Shape liquid bridges

The concept of surface tension is a very old one. Reportedly, Leonardo da Vinci had already observed and recorded the spontaneous rise of liquids in narrow, wetted capillaries, bores and plugs 1). From this rising the phenomenon acquired its name capillus (lat.) = hair the bores should be as narrow as a hair. Nowadays the term capiUaiy phenomena is used more widely (in this book also) to Indicate not only capillary rise, involving curved interfaces, but also all phenomena determined by the tendency of interfaces to adopt a minimum curea, such as drop shapes, bubble shapes, liquid bridges and wetting. 

Due to their disperse character and small particle size, silicas are used as flow aids, i.e. they are used to improve the flow behaviour of other materials. The adsorption of the fine silica particles on other type powdered compounds reduces interparticle interactions. Particle adhesion, electrostatic adhesion, Van Der Waals forces and liquid bridge formation is reduced or avoided.33 This allows free-flowing behaviour of strongly interacting or irregularly shaped powdered materials. 

Figure 2.2. Shape of a drop when it contacts the substrate in the dispensed drop method (a) or when the liquid bridge is detached from the lower substrate in the transferred drop method (b).

As it can be seen from the Table 3 that for the saturation region, S=0%, the shear strength is independent of the shape factor, namely independent of the type of the mineral. In contrast to that, as the saturation degree increases, the shear strength is absolutely dependent on the shape factor of the mineral particles. The reason is probably the change in the adhesion forces and liquid bridges between the particles with different shape factors in the more saturated regions. 

Liquid bridges occur when a liquid is sprayed to wet the surface of the particles, then they colhde with other particles and the hquid connects the particles. Molecular, electrical, or magnetic forces between particles is another binding mechanism. Interlocking occurs when irregular-shaped particles collide and lock together. A matrix binder has particles that are imbedded in a continuous matrix of the binder. 

The mutual attraction through the slit gap affects liquid film stability, and at a certain critical vapor pressure (or film thickness) the two films form a liquid bridge (Fig. 1-1 c) followed by a spontaneous filling up of the slit (assuming the film is in contact with the bulk liquid phase). The liquid-vapor interface moves to the plate boundaries. This phase transition from dilute vapor to a dense liquid is known as capillary condensation and was observed experimentally with the surface force apparatus by Christenson (1994) and Curry and Christenson (1996). Extensive theories for this phenomenon and its critical points are provided by Derjaguin and Chu-raev (1976), Evans et al. (1986), Forcada (1993), and Iwamatsu and Horii (1996). In general, slit-shaped pores fill up at a film thickness of about HI3, or when <) l(H,h)/dh = 0, such that... 

Consider two identical particles contacting tangentially (Figure 1). Assuming the shape of the liquid bridge is a toroid, the capillary pressure in the water/oil menisci can be written as (Nomenclature is at the end)... 

Bika et al (2005) have extended the models of Rumpf and Kendall to agglomerates with solid bridge bonds between primary particles. The solid bridge bonds are formed by evaporation of a liquid bridge and precipitation of dissolved solids. It is assumed that the liquid bridge conserves its shape as it shrinks and solidifies. 

For a liquid bridge with a given volume, the resolution of the meniscus shape is not trivial. A numerical resolution was proposed using a double-iterative method. It can handle any surface shapes and boundary conditions and compute the capillary force from the geometrical method. ... 

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