Surface-tension driven convection

Pojman discusses thermal frontal polymerization in Chapter 4. He focuses on thermal frontal polymerization in which a locahzed reaction zone propagates through the coupling of thermal diffusion and the Arrhenius dependence of the kinetics of an exothermic polymerization. Frontal polymerization is close to commercial apphcation for cure-on-demand appHcations and is also showing value as a way to make some materials that are superior to those prepared by traditional methods. It also manifests many types of instabihties, including buoyancy-driven convection, surface-tension-driven convection, and spin modes. 

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. 

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. 

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. 

This parameter is termed the Marangoni number. As discussed beJow, if Ma exceeds a critical value, an unstable convective flow will develop. The Marangoni number can also be interpreted as a thermal Peclet number (Eq. 3.5.16) if the characteristic velocity for the surface tension driven viscous flow is taken to be that of Eq. (10.5.5). We emphasize that this velocity is not a given parameter but rather a derived quantity. Expressing this velocity in terms of the imposed uniform temperature gradient p, with the aid of continuity, we arrive at Eq. (10.6.10). Interpreted as a Peclet number, the Marangoni number is a measure of the heat transport by convection due to surface tension gradients to the bulk heat transport by conduction. 

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. 

Figure 7.3.30. Surface tension driven defect Convection cells.

Muller, S. L., Plesser, T. Hess, B. (1985a). Surface tension driven convection in chemical and biochemical solution layers. Ber. Bunsenges. Phys. Chem., 89, 654-8. 

At the polarized water/DCE interface, the photoisomerization of DBA has been studied by Naujok et al. [38]. In this study, it is observed that nearly a full mono-layer of trans-DBA may be converted to a full monolayer of cis-DBA, with no appreciable thermal conversion back to the trans-DBA form. Also, the achievement of the conversion of the complete monolayer on a short time scale was attributed to surface mixing and surface tension driven convection effects. Interestingly, the conversion of the monolayer back to the trans-DBA form could easily be performed by proper illumination of the interface. 

Surface tension is affected both by chemical concentration and by temperature. Figure 9.10 shows how a hot spot can cause convection by locally lowering the surface tension. The cooler fluid has a higher surface tension and draws the warm fluid towards itself. If the temperature gradient is perpendicular to the interface, both buoyancy-driven convection and Marangoni (surface-tension-driven) convection are possible (Antar and Nuotio-Antar, 1993). 

Fundamental studies on the kinetics of crystal nudeation and growth in glassy melts under the influence of surface tension-driven (Marangoni) convection that, under Ig conditions, would be superseded by gravity-driven (B nard or Rayleigh) convection. 

Eckert, K., Besterhorn, M., and Thess, A. (1998) Square cells in surface-tension-driven Benard convection experiment and theory. J. Fluid Mech. 356 155-197. 

Van Hook, S., Schatz, M. S., Me Cornick, W., Swift, J. B., and Swinney, H. D. (1995) Long-wavelength instability in surface-tension-driven Benard convection. Phys. Rev. Lett. 75 4397-4400. 

Vidal, A. and Acrivos, A. (1966) Nature of the neutral state in surface-tension driven convection. Phys. Fluids 9 615-616. 

Now, it is important to note that in the case of the Benard-Marangoni convection in a liquid layer with a deformable interface, as was previously shown by Takashima (1981a) through a linear stability analysis (see the 7), there exist two monotonous modes of surface tension driven instability. 

Buoyancy-driven and surface-tension driven convection can affect a wide variety of polymer process. Often the role can be studied on earth by varying the viscosity or orientation or the system. Yet, performing experiments in weightlessness can be the only way to determine the relative effects of the two processes or if the viscosity can not be independently varied. 

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