Funicular saturation

Funicular saturation Similar to residual saturation, except that each grain is surrounded by a water film and has a large air content. 

It has been established (P8, R5) that when the value of S exceeds about 0.25, the liquid bridges begin to coalesce with one another and the bonding mechanism changes over from the pendular to the funicular state. When S exceeds 0.8, the existence of discrete liquid bridges is no longer possible and now the capillary pressure state alone exists. Thus, the funicular state lies in a range of saturation bounded by the lower and upper critical limits denoted by Sp and Sc, respectively. 

Figure 59. Different models of liquid distribution in wet agglomerates, (a) Liquid bridges or pendular state, (b) transition region, partially saturated pores, or funicular state, (c) capillary state, saturated pores, (d) liquid droplet filled with particles...

Figure 64(a) shows schematically the maximally transferable tensile stress as a function of the liquid saturation The capillary pressure curve (Figure 64b) is used to calculate (Jtc = LPc for lc l The capillary state ends when liquid bridges between the particles start to form (t/ L lc)- The funicular state exists in the region J Lb / l / lc Tor the pendular state (i/ Ldiscussed equation (45) is valid. 

As the liquid content is increased, the pendular state will remain until the pendular bonds start to coalesce and liquid bridges form between non-touching points. This is known as the funicular state (Figure 11.20). The state depends on the degree of liquid saturation or voidage saturation, which is defined as the ratio of the liquid volume to the total volume of pores in the powder bed. Typically, a powder bed will remain in the pendular state until the liquid saturation reaches around 25 percent, and in the funicular state between 25 and 80 percent. 

An approximation of the agglomerate strength o in the transitional ( funicular ) state, in which a certain percentage S (= saturation, see Section 5.1) of the pore volume is filled with liquid, is possible by multiplying the maximum strength a,c with the appropriate saturation S ... 

Fig. 3.2 Diagrams of different liquid saturations in particulate bulk solids or agglomerates a) dry b) adsorption layers c) liquid bridges ( pendular state) d) transitional ( funicular state) e) fully saturated ( capillary state) f) droplet...

The moist agglomerates can exist in the following three states, based on the amount of the liquid they contain the pendular state, the funicular state, and the capillary state. The three states can be distinguished by the relative hquid saturation of the pores S, which is the ratio of pore volume occupied by the liquid to the total volume of the pores available in the agglomerate. 

Agglomerates are in the pendular state when the liquid saturation of the pores S < 25% in the funicular state when S is between 25% and 80% and in the capillary state when S > 80 /o. The liquid saturation S is determined by the amount of binder solution and the intragranular porosity, which can be calculated based on the following equation (17) ... 

Illustration of pendular state, where liquid (light gray) exists in isolated pockets in regions of negative curvature between particles (dark gray) funicular state, where liquid is contiguous but does not fill the pore space and saturated state, where pore space is filled with liquid. 

Transition zone (also funicular region) Over the transition zone changes of saturation take place. This region reflects the most abundant and accessible pore-throat sizes the steeper the capillary pressure curve in this region, the less uniform the pore throats (Jorden and Campbell, 1984). 

---