Surface Tension Driven Flow

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... 

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. 

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. 

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. 

During the 1870 s, Carlo Marangoni, who was apparently aware of Carra-dori s work but not of Thompson s, formulated a rather complete theory of surface tension driven flow (M2, M3). He noted that flow could result from surface tension variations as they are caused by differences in temperature and superficial concentration, and that, conversely, variations in temperature and concentration could be induced by an imposed surface flow. Marangoni ascribed several new rheological properties to the surface (notably surface viscosity, surface elasticity, and even surface plasticity), while remarking that perhaps some of these properties could be associated only with surface contamination. Most present-day authors ascribe the first explanation of surface tension driven flow to Marangoni, and term such flow a Maragoni effect. ... 

As far as is known to the authors, none of the nonlinear theories has been able to predict a preferred wavelength. Also it appears that no nonlinear analysis has been attempted for surface tension driven flows. Convection in deep layers of fluid has also never been treated theoretically. 

The flow phenomena involved in zone refining will be discussed briefly. In particular we shall consider surface tension driven flow in a cavity containing a low Prandtl number, Pr, fluid (a low Pr number is typical of liquid metals and semiconductors). It will be shown that simplified models of such flow, which simulate the melt configuration in zone refining, predict multiple steady-state solutions to the Navier-Stokes equations exist over a certain range of the characteristic parameter. 

Simplified Model of Surface Tension Driven Flow in a Two-dimensional... 

We speculate that the existence of multiple solutions to the Navier-Stokes equations for surface tension driven flow in a cavity is evidence of instability in this system, and this suggests the need for a stability analysis of the velocity profiles. It should be noted that the simplified model of the molten zone which we are using does not include the blocking effect of the solid-liquid interface at x = +L. 

McNeil, T. Cole, R. Subramanian, S. "Surface Tension Driven Flow in Glass Melts and Model Fluids" in Materials Processing in the Reduced Gravity of Space, Guy Rindone, Ed, Elsevier, 1982, p. 289-299. 

Hydrophilic and Hydrophobic Patterning Surface-Tension-Driven Flow... 

In a qualitative sense, the measured position of the meniscus as a function of time was found to qualitatively follow the Washburn model (refer to the entry on Surface-Tension-Driven Flow, for details of this model). Quantitatively, however, a lowering of capillary filling speed could be noted, which might be attributed to the electroviscous effects and stronger surface influences over nanoscopic length scales. Future efforts need to be directed to develop more rigorous mathematical models to predict the quantitative trends of capillary fiUing in nanofluidic channels to resolve these issues. 

Huang W, Bhullar RS, Fung YC (2001) The surface-tension-driven flow of blood from a droplet into a capillary tube. ASME J Biomed Eng 123 446 54... 

The basic idea behind the VOF method is to discretize the equations for conservation of volume in either conservative flux or equivalent form resulting in near-perfect volume conservation except for small overshoot and undershoot. The main disadvantage of the VOF method, however, is that it suffers from the numerical errors typical of Eulerian schemes such as the level set method. The imposition of a volume preservation constraint does not eliminate these errors, but instead changes their symptoms replacing mass loss with inaccurate mass motion leading to small pieces of fluid non-physically being ejected as flotsam or jetsam, artificial surface tension forces that cause parasitic currents, and an inability to calculate accurately geometric information such as normal vector and curvature. Due to this deficiency, most VOF methods are not well suited for surface tension-driven flows unless some improvements are made [19]. 

Surface-tension-driven flow concerns the actuation and control of fluid dynamic transport through a manipulation of the surface tension forces. The manipulation, in principle, can be hydrodynamic, thermal, chemical, electric, or optical in namre. It is also important to mention here that there must be a free surface or a liquid-fluid interface in order to have a surface-tension-driven flow. 

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