Concentrically Embedded Bubbles alter Surface Waves of Viscous Drop

Jay Mudholkar

My advice to high school students looking to work on a research project that combines science and mathematics is to be invested in learning a lot of new things and keep an open mind as high schoolers, there’s a lot of mathematics we are unfamiliar with, and sometimes it’s easy to get overwhelmed. However, I would say that the beauty of combined science and math research is that you learn so much about mathematical theory that can be applied to the science a double-pronged approach, if you will! It’s a fantastic opportunity, and with an open mind and willingness to learn it becomes that much better and more rewarding … This research describes how a concentrically embedded bubble alters the surface wave of a suspended viscous drop. The analysis considers small amplitudes of the interfacial pulsation so that the nonlinear convective terms can be neglected in the flow equation. The consequent linearized system is represented by a matrix formulation which predicts the natural frequencies and decay constants for different modes of oscillation. The involved matrices have a block diagonal structure separating the deformational and rotational groups. The presented work includes the mathematical derivations for both groups proving that the former manifests both oscillating and decaying features while the latter only exhibits monotonic decrease. The results reveal the variation in decay constants with bubble-drop size-ratio for different rotational modes …