Hydrodynamics surface tension

General hydrodynamic theory for liquid penetrant testing (PT) has been worked out in [1], Basic principles of the theory were described in details in [2,3], This theory enables, for example, to calculate the minimum crack s width that can be detected by prescribed product family (penetrant, excess penetrant remover and developer), when dry powder is used as the developer. One needs for that such characteristics as surface tension of penetrant a and some characteristics of developer s layer, thickness h, effective radius of pores and porosity TI. One more characteristic is the residual depth of defect s filling with penetrant before the application of a developer. The methods for experimental determination of these characteristics were worked out in [4]. 

Since the drop volume method involves creation of surface, it is frequently used as a dynamic technique to study adsorption processes occurring over intervals of seconds to minutes. A commercial instrument delivers computer-controlled drops over intervals from 0.5 sec to several hours [38, 39]. Accurate determination of the surface tension is limited to drop times of a second or greater due to hydrodynamic instabilities on the liquid bridge between the detaching and residing drops [40],... 

A recent design of the maximum bubble pressure instrument for measurement of dynamic surface tension allows resolution in the millisecond time frame [119, 120]. This was accomplished by increasing the system volume relative to that of the bubble and by using electric and acoustic sensors to track the bubble formation frequency. Miller and co-workers also assessed the hydrodynamic effects arising at short bubble formation times with experiments on very viscous liquids [121]. They proposed a correction procedure to improve reliability at short times. This technique is applicable to the study of surfactant and polymer adsorption from solution [101, 120]. 

Surface waves at an interface between two innniscible fluids involve effects due to gravity (g) and surface tension (a) forces. (In this section, o denotes surface tension and a denotes the stress tensor. The two should not be coiifiised with one another.) In a hydrodynamic approach, the interface is treated as a sharp boundary and the two bulk phases as incompressible. The Navier-Stokes equations for the two bulk phases (balance of macroscopic forces is the mgredient) along with the boundary condition at the interface (surface tension o enters here) are solved for possible hamionic oscillations of the interface of the fomi, exp [-(iu + s)t + i V-.r], where m is the frequency, is the damping coefficient, s tlie 2-d wavevector of the periodic oscillation and. ra 2-d vector parallel to the surface. For a liquid-vapour interface which we consider, away from the critical point, the vapour density is negligible compared to the liquid density and one obtains the hydrodynamic dispersion relation for surface waves + s>tf. The temi gq in the dispersion relation arises from... 

Rizzuti et al. [Chem. Eng. Sci, 36, 973 (1981)] examined the influence of solvent viscosity upon the effective interfacial area in packed columns and concluded that for the systems studied the effective interfacial area a was proportional to the kinematic viscosity raised to the 0.7 power. Thus, the hydrodynamic behavior of a packed absorber is strongly affected by viscosity effects. Surface-tension effects also are important, as expressed in the work of Onda et al. (see Table 5-28-D). 

We expect more insight from simulations in the future, particularly in situations where these multicomponent systems show effects of coupling between the different degrees of freedom, surface tensions depending on temperature and concentration, hydrodynamic flow induced by concentration gradients in addition to thermal buoyancy. 

Capillary waves occur spontaneously at liquid surfaces or liquid liquid interfaces due to thermal fluctuations of the bulk phases. These waves have been known as surface tension waves, ripples, or ripplons for the last century, and Lamb described their properties in his book Hydrodynamics in 1932 [10]. Before that, William Thomson (Lord Kelvin) mentioned these waves in some of his many writings. 

In a hydrodynamic theory of the free, clean, surface of a turbulent liquid, Levich 19a) postulates that there exists an upper zone of liquid, of thickness X, in which the turbulent regime is so altered by the surface tension (which opposes local deformations) that within this zone the turbulence is severely damped. Right in the plane of the surface (at... 

Another possible approach to burn-out prediction is to study film breakdown due to hydrodynamic effects. Presumably, if thin spots occur in a film for any reason, the film becomes hotter, the surface tension is reduced, and increased vaporization tends to cause a break in the liquid layer. Although studies of surface tension and wetting angle in thin-film flow have been made, no successful correlation of burn-out in these terms has yet been offered. 

In the narrow tubes used by Beek and van Heuven, the bubbles assumed the shape of Dumitrescu (or Taylor) bubbles. Using the hydrodynamics of bubble rise and the penetration theory of absorption, an expression was developed for the total absorption rate from one bubble. The liquid surface velocity was assumed to be that of free fall, and the bubble surface area was approximated by a spherical section and a hyperbola of revolution. Values calculated from this model were 30% above the measured absorption rates. Further experiments indicated that velocities are reduced at the rear of the bubble, and are certainly much less than free fall velocities. A reduction in surface tension was also indicated by extreme curvature at the rear of the bubble. 

Surface contaminants affect mass transfer via hydrodynamic and molecular effects, and it is convenient to consider these separately. Hydrodynamic effects include two phenomena which act in opposition. In the absence of mass transfer, contaminants decrease the mobility of the interface as discussed in Section ILD. In the presence of mass transfer, however, motion at the interface may be enhanced through the action of local surface tension gradients caused by small differences in concentration along the interface. This enhancement of surface... 

At larger Re and for more marked deformation, theoretical approaches have had limited success. There have been no numerical solutions to the full Navier-Stokes equation for steady flow problems in which the shape, as well as the flow, has been an unknown. Savic (S3) suggested a procedure whereby the shape of a drop is determined by a balance of normal stresses at the interface. This approach has been extended by Pruppacher and Pitter (P6) for water drops falling through air and by Wairegi (Wl) for drops and bubbles in liquids. The drop or bubble adopts a shape where surface tension pressure increments, hydrostatic pressures, and hydrodynamic pressures are in balance at every point. Thus... 

Miller, R., Bree, M., and Fainerman, V.B. 1998. Hydrodynamic effects in measurements with the drop volume technique at small drop times-3. Surface tension of viscous liquids. Colloids Surf. 142 237-242. 

The solution of the hydrodynamic problem of boundary layer flow, excluding the effects of surface tension, requires simplification of the formulation this is achieved by introducing the flow function t /. Then the transition to a system of differential equations written for a new coordinate system (turn angle and flow function) can be made, and we can find the form of the free surface... 

To provide a specific example, Imae and Ikeda (ref. 479) state that amine oxide is very hydrophilic and can constitute a good polar head group for nonionic surfactants at neutral pH. Dimethyl-dodecylamine oxide was first prepared by Hoh et al. (ref. 494), and its surface-active properties in aqueous solutions were investigated by measurements of surface tension (ref. 495), light scattering (ref. 496-498), and hydrodynamic properties (ref. 499). It was found that dimethyldodecylamine oxide can form only spherical micelles in water and aqueous NaCl solutions, when the micelle concentration is dilute (ref. 496,498). Similarly, the homolog dimethyltetradecylamine oxide forms only spherical micelles in water (ref. 496). 

Gas holdup is an important hydrodynamic parameter in stirred reactors, because it determines the gas-liquid interfacial area and hence the mass transfer rate. Several studies on gas holdup in agitated gas-liquid systems have been reported, and a number of correlations have been proposed. These are summarized in Table VIII. For a slurry system, only a few studies have been reported (Kurten and Zehner, 1979 Wiedmann et al, 1980). In general, the gas holdup depends on superficial gas velocity, power consumption, surface tension and viscosity of liquids, and the solid concentration. The dependence of gas holdup on gas velocity, power consumption, and surface tension of the liquid can be described as... 

A block-scheme of the apparatus for the study of foam films under applied pressure is shown in Fig. 2.11. The films are formed in the porous plate of the measuring cell (Fig. 2.4, variant D and E). The hydrodynamic resistance in the porous plate is sufficiently small and the maximum capillary pressure which can be applied to the film is determined by the pore material. The porous plate measuring cell (Fig. 2.4, variants D and E) permits to increase the capillary pressure up to 105 Pa, depending on the pore size and the surface tension of the solution. When the maximum pore size is 0.5 pm, the capillary pressure is 310s Pa (at cr = 70 mN/m). The cell is placed in a thermostating device, mounted on the microscopic table. 

The theoretical analysis indicated that asymmetric drainage was caused by the hydrodynamic instability being a result of surface tension driven flow. A criterion giving the conditions of the onset of instability that causes asymmetric drainage in foam films was proposed. This analysis showed as well that surface-tension-driven flow was stabilised by surface dilational viscosity, surface diffusivity and especially surface shear viscosity. 

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