(454a) Suppressing Surface Tension Gradient-Driven Flow Using Resonant Forcing

In this work, we show how we may use resonant forcing to stabilize a fluid layer that is subject to destabilizing surface tension gradient-driven flow. The surface tension gradient-driven flows or Marangoni flows arise when a layer of fluid is heated from the liquid side beyond a critical temperature gradient. These flows lead to interface deformations and convective flow patterns in the fluid layer. Previous experimental and theoretical investigations on the Marangoni effect on thin films (VanHook et.al.) showed that surface tension gradient-driven flows create large depressions at the free surface leading to the dry-out of thin films. In another instability and in the absence of heating, if a fluid layer is vertically oscillated commensurate with its natural frequency and at an amplitude greater than a critical value, violent undulations are formed at the interface on account of resonance.

We ask if we may use the resonant instability to quench the Marangoni instability. To this end, linear stability analysis on the effect of resonant forcing on surface tension gradient-driven flow is carried out. The analysis shows that resonant forcing delays the onset of Marangoni instability in thin films by suppressing the surface tension-gradient driven flows. The effect of resonant forcing on dry-outs in thin layers is also studied using a powerful reduced-order model derived using the Weighted Residual Integral Boundary Layer (WRIBL) technique. The calculations show that the dry-out formation can be avoided by oscillating the fluid layer beyond a critical amplitude. Resonant forcing at low frequencies suppresses the surface tension gradient flows completely, giving rise to a quiescent stable fluid layer. Further increase in amplitude beyond a second threshold gives rise to an oscillatory flow on account of resonance. At higher frequencies, the free surface does not transition to a flat surface. Instead, the resonant forcing subverts the thermocapillary flows, constraining the interface to a saturated form and preventing dry-out. Suppressing the formation of dry-out in thin films is important in its applications in coating industries for the manufacture of optical films and in additive manufacturing of metals in microgravity environments for human habitation in space.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge funding from NSF via grant number CBET-2025117 and NASA 80NSSC23K0457.

_{[1] S. J. VanHook, M. F. Schatz, J. B. Swift, W. D. Mccormick, and H. L. Swinney, “Long-wavelength surface-tension-driven Bénard convection: experiment and theory,” Journal of Fluid Mechanics, vol. 345, p. 45–78, 1997}