LAUSR

Abstract The dynamic interaction of a fluid particle with a continuous phase has been often a topic of study, for its broad range of applications in various industries. Better understanding of particle-fluid interface instability can assist to enhance the efficiency of different processes and possibly avoid unfavorable consequences. In the present work, a weakly nonlinear instability analysis is performed to study the driven shape oscillations of a fluid particle (droplet or bubble) immersed in another fluid (liquid or gas). The analysis is conducted using a perturbation expansion approach, allowing for shape mode interactions for any arbitrary number of modes. The present work intends to provide an analytical solution to forced shape oscillations of a fluid particle, which accounts for viscosity of both fluids involved, instability nonlinearities, and shape mode interactions. The model proposed is used to study the effect of various parameters on the deformation of fluid particle interface. The cases studied provide an insight into shape mode interactions and resonances due to nonlinearity. Moreover, the results show that the viscosity of the fluid particle can play a role in increasing the chances of greater mode interaction and parametric resonance effects, especially for relatively large initial deformations.