Pendular liquid

Pendular liquid bridge Bacteria, E. coli. Red blood cells Interfacial tension of water... 

Fig. 5. Estimated characteristic strength of typical biological particles of interest to biotechnology data are based on in-situ measurements of the minimum stresses necessary to cause permanent breakage of particles. For comparison data are shown based on Van der Waals and pendular liquid bridges between two 10-pm particles, 0.01 pm apart...

Figure 22. Pendular liquid bridge between two spherical particles. (From Ennis, etal., Powder Technol., 65 257-272, 1991, with kind permission from Elsevier Science S.A., P.O. Box 564, 1001 Lausanne, Switzerland.)...

The influence of viscosity on the strength of an axially strained pendular liquid bridge, Chem. 

The kinetics of a granulation process can be dramatically improved by the addition of recycled seed agglomerates. These nuclei readily pick up the fine feed material in layer growth since the pendular liquid bond between two particles increases in strength as the size difference between the particles becomes larger [15]. It has been suggested [16] that the coalescence proba-... 

Figure 11.21 Calculation of the strength of a pendular liquid bridge.

Ennis BJ, Li J, Tardos GI, Pfefler R. The influence of viscosity on the strength of an axially strained pendular liquid bridge. Chem Eng Sci 45 3071-3087, 1990. 

X. Pepin, D. Rossetti, S. M. Iveson, and S. J. R. Simons, Modeling the evolution and rupture of pendular liquid bridges in the presence of large wetting hysteresis,/ Colloid Interface ScL, 232, 289-297 (2000). 

This effect assumes importance only at very small radii, but it has some applications in the treatment of nucleation theory where the excess surface energy of small clusters is involved (see Section IX-2). An intrinsic difficulty with equations such as 111-20 is that the treatment, if not modelistic and hence partly empirical, assumes a continuous medium, yet the effect does not become important until curvature comparable to molecular dimensions is reached. Fisher and Israelachvili [24] measured the force due to the Laplace pressure for a pendular ring of liquid between crossed mica cylinders and concluded that for several organic liquids the effective surface tension remained unchanged... 

Pendular Funic alar Capillary Particles dispersed in bridging liquid ... 

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).]... 

The function Fp, which is a dimensionless or reduced bonding force, has been displayed graphically by Pietsch and Rumpf (P6) for various sets of variable p and parameters 0 and l/Dp. The volume of the liquid in the pendular bridge K is given by... 

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 5.3 Mobile liquid bonds (a) pendular (b) funicular (c) capillary. From Sherrington, P.J. and Oliver, R., Granulation, Heyden, 1981. Copyright John Wiley Sons Limited. Reproduced with permission.

Newitt and Conway-Iones4 found that there are four types of liquid state of granules depending on the liquid content in the granules. These states are known as pendular, funicular, capillary and droplet. 

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