Dynamic Capillary Force

In the previous section we described static capillary forces. Viscous forces may also bring an additional contribution that will be readily measured with AFM dynamical modes. Therefore, in the framework of AFM studies, it is of interest to evaluate the effect of the liquid viscosity. We distinguish two cases corresponding to different configurations discussed in the next section of this chapter. We first evaluate the viscous force compared to the capillary one and then the effect of the boundary condition. 

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It can be shown, (Gibbs, Scientific Papers, I. J. J. Thomson, Applications of Dynamics to Physics and Chemistry), that a chemical equilibrium can be modified by the action of capillary forces. Thus, a state of equilibrium in solution may conceivably be modified if the latter is in the form of thin films, such as soap bubbles. Since, according to Freundlich (Kapillarchemie, 116), there is at present no direct evidence of the existence of such modification (which would no doubt be exceedingly, though possibly measurably, small) we shall not enter any further into the matter here. 

The multiplicity of phenomena characteristic of flow in heated micro-channels determined the content of the book. We consider a number of fundamental problems related to drag and heat transfer in flow of a pure liquid and a two-phase mixture in micro-channels, coolant boiling in restricted space, bubble dynamics, etc. Also considered are capillary flows with distinct interfaces developing under interaction of inertia, pressure, gravity, viscous and capillary forces. 

For solid surfaces interacting in air, the adhesion forces mainly result from van der Waals interaction and capillary force, but the effects of electrostatic forces due to the formation of an electrical double-layer have to be included for analyzing adhesion in solutions. Besides, adhesion has to be studied as a dynamic process in which the approach and separation of two surfaces are always accompanied by unstable motions, jump in and out, attributing to the instability of sliding system. 

Relative permeability and capillary pressure functions, collectively called multiphase flow functions, are required to describe the flow of two or more fluid phases through permeable media. These functions primarily depend on fluid saturation, although they also depend on the direction of saturation change, and in the case of relative permeabilities, the capillary number (or ratio of capillary forces to viscous forces). Dynamic experiments are used to determine these properties [32]. 

In MCFCs, which operate at relatively high temperature, no materials are known that wet-proof a porous structure against ingress by molten carbonates. Consequently, the technology used to obtain a stable three-phase interface in MCFC porous electrodes is different from that used in PAFCs. In the MCFC, the stable interface is achieved in the electrodes by carefully tailoring the pore structures of the electrodes and the electrolyte matrix (LiA102) so that the capillary forces establish a dynamic equilibrium in the different porous structures. Pigeaud et al. (4) provide a discussion of porous electrodes for MCFCs. 

J. Lucassen, Capillary forces between solid particles in fluid interfaces, Colloids Surf. 65, 131-137 (1992) Dynamic dilational properties of composite surfaces, Colloids Surf. 65, 139-149 (1992). 

For micro-pores, molecular dynamics calculations can be used to find the pressures at which pores of simple shape fill and empty In meso-porous materials capillary condensation can occur and the behaviour is then better described in terms of the theory of capillarity combined with percolation theory. For macro-porous materials, such as oil reservoir rocks, capillary forces can dominate the displacement of one fluid by another. Percolation or pore blocking which is the shielding of large pores by smaller pores can occur in all of these processes and can make a significant difference when the processes are analysed theoretically. 

The process of nanomanipulation involves control of a number of forces. The main two forces are the force of adhesion between the AFM tip and the adsorbate particle which will be manipulated and that between the particle and the substrate (FaP ). These forces are mediated by the surface forces [98] and depend on the formation of a meniscus on the substrate. While stabilizes the particle on the substrate, F T rnakes the particle stick to the tip. The contact force between the tip and the particle F makes the particle move. The movement of the cantilever from its equilibrium position and the force constant of the cantilever determine the contact force in turn. In addition, since the experiments are carried out in ambient air, there are capillary forces between the tip and the particle as well as the van der Waal forces between the tip and the particle and between the particle and the substrate. It is the balance of these forces that determines the final dynamics of the particle movement. 

In the dynamic experiments knowing the capillary force F (from Equation 5.160), and measuring the particle velocity, X, we can determine the drag force, F ... 

On the other hand, if a = 0, and the dynamics of the film is still dominated by body forces, then it appears from (6-3) that uc = eil1cpg/ii. In other cases, however, gravitational forces may play only a secondary role in the motion of the film, which is instead dominated by capillary forces. Then the appropriate choice for uc would involve the surface tension rather than either of the choices previously listed and the body-force terms in both (6-2) and (6-3) would be asymptotically small for the limit e -> 0. This then is a fundamental difference between this class of thin-film problems and the lubrication problems of the previous chapter. Here, the characteristic velocity will depend on the dominant physics, and if we want to derive general equations that can be used for more than one problem, we need to temporarily retain all of the terms that could be responsible for the film motion and only specify uc (and thus determine which terms are actually large or small) after we have decided which particular problem we wish to analyze. 

The dynamic interaction between flow and drops and bubbles floating in the flow may deform or even destroy them. This phenomenon is important for chemical technological processes since it may change the interfacial area and the relative velocity of phases and cause transient effects. In this case, the viscous and inertial forces are perturbing actions, and the capillary forces are obstructing actions. The bubble shape depends on the Reynolds number Re = aeU,p/p and the Weber number We = aeU2p/cr, where p, and p are the dynamic viscosity and the density of the continuous phase, a is the surface tension coefficient, and ae is the radius of the sphere volume-equivalent to the bubble. 

There are a number of modes of jet breakup, but we consider only the breakup into spherical drops caused by capillary forces, which implies low jet velocities into an external medium whose density is low by comparison with the jet, say, air. At high velocities the dynamic effect of the surrounding medium on the jet surface will alter the surface pressure, and tangential stresses at the surface due to viscosity may also affect the breakup. It is a well-known observation that at sufficiently high velocities a jet will atomize into a large number of small droplets compared with a relatively smaller number of big drops at low velocities. 

Foam structure and dynamics. Surface layers surrounding the bubbles in a foam act as a membrane or skin that can stretch and relax in response to the lateral forces acting on it. At first, drainage of liquid taking place at the surface layer is entirely hydrod)niamic, but once spherical bubbles are in contact, flat walls develop between them, and polyhedral cells appear in the foam (Fig. 14.9c). Capillary forces be-... 

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