period. The drying rate is now governed by the rate of internal moisture movement the influence of external variables diminishes. This period usually predominates in determining the overall drying time to lower moisture content. 

Krischer (K7) gave a comprehensive treatise on the subject. The second falling-rate period starts when the moisture content at the surface reaches the equilibrium value. In both periods the vapor diffuses from the interior of the solid and the rate of vapor diffusion determines the rate of drying. 

For any material, the critical moisture content decreases as the particle size decreases. Eventually, moisture ceases to reach the surface which becomes dry. The plane of evaporation recedes into the solid, the vapor reaching the surface by diffusion through the pores of the bed. This section is called the second falling-rate period and is controlled by vapor diffusion, a factor which is largely independent of the conditions outside the bed but markedly affected by the particle... 

Texture modifications occur mainly during the first step of drying (the constant rate period) and are related to the visco-elastic properties of the gel network [6]. During the second step of drying (the falling rate period), liquid water leaves the capillaries and the pore walls can be damaged by forces linked to the existence of liquid-gas meniscus [6, 7],... 

When drying continues the liquid film near the surface first breaks up into isolated pockets (pendular state) and finally this state spreads over the complete thickness of the gel. This situation is called the second falling rate period (FRP2) where evaporation takes place inside the gel body and the principal transport process is expected to be Knudsen diffusion of vapour. 

The second falling rate period was not clearly observed. The change-over from CRP to FRPl became smoother and more gradual with thinner layer. This behaviour is also observed in granular (clay) materials and has been explained by a smoother fluid concentration profile within the thinner drying samples [30]. 

It is generally believed that solvent evaporation involves three periods, namely a constant rate drying, a first falling rate, and a second falling rate period [20]. 

The second falling rate period—which is governed by the rate of evaporation, migration and diffusion of moisture within the carbon fiber tows. The surface appears dry and air humidity no longer influences the rate. 

FIGURE 15.2 Rates of dr5dng. Curve A is characteristic for materials such as sand curve B is characteristic for materials such as soap and catalyst supports. Curve A initially exhibits a constant rate and, subsequently, a linear drop in drying rate (the first falling-rate period), and finally, a more slowly falling rate (the second falling-rate period). 

The second falling-rate period begins at point D when the surface is completely dry. The plane of evaporation slowly recedes from the surface. Heat for the evaporation is... 

At the beginning of the falling-rate period at point C in Fig. 9.5-lb, the water is being brought to the surface by capillary action, but the surface layer of water starts to recede below the surface. Air rushes in to fill the voids. As the water is continuously removed, a point is reached where there is insufficient water left to maintain continuous films across the pores, and the rate of drying suddenly decreases at the start of the second falling-rate period at point D. Then the rate of diffusion of water vapor in the pores and rate of conduction of heat in the solid may be the main factors in drying. 

In fine pores in solids, the rate-of-drying curve in the second falling-rate period may conform to the diffusion law and the curve is concave upward, as shown in Fig. 9.5-2b. For very porous solids, such as a bed of sand, where the pores are large, the rate-of-drying curve in the second falling-rate period is often straight, and hence the diffusion equations do not apply. 

As shown in Fig. 5.17, the drying process can be divided into two major stages (1) a constant rate period (CRP) where the evaporation rate is nearly constant and (2) a falling rate period (FRP) where the evaporation rate decreases with time or the amount of liquid remaining in the body. In some materials it is possible to further separate the FRP into two parts. In the first falling rate period (FRPl), the evaporation rate decreases approximately linearly with time, while in the second falling rate period (FRP2), the rate decreases in a curvilinear manner. 

As the distance between the liquid-vapor interface (the drying front) and the surface increases, the pressure gradient decreases and the flux of liquid also decreases. If the gel is thick enough, eventually a stage is reached where the flux becomes so slow that the liquid near the surface is in isolated pockets. (The liquid is now said to be in the pendular state.) Flow to the surface stops, and the liquid is removed from the gel by diffusion of the vapor. This marks the start of the second falling rate period (FRP2), where evaporation occurs inside the gel (Fig. 5.22b). 

---