Funicular state

It is evident, by comparing equations 2 and 3, that tensile strength in the pendular state is about one-tbhd that in the capillary state. Intermediate Hquid contents in the funicular state (Fig. lb) yield intermediate values that can be approximated as foUows ... 

Funicular state is that condition in diying a porous body when capillary suction results in air being sucked into the pores. 

Pendular state is that state of a liquid in a porous solid when a continuous film of liquid no longer exists around and between discrete particles so that flow by capillary cannot occur. This state succeeds the Funicular state. 

FIG. 20-64 Three states of liquid content for an assembly of spherical particles. (a) Pendular state, (h) Funicular state, (c) Capillary state. [Newitt and Con-way-Jones, Trans. Inst. Chem. Eng. (London), 36, 422 (1958).]... 

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. 

Fig. 2.3. Mobile liquid bonding states of liquid content in an agglomerate. (A) pendular state (B) funicular state (C) capillary state (D) particles in liquid droplet.

Comparing eqn. (10) and eqn. (13), tensile strength in the pendular state is about of that in the capillary state, while the funicular state yields intermediate values. As shown in Fig. 2.6, tensile strength in the funicular state can be approximated by ... 

Liquid flow in the FRPl is driven by the gradient in capillary pressure [20] along adsorbed films (Fig. 8.7c) or continuous patches of adsorbed film (the funicular state). 

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. 

In the transition range, the funicular state (i/ Lb / L / Lc) which liquid bridges coexist with liquid-filled pores, two cases can be constructed which follow a model published first by Rumpf ... 

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...

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