Dynamic Capillarity

It has also been shown that the thickness of the wetting film can be deduced from the behavior of the film tension as a function of disjoining pressure (this was done explicitly by, among others, Derjaguin, and in Ref. 52). If a capillary is placed vertically and a meniscus coexists with a wetting film on the sides of the capillary, then the weight of the liquid column is carried by the tension of the wetting film. 

In thermodynamic equilibrium, a small vertical displacement of the meniscus together with the liquid column below it, 8s, implies that the weight of the liquid column performs an amount of work per unit length of the column that is equal to an increase of the free energy of the film. It is then possible to find the thermodynamic thickness of the wetting film on the channel wall from the known isotherm of the disjoining pressure and the film tension  

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Qiu W, Kang YL, Li Q, Lei ZK, Qin QH (2008) Experimental analysis for the effect of dynamic capillarity on stress transformation in porous silicon. Appl Phys Lett 92 041906 Scherer GW (1990) Theory of drying. J Am Ceram Soc 73(1) 3-14... 

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. 

Capillarity phenomena are everyday occurrences that result from the existence of surface tension or interfacial tensions. In addition to the static phenomena discussed herein, surface tension and capillarity are also responsible for numerous dynamic phenomena that may result from localized gradients in temperatures or in compositions the study of dynamic capillary phenomena (e.g., Marangoni flows, Benard cells) is the subject of much literature coverage and is beyond the scope of this survey. 

It may be added here that the four basic laws of capillarity, i.e., the equations of Gibbs [(10.2)], Laplace [(10.7)], Kelvin [(10.9)] and Young [(10.10)], all describe manifestations of the same phenomenon the system tries to minimize its interfacial free energy. (Another manifestation is found in the Hamaker equations see Section 12.2.1.) These laws describe equilibrium situations. Moreover, dynamic surface phenomena are of great importance. 

The microrheology makes it possible to expect that (i) The drop size is influenced by the following variables viscosity and elasticity ratios, dynamic interfacial tension coefficient, critical capillarity number, composition, flow field type, and flow field intensity (ii) In Newtonian liquid systems subjected to a simple shear field, the drop breaks the easiest when the viscosity ratio falls within the range 0.3 < A- < 1.5, while drops having A- > 3.8 can not be broken in shear (iii) The droplet breakup is easier in elongational flow fields than in shear flow fields the relative efficiency of the elongational field dramatically increases for large values of A, > 1 (iv) Drop deformation and breakup in viscoelastic systems seems to be more difficult than that observed for Newtonian systems (v) When the concentration of the minor phase exceeds a critical value, ( ) >( ) = 0.005, the effect of coalescence must be taken into account (vi) Even when the theoretical predictions of droplet deformation and breakup... 

Thus last result is independent of t he velocity and agr( es wit h the experimentally c bservo(l dcpciulence on the radius. For a 1-inm drop, the time is of the order of a few milluseconds. The time r scales as the characterhstic o.scillation period of a drop vibrating in air. d he dynamics of the oscillations is de.seribed by writing the equilibrium betw een capillarity and inertia. The calculations were done by Lord Rayleigh. He W orked out the appropriate numerical coefficients applicable to the various vibration modes of drops an is.sne already touched upon in. section 5.2. 

Theisen et al. presented a dynamic model to describe the oscillations resulting from the competition between liquid inertia and capillarity [8]. They demonstrated that gravity was weaker than surface tension but exerted a non-negligible effect. It was found that gravity could distort the shapes of... 

Q. Z. Yuan and Y. P. Zhao, Precursor film in dynamic wetting, electrowetting, and electro-elasto-capillarity. Phys. Rev. Lett. 104, 246101 (2010). 

All drop and bubble methods are based on the Laplace equation of capillarity. In order to study dynamic aspects of adsorption, the growing drop or bubble and the expanded drop methods are suitable (3). In Figure 12.13, the schematic of a static or growing drop instrument is shown. In applications of capillary pressure tensiometry, an equation which is equivalent... 

The description of liquids interfaces, in particular in the presence of solid surfaces, is an old question at the confluent between physics, chemistry, and engineering. It was examined by pioneers like Young and Laplace, whose formalism remains the basis of the description of capillarity. The dynamics of wetting has been intensively studied in the second part of the twentieth century, when many experiments and theories were developed. These studies emphasized the importance of a precise description of boundary... 

Interfacial and capillary phenomena are present in multiple biological processes. Some examples are duck s feathers impermeability, spiders sticky traps, and Lotus leaf s effect. The last subject is considered in a separate chapter due to its important technological applications. The basis to understand all those processes is the focus of the present chapter, divided into three subsections. The first one addresses the fundamentals of interfacial tension and wetting conditions as thermodynamical concepts. In the second, capillarity effects under dynamical conditions are considered. The third section is devoted to liquid films, their stability, and the spontaneous retraction in simple geometries. 

Exercise limitation and functional disability in COPD have a complex, multifactorial basis. Ventilatory limitation is caused by increased airways resistance, static and dynamic hyperinflation, increased elastic load to breathing, gas exchange disturbances, and mechanical disadvantage and/or weakness of the respiratory muscles (4-6). Car-diocirculatory disturbances (7,8), nutritional factors (9), and psychological factors, such as anxiety and fear, also contribute commonly to exercise intolerance. Skeletal muscle dysfunction is characterized by reductions in muscle mass (10,11), atrophy of type I (slow twitch, oxidative, endurance) (12,13) and type Ila (fast twitch) muscle fibers (14), altered myosin heavy chain expression (15), as well as reductions in fiber capillarization (16) and oxidative enzyme capacity (17,18). Such a dysfunction is another key factor that contributes... 

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