Surface tension gradients

A drop of surfactant solution will, under certain conditions, undergo a fingering instability as it spreads on a surface [27, 28]. This instability is attributed to the Marongoni effect (Section IV-2D) where the process is driven by surface tension gradients. Pesach and Marmur have shown that Marongoni flow is also responsible for enhanced spreading... 

The role of coalescence within a contactor is not always obvious. Sometimes the effect of coalescence can be inferred when the holdup is a factor in determining the Sauter mean diameter (67). If mass transfer occurs from the dispersed (d) to the continuous (e) phase, the approach of two drops can lead to the formation of a local surface tension gradient which promotes the drainage of the intervening film of the continuous phase (75) and thereby enhances coalescence. It has been observed that d-X.o-c mass transfer can lead to the formation of much larger drops than for the reverse mass-transfer direction, c to... 

Circulation of fluid is promoted by surface tension gradients but inhibited by viscosity, which slows the flow, and by molecular diffusion, which tends to even out the concentration differences. The onset of instabibty is described by a critical Marangoni number (Mo), an analogue of the Rayleigh... 

Here we also consider sorption kinetics as the mass-transfer barrier to surfactant migration to and from the interface, and we follow the Levich framework. However, our analysis does not confine all surface-tension gradients to the constant thickness film. Rather, we treat the bubble shape and the surfactant distribution along the interface in a consistent fashion. 

During the transfer of a surface-active solute across the surface, unstable surface-tension gradients may occur in the plane of the surface. A good example is furnished by Langmuir s experiment (10) on the evaporation of ether from a saturated (5.6%) solution in water talc... 

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... 

To explain this spreading rate behavior, Nikolov et al. [35] postulated that the excess driving force (assuming that capillary and hydrostatic forces balance each other) is a radial surface tension gradient, which can be approximated as... 

Chengara A, Nikolov A, Wasan D (2002) Surface tension gradient driven spreading of trisiloxane solution on hydrophobic solid. Colloid Surf A 206 31-39... 

A. i.e,. E — da/din A. If the film of liquid separating two neighboring bubbles in a foam develops a thin spot, the surface tension gradient in the vicinity of the thin spot will induce a Muraugoni flow of liquid toward Ihe direction of higher cr. This flow of liquid toward the thin spot helps heal the fluctuation and thus keeps the neighboring bubbles from coalescing. 

Convection in Melt Growth. Convection in the melt is pervasive in all terrestrial melt growth systems. Sources for flows include buoyancy-driven convection caused by the solute and temperature dependence of the density surface tension gradients along melt-fluid menisci forced convection introduced by the motion of solid surfaces, such as crucible and crystal rotation in the CZ and FZ systems and the motion of the melt induced by the solidification of material. These flows are important causes of the convection of heat and species and can have a dominant influence on the temperature field in the system and on solute incorporation into the crystal. Moreover, flow transitions from steady laminar, to time-periodic, chaotic, and turbulent motions cause temporal nonuniformities at the growth interface. These fluctuations in temperature and concentration can cause the melt-crystal interface to melt and resolidify and can lead to solute striations (25) and to the formation of microdefects, which will be described later. 

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