Weakly nonlinear shape oscillations of a Newtonian drop

Nonlinear axisymmetric shape oscillations of a Newtonian drop in vacuum are investigated theoretically, for fundamental interest and their relevance transport processes across the surface. The weakly nonlinear analysis is carried out for, but not limited to, modes initial deformation up to m = 4. Ohnesorge number covers range between 0.01 1. approach, which third order, accounts coupling different oscillation modes. With increasing surface deformation, develop an asymmetry times during one period spends states frequency decrease below linear value, quasi-periodicity motion. In contrast inviscid case [D. Zrni? G. Brenn, “Weakly drops,” J. Fluid Mech. 923, A9 (2021)], present reveals already second-order approximation. results positively validated against relevant literature. theory quantifies effects viscosity, measured by number, dampening behavior enhancing [E. Becker et al., “Nonlinear dynamics viscous droplets,” 258, 191 (1994)]. at strong deformation. resultant motion, starting from higher-order mode exhibits aperiodic behavior, may turn into damped oscillatory with ongoing time due lower-order