(180n) Two-Phase Faraday Resonance with Patterned Substrates- Theory and Experiments

Parametric resonance of an interface between two immiscible fluids bound between a flat top wall and a corrugated bottom wall is analysed both numerically and experimentally. This work is motivated by its implications in thermal management in microgravity as well as in the estimation of surface tension between fluids at high temperature (Brosius et al., 2018). When a system of two immiscible fluids is subject to periodic mechanical forcing, it can become unstable and lead to different interfacial patterns.

In this work, a simplified model based on the long-wave WRIBL theory (Weighted Residual Integral Boundary Layer) (Dietze & Ruyer-Quil, 2013) is developed to track the nonlinear evolution of the interface. This reduced order but very powerful model, while retaining the essential physics of the problem, has the advantage of being computationally less intensive compared to a full Direct Numerical Simulation (DNS). Experiments are carried out using silicone oil and FC70 as working fluids, which have been shown to uphold the stress free boundary condition at the sidewalls (Batson et al., 2013). First, the results obtained from the WRIBL model are compared with the experiments for the case of a flat bottom wall. The WRIBL model is shown to accurately predict the experimentally observed threshold corresponding to the onset of instability. The WRIBL model is then used to predict the effect of wavy bottom wall on the stability threshold. Further, it is also investigated whether the topography of the bottom wall alters the nature of the bifurcation from supercritical standing waves to subcritical breakup of the interface. These predictions from the WRIBL model are then corroborated by complementary experiments.

Acknowledgments: NASA 80NSSC18K1173, NASA NNX17AL27G and FSGC08/NNX15025

References:

Batson, W., Zoueshtiagh, F., & Narayanan, R. (2013). The Faraday threshold in small cylinders and the sidewall non-ideality. Journal of Fluid Mechanics, 729, 496–523.

Brosius, N., Ward, K., Matsumoto, S., Sansoucie, M., & Narayanan, R. (2018). Faraday forcing of high-temperature levitated liquid metal drops for the measurement of surface tension. Npj Microgravity, 4(1), 1–5.

Dietze, G. F., & Ruyer-Quil, C. (2013). Wavy liquid films in interaction with a confined laminar gas flow. Journal of Fluid Mechanics, 722, 348–393.