Marangoni convection in two liquid layers:
We have begun experiments on surface-tension-driven convection in two liquid layers, for both heating from below and heating from above. While instability only appears in liquid-gas systems for heating from below (i.e., the liquid side), we see instability for both directions of heating in the liquid-liquid system for certain liquids and depth ratios. The length scales and critical temperature gradients are different for the two directions of heating. We have also performed the full linear stability analysis for the experiment (including buoyancy effects and oscillatory instabilities) and have begun some nonlinear analysis, as well.
Effect of surface profile and sidewalls upon onset of long-wavelength surface-tension-driven convection [1]:
We have analyzed the effect of the presence of sidewalls in our experiments on the long-wavelength instability in surface-tension-driven convection. We found that sidewall effects account for a significant portion of the observed deviation between our experiments and linear stability theory.
Nonlinear control of a liquid bridge [2]:
We have developed a method to control nonlinear systems in unstable states far from equilibrium, even without a priori knowledge of the underlying equations of motion. The method has been applied to a liquid bridge surface-tension driven convection system that models the float zone refining process. The algorithm routines along with several example programs written in the MATLAB language can be found at ftp://ftp.mathworks.com/pub/contrib/v5/control/nlcontrol.
Pattern formation in systems far from equilibrium [3]:
The principles of pattern formation in nonequilibrium continuum systems are reviewed along with a discussion of some applications and open questions.
[1] R. Becerril, S. J. Van Hook, and J. B. Swift, "Effect of Interface Profile on Long-Wavelength Surface-Tension-Driven Convection" submitted to Physics of Fluids. [2] V. Petrov,, A. Haaning, K. A. Muehlner, S. J. Van Hook, and H. L. Swinney, "Model-independent nonlinear control algorithm with application to a liquid bridge experiment" Phys. Rev. E 58, 427-433 (1998). [3] H. L. Swinney, "Emergence and evolution of patterns," in Critical Problems in Physics, edited by V. L. Fitch, D. R. Marlow, and M. A. E. Dementi (Princeton University Press, 1997), pp. 51-74.