Capillary liquid bridges between particles

Capillary pressures also recur widely. Capillary liquid bridges between particles tend to pull these particles together. It is one of the reasons for the coherence of moist powders, which may become flufly upon drying. Such capillary forces have to compete wdth double layer repulsion and Van der Waals attraction, and under some conditions may outweigh these. 

At low relative humidities, moisture produces a layer of adsorbed vapour on the surface of particles. Above a critical humidity, typically in the range 65-80 percent, it will form liquid bridges between particles. The attractive force due to the adsorbed layer may be about 50 times the van der Waals force for smooth surfaces, but surface roughness will reduce the effect. Where a liquid bridge forms, it will give rise to an attractive force between the particles due to surface tension or capillary forces. 

Pc capillary pressure. Pa Pw> Po water and oil pressures. Pa P2 far-field reservoir pressure. Pa Q fluid production, mVs Qw. Qo water and oil production rates, mVs r radius of liquid bridge between particles, m distance from wellbore, m R radius of the particles, m... 

Capillary forces generated by liquid bridges between particles,... 

Capillary Forces Due to Liquid Bridges Between 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. 

The capillary forces according to liquid bridges between two particles are approximately two orders of magnitude greater than van der Waals forces. In Fig. 8.4-13 the dimensionless adhesion force F = L) is plotted against the... 

If a latex paint is dried below the MFFT, no particle deformation occurs. However, if the temperature of the dried (but not coalesced) latex is then raised to slightly above the MFFT, no coalescence as described in Section 3.3 should occur no receding air-water interface exists to generate capillary forces, and thus no particle deformation occurs. If the temperature is further raised, however, particle deformation eventually occurs. This is because some residual water is always left between the particles due to capillary condensation. At the higher temperature, these liquid bridges between the particles can exert enough force to deform the particles. 

Ffe. 2.5 Porous system of solid particles wetted by a liquid at an elevated temperature. Due to capillary forces arising in liquid bridges between the particles, the system is in a state corresponding application of an external hydrostatic compressive stress which is the driving force. For sintering increasing the packing density of particles with elimination of pores... 

Capillary forces increase in relationship to the relative humidity (RH) of the ambient air. At greater than 65% RH, fluid condenses in the space between adjacent particles. This leads to liquid bridges causing attractive forces due to the surface tension of the water. 

If the particles are wetted only partially by the fluid (melt), liquid bridges form and capillary forces develop between them. These can be divided into two parts that related to surface tension ... 

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) ... 

Figure 9.5 schematically shows the capillary effect and the resulting effect on the particle adhesion. A liquid bridge forms between the particle and the substrate and holds the particle to the surface by surface tension. The liquid film could be a result of capillary condensation in high relative humidity or of a retention of liquid during substrate removal from the liquid bath. The attractive force is composed of the force caused by surface ten-... 

For the case of a static liquid bridge of contact angle 0, surface tension induces an attractive capillary force Fcap between the two particles... 

Capillary forces develop when liquid bridges are formed in small gaps between two surfaces. Above a critical relative humidity, capillary forces are the dominant attractive force between aerosol particles [269,270]. The magnitude of this force depends on other parameters as well, such as particle surface chemistry and size. For two particles attached by a liquid bridge, the adhesive force is [260] ... 

Figure 12.8d shows a liquid neck between solid particles in a fluid, which holds the particles together by capillary forces (see Section 10.6) the attractive interaction energy can be very large. An example is bridging of various particles in cocoa mass (a melted chocolate)—where oil is the continuous phase—induced by tiny water droplets this then gives the cocoa mass a greatly enhanced viscosity. 

One of the most common binding mechanism of wet agglomeration is liquid bridges at the coordination points between the particles forming the agglomerate. Liquid bridges can develop from free water or by capillary condensation. They are often the precondition for the formation of solid bridges (see above, 1.6). 

On the left. Fig. 5.28 shows three curves for different dimensionless values ajx that were calculated using Equations 5.7 and 5.9. It can be assumed that up to a saturation of S = 30-40 % discrete liquid bridges prevail at the coordination points between the particles forming the agglomerate. In the right part of Fig. 5.28 the experimentally determined capillary pressure is plotted (solid dots). This curve is obtained when... 

Capillary Condensation. Condensation of water vapor takes place in the gap between contiguous bodies (Fig. IV.6.a). The liquid bridge or meniscus thus formed will, on the one hand, draw up on the particle by means of surface ten-... 

These data indicate that particle adhesion in vacuum is less than in air water vapor increases the adhesive force there are no capillary forces when the particles are under vacuum, while in air these forces are manifested upon the appearance of a liquid bridge in the gap between the contiguous bodies in an atmo-... 

Capillary forces appear when a liquid bridge (meniscus) is present in the gap between the particles and the surface these forces are manifested only after the particles have been deposited and when the relative humidity of the air is above 65%. The capillary forces, without or with allowance for the disjoining pressure of the liquid layer as determined by Eqs. (IV.37) or (IV.46), depend on the particle size. 

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