If chemical adsorption plus condensation adsorbs so much water that the tightest passages of small capillaries are filled with liquid and a concave liquid surface has been formed, capillary condensation sets in. Analogously to the vapour pressure reduction when drops of liquid become larger, a lower vapour pressure then above a level surface becomes effective in tight capillaries with a concave liquid surface. From this, Lord Kelvin deduced the following interrelation for the change of vapour pressure:
Formula 6.3.4.1
dp = vapour pressure
s = surface tension
d = edge angle (miniscus)
r = pore radius
V = mol. volume of the vapour
T = temperature
R = general gas constant
Whereas on level surfaces condensation sets in only when saturation vapour pressure has been reached, water condenses inside the pores already at low vapour pressures. The capillaries become filled with the substance (in this case water) to be adsorbed. It follows from the Kelvin equation according to Formula 6.3.4.1, that the vapour pressure reduction inside the capillaries will be the stronger, the narrower the pores. This means that the tightest pores within the silica gel will be filled with water in the first instance and only after this, the pores with larger diameter. The process of condensation continues until vapour pressure equilibrium is reached, i.e. up to the point at which the vapour pressure of the water in the surrounding gaseous phase is equal to the vapour pressure inside the pores. The larger the internal surface of a particular silica gel, the greater will be the number of silanol groups, and the tighter the pores, the stronger will be the effect of capillary condensation, thus making the gel a particularly effective drying medium. This process corresponds to the sequence of the isothermal of type 1 (Fig 6.3.1.1).
Diagram 6.3.4.1
The dotted line entered into Diagram 6.3.4.1 shows the equilibrium relationship between water loading, regeneration temperature of the drying medium and the dewpoint. At an ambient temperature of tamb = 25°C and relative humidity of RH = 60%, the real dewpoint temperature of the regenerating gas and Tdp = 15°C, entered above on the Y axis. Likewise on the Y axis, one finds the horizontal line of the dewpoint of the compressed air with Tp = -40°C. On the X axis, the inlet temperature of the compressed air is assumed to be Ti = 35°C. Parallel to the line of constant residual water loading expressed in weight percentages, the equilibrium relation to the regeneration temperature TReg = 140°C can be established. The larger the pores, and therefore the total pore volume, the larger the quantity of water which the silica gel can take up, i.e. the capacity is correspondingly higher. This is demonstrated by isothermal type 2 (Fig. 6.3.1.2).
Diagram 6.3.4.2
Diagram 6.3.4.2 shows the equilibrium relationship of a drying medium typical for isothermal type 2.
