Stabilisation of cylindrical liquid bridges using radial, oscillatory body force: theoretical and computational analysis.

Dynamic stabilisation of Rayleigh-Plateau modes on a liquid cylinder employing a radial oscillatory body force has been recently shown in (Patankar, Basak & Dasgupta, J. Fluid Mech. 2022, In Press). In this study, we show that this mechanism can be employed to stabilise cylindrical liquid bridges of finite length with pinned contact line at the end substrate. We derive a matrix Mathieu equation via linear stability analysis, extending the scalar Mathieu equation derived earlier in (Patankar, Farsoiya & Dasgupta, J. Fluid Mech. 2018, vol. 857) to the pinned case. Solutions to this equation predict that hitherto unstable modes can be stabilised via forcing. Analytical predictions show excellent agreement with numerical simulations of the incompressible, Euler's equations with surface tension. The stability diagram of the matrix Mathieu equation and the combination resonance regions will be discussed in the presentation.