Surface-tension driven

In the absence of gravity, the properties of a candle flame change dramatically [36,39,41]. Figure 8.1.3 shows a candle flame on the Mir space station, in which the melt layer was hemispherical and much thicker than that in normal gravity, and the flame was smaller, spherical, and less sooty, uncovering the blue flame zone. There was significant circulation in the liquid phase (as a result of surface-tension-driven flow caused... 

At low Rayleigh numbers, Wragg (W6) found a smaller Ra dependence, resembling more the dependence in laminar free convection. In this range of Ra numbers, a cellular flow pattern is believed to exist, analogous to that of thermal and surface tension-driven cellular convection (Benard cells F3). In the range where the convection is turbulent, the Ra1/3 dependence has been confirmed over seven powers of Ra by Ravoo (R9), who used a centrifuge to vary the body force at constant bulk composition. 

N. Watanabe, K. Kutsumi, and O. Sano, Surface tension driven random motion of a mercury drop in HNO3 and K2Cr207 solution, /. Phys. Soc. Jpn. 63(8), 2955-2963 (1994). 

At such small scales, the experimenters cannot see the motor working by any means except an electron microscope. Although the motor is simple conceptually, its precision is incredible—it operates at the atomic level, controlling the motion of atoms as they shuffle back and forth between nanoparticles. B. C. Regan, Zettl, and their colleagues published the report Surface-Tension-Driven Nanoelectromechani-cal Relaxation Oscillator in Applied Physics Letters in 2005. As the researchers note in their report, [SJurface tension can be a dominant force for small systems, as illustrated in their motor. This is a prime example of the different forces and situations that must be taken into account in the nanoworld. 

Regan, B. C., S. Aloni, K. Jensen, and A. Zettl. Surface-Tension-Driven Nanoelectromechanical Relaxation Oscillator. Available online. URL http //scitation.aip.org/vsearch/servlet/VerityServlet KEY=APPLAB smode=results8onaxdisp=108q ossiblel=surface-tension-driven%5... 

A very recent development is encapsulation of actives in colloidosomes [16, 41]. The method is analogous to liposome entrapment. Selectively permeable capsules are formed by surface-tension-driven deposition of solid colloidal particles onto the surface of an inner phase or active ingredient in a water-in-oil or an oil-in-water emulsion composed of colloidal particles. Initially synthetic polymer microparticles were used but more recently a natural alternative has been described based on small starch particles. After spray-drying, redispersible emulsions can be formed. 

Similar analyses are available for surface-tension-driven flows in a slender cavity with the additional assumption that the meniscus at the top of the cavity is also flat (36). Smith and Davis (37-39) have used this configuration to study the stability of the flow with respect to wavelike instabilities (see also reference 40). Homsy and co-workers (41, 42) have analyzed the effect of a surface-active agent on the thermocapillary motion in a slender cavity. 

Transitions from steady-state to time-dependent surface-tension-driven motions are well known also and are important in meniscus-defined crystal growth systems. For example, the experiments of Preisser et al. (51) indicate the development of an azimuthal traveling wave on the axisymmetric base flow in a small-scale floating zone. 

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. 

P. Colinet, I.C. Legros and M.G. Velarde, Nonlinear Dynamics of Surface-Tension-Driven Instabilities, Wley-VCH, Berlin, 2001. 

Single crystal silicon is one of the important fundamental materials for the modern photovoltaic industry. The Czochralski method of growing single crystal silicon is affected by the thermocapillary convection. Temperature and concentration gradients at the free surface of the melt give rise to surface tension-driven Marangoni flow, which can lead to crystal defects, if it is sufficiently large. 

Reaction between a gas and a liquid normally involves absorption and physical solution of the gas followed by homogeneous reaction between the dissolved species. The problem of gas absorption with chemical reaction has been extensively studied and in such systems the observed rate of gas absorption will be a function of the chemical reaction rate, the diffusion of the dissolved gas in the liquid, and, possibly, the fluid dynamics of the system (the rate of surface renewal) if surface tension driven or other circulation effects occur. There is no evidence of these so far in the thin films employed in practical catalysts. Danckwerts and Astarita give comprehensive treatments of the subject of gas absorption accompanied by reaction. 

Lee, J. Kim, C.-J. Surface-tension-driven microactuation based on continuous electrowetting. J. Microelectromech. Syst. 2000, 9 (2), 171-180. 

Reichenbach, J. and Linde, H., Linear perturbation analysis of surface-tension-driven convection at a plane interface (Marangoni instability), J. Colloid Interface Sci., 84, 433 143, 1981. Nepomnyashchy, A.A., Velarde, M.G., and Colinet, R, Interfacial Phenomena and Convection, CRC Press/Chapman Hall, London, 2002. 

Figure 2-15. Photographs of the relaxation of a pair of initially deformed viscous drops back to a sphere under the action of surface tension. The characteristic time scale for this surface-tension-driven flow is tc = fiRi 1 + X)/y. The properties of the drop on the left-hand side are X = 0.19, /id = 5.5 Pa s, ji = 29.3 Pa s, y = 4.4 mN/rn, R = 187 /an, and this gives tc = 1.48 s. For the drop on the right-hand side, X = 6.8, lid = 199 Pa s, //. = 29.3 Pa s, y = 4.96 mN/m, R = 217 /an, and tc = 9.99 s. The photos were taken at the times shown in the figure. When compared with the characteristic time scales these correspond to exactly equal dimensionless times (/ = t/tc) (a) t = 0.0, (b) t = 0.36, (c) t = 0.9, (d) t = 1.85, (e) t = 6.5. It will be noted that the drop shapes are virtually identical when compared at the same characteristic times. This is a first illustration of the principle of dynamic similarity, which will be discussed at length in subsequent chapters.

For solids with continuous pores, a surface tension driven flow (capillary flow) may occur as a result of capillary forces caused by the interfacial tension between the water and the solid particles. In the simplest model, a modified form of the Poiseuille flow can be used in conjunction with the capillary forces equation to estimate the rate of drying. Geankoplis (1993) has shown that such a model predicts the drying rate in the falling rate period to be proportional to the free moisture content in the solid. At low solid moisture contents, however, the diffusion model may be more appropriate. 

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