Capillary state

When the void space in an agglomerate is completely filled with a Hquid (Fig. Ic), the capillary state of wetting is reached, and the tensile strength of the wet particle matrix arises from the pressure deficiency in the Hquid network owing to the concave Hquid interfaces at the agglomerate surface. This pressure deficiency can be calculated from the Laplace equation for chcular capillaries to yield, for Hquids which completely wet the particles ... 

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 ... 

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).]... 

From Eqs. (18) and (25), the ratio of the tensile strengths in the pendular and capillary states is... 

Nucleation This is where individual powder particles adhere to each other due to the liquid films. These particles will go through the different states discussed above from the pendular to the capillary state. These agglomerated particles in the capillary state will serve as nuclei for further granule growth. 

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.

In the capillary state the contribution to the tensile strength of a particle assembly due to the pressure deficiency in the liquid is much larger than that due to the interfacial tension at the surface of the assemnly. The tensile strength of a capillary state agglomerate can therefore be equated to this pressure deficiency which can be calculated from the Laplace equation for a circular capillary ... 

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 ... 

With liquid contents beyond the capillary state, liquid completely envelopes the particles (Fig. 2.3D). Only the interfacial tension of the convex surface of a continuous liquid drop tends to hold the particles captive. 

Agglomerates formed by wet pelletization are generally considered to be in the capillary state, that is the internal pore structure is just saturated with binding liquid. Eqn. (2) can then be derived for the liquid content of such an agglomerate on a wet basis ... 

In the second group of mixer agglomeration techniques, powders are moistened to a much lesser extent than the wet capillary state. Relatively weak powder clusters are formed. An example is the moistening, equilibration, drying and cooling sequence used to produce instantized food products. 

Several saturation regions can be identified on this curve. S<0,3 represents a pendular saturation state or bridging range. For S>0,8 no liquid bridges exist in the capillary state and ends when the first liquid bridges form between the particles. The relation between maximum tensile strength and the saturation of the cake with the special case of the capillary entry pressure can be written as follows (9,10) ... 

Fig. 2 Shearing path of mixer blades through wet mass at capillary state. (From Ref John Wiley and Sons, Inc.)...

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...

In the capillary state the strength of agglomerates is determined by the capillary suction. Since only those pores filled with the liquid contribute to the strength, equation (3) must be rewritten ... 

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. 

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