Pendular bridge

Mobile liquids 1. Liquid bridges (pendular 1. Flocculation of fine par- 63... 

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...

Pendular Funic alar Capillary Particles dispersed in bridging 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...

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... 

The flatness of the computed curves in Fig. 6 shows that in the case of spheres in contact F is insensitive to rather large changes in V (or / ). Mason and Clark (M3) have measured the pendular bonding force as a function of the separation distance and bridge volume. Considering the experimental uncertainty involved, their results follow the expected trend quite satisfactorily. 

Fig. 6. Reduced pendular bonding force-reduced bridge volume curves when spheres are in contact.

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 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.)...

Figure 29. Schematic diagram of the pendular bridge apparatus. (From Ennis, et al., Chem. Eng. Sci., 45 3071-3088, 1990, with kind permission from Elsevier Sciences Ltd., The Boulevard, Langford Lane, Kidlington OX5 1GB, UK.)...

In the pendular state, the particles have been exposed to sufficient granulating solution for liquid bridges to begin to form. Since the pendular state is characterized by a... 

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

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) ... 

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