Capillary attractive forces

An interesting phenomenon based on capillarity is the appearance of a capillary attractive force between particles of moistened solids. As a result of wetting, a meniscus is formed upon the particle contact (Fig. 1-14). This meniscus between two contacting particles of radii r0 has a shape of surface of rotation, and can be characterized at each point by the two curvature radii r, and r2 (in Fig. 1-14, a these radii are of opposite sign, i.e. r,>0 and r2<0), which are related to each other as 1/r, + /r2 = const. If r, r0, both rx and r2 may be considered to be constant. 

For the case of perfect wetting (0=0°), the capillary attractive force F that one needs to overcome in order to separate the particles consists of two components. One of them is the capillary pressure force, Fx ... 

Fig. 1-14. The shape of the meniscus is indicative of the strength of the capillary attractive force, F, between two wetted particles...

The capillary attractive force is responsible for the commonly observed strong adhesion between slightly moistened sand grains, as well as for much the weaker attachment between them at high water content. Capillary phenomena play an important role in determining the extent of particle adhesion and thus are critical for the stability and mechanical properties (see Chapter IX) of various clays, pastes, and powders. 

FIG U RE 1.21 Estimation of the capillary attractive force between two spherical particles in the presence of a liquid meniscus. (Redrawn from Shchukin, E.D. et ah, Colloid and Surface Chemistry, Elsevier, Amsterdam, the Netherlands, 2001.)... 

The net adhesive force between the particles in a contact formed in a nonwetting liquid, p i, is given by the sum of the molecular adhesive force between the particles, p, acting in the gas phase and the capillary attractive force, Ap=p + ph... 

Equation 1.23 is a well-known limiting relationship for the capillary attractive force, which for the general case of convex particles of arbitrary shape can be written as [18]... 

The values of p and p, estimated from Equations 1.17 and 1.18, using the experimentally determined cavity diameter (Table 1.1), indicate that in these systems, the pressure difference contributes approximately 90% to the total value of the capillary attractive force, Ap. The remaining 10%... 

An important subject that one needs to address here is the role of moisture. Typically, in the case of a complete flooding of powder with a wetting liquid, the internal friction and critical tilt angle are significantly lower than in a dry system. However, at a certain average content of the liquid phase, the cohesion between particles and the resistance to shear significantly increase due to the appearance of capillary attractive force (see Chapter 1). 

In the range Ijum to 100 nm of the surface, the tip is subjected to electrostatic forces that can be either repulsive or attractive depending on the surface. Within 100 nm, the tip will experience capillary attractive forces. When operating in air, this is due to surface water. Although this is not the problem that it is in contact mode (see Section 3.3.3), these forces do affect the cantilever oscillation. Figure 3.31 shows the amplitude and phase signal (as [90 - ]°) in a frequency sweep of a cantilever far from the surface, and then near to but not contacting the surface. Far from the surface, 200/rm above it, Q is 640 and the resonant frequency is... 

The capillary effect is apparent whenever two non-miscible fluids are in contact, and is a result of the interaction of attractive forces between molecules in the two liquids (surface tension effects), and between the fluids and the solid surface (wettability effects). 

KapiUarititt, /. capillarity. Kapillaritittsanziehung./. capillary attraction. Kapillar-kraft,/, capillary force, -kreislauf, n. capillary circulation, -rohr, -rohrchen, n, -rohre, /. capillary tube, -spaonung, /. capillary tension, -stromung, /. capillary flow, -versuch, m. capillary test or experiment. -wirkung./. capillary action. 

In equation (2) Rq is the equivalent capillary radius calculated from the bed hydraulic radius (l7), Rp is the particle radius, and the exponential, fxinction contains, in addition the Boltzman constant and temperature, the total energy of interaction between the particle and capillary wall force fields. The particle streamline velocity Vp(r) contains a correction for the wall effect (l8). A similar expression for results with the exception that for the marker the van der Waals attraction and Born repulsion terms as well as the wall effect are considered to be negligible (3 ). 

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. 

Vapor sorption onto porous solids differs from vapor uptake onto the surfaces of flat materials in that a vapor (in the case of interest, water) will condense to a liquid in a pore structure at a vapor pressure, Pt, below the vapor pressure, P°, where condensation occurs on flat surfaces. This is generally attributed to the increased attractive forces between adsorbate molecules that occur as surfaces become highly curved, such as in a pore or capillary. This phenomenon is referred to as capillary condensation and is described by the Kelvin equation [19] ... 

A combination of adhesion and surface tension gives rise (pardon the pun) to capillary action. By its adhesion to the solid surface of the soil particles, the water wants to cover as much solid surface as possible. However, by the effect of surface tension, the water molecules adhering to the solid surface are connected with a surface him in which the stresses cannot exceed the surface tension. As water is attracted to the soil particles by adhesion, it will rise upward until attractive forces balance the pull of gravity (Figure 3.28). Smaller-diameter tubes force the air-water surface into a smaller radius, with a lower solid-surface-to-volume ratio, which results in a greater capillary force. Typical heights of capillary rise for several soil types are presented in Table 3.9. The practical relationship between normal subsurface water and capillary rise is presented in the following equation. 

The interplay between the attractive (e.g.. Van der Waals or capillary forces) and repulsive forces involved during the approach of the tip to different surfaces under different environments are presented in Fig. 5 and discussed here. When the cantilever approaches a hard and non-compressible surface (Fig. 5a), at first the forces are too small to produce any measurable deflection of the cantilever, and therefore the position of the cantilever remains unchanged. At a certain distance the attractive forces overcome the cantilever spring constant and the tip leaps into contact with the specimen surface (Fig. 5b). As the cantilever continues to press down while the tip rests on the surface, the separation between the base of the tip and the sample decreases further, which results in the deflection of the tip with a subsequent increase... 

In the non-contact mode (Fig. 6b), AFM acquires the topographic images from measurements of attractive forces in close proximity of the surface, as the tip does not touch the sample and the cantilever oscillates close to the sample surface [12]. This mode is difficult to work with in ambient conditions due to the interference of the capillary forces. Very stiff cantilevers are needed so that the attraction does not overcome the spring constant of the cantilever. However, the lack of contact with the sample means that this mode should be the least invasive and hence cause the least disruption. The disadvantage of this method is that the tip may jump into contact with the surface due to attractive forces. 

The main difference between carbon nanotubes and high surface area graphite is the curvature of the graphene sheets and the cavity inside the tube. In microporous solids with capillaries which have a width not exceeding a few molecular diameters, the potential fields from opposite walls will overlap so that the attractive force which acts upon adsorbate molecules will be increased in comparison with that on a flat carbon surface [16]. This phenomenon is the main motivation for the investigation of the interaction of hydrogen with carbon nanotubes (Figure 5.14). 

The concept of a pore potential is generally accepted in gas adsorption theory to account for capillary condensation at pressures well below the expected values. Gregg and Sing ° described the intensification of the attractive forces acting on adsorbate molecules by overlapping fields from the pore wall. Adamson has pointed out that evidence exists for changes induced in liquids by capillary walls over distances in the order of a micron. The Polanyi potential theory postulates that molecules can fall into the potential field at the surface of a solid, a phenomenon which would be greatly enhanced in a narrow pore. 

Note, that the surface and deformation forces are of the same order of magnitude. Therefore, surface forces should be as small as possible to minimise damaging and indentation of soft polymer samples. For example, sharp probes have a lower capillary attraction and adhesion forces, and therefore enable more gentle probing of a soft polymer than a blunt tip. A sharp tip can also be moved in and out of the contamination layer more readily than a blunt tip. This is particularly important for non-contact intermittent contact imaging described in Sect. 2.2.1. 

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