Flames, Splashes and Microdroplets: A Mathematical Approach to Three Fluid Dynamics Problems

Abstract

Three different problems in fluid mechanics are presented in this thesis. The first one deals with the mechanism behind the extinction of a flame by an alternating electric field. A simple model for the interaction between the field and the ions produced by the reaction is presented, which agrees quantitatively with the experiments. It also indicates that charges diffusion is responsible for the non-zero time averaged force on the flame. The second problem focuses on the role of viscosity during the splash of liquid droplets. We show that contrary to what was done in previous theoretical studies, the role of viscosity cannot be investigated within the framework of a boundary layer approximation. Rather, the full viscous term must be included in the equations. Finally, we present the theory behind a new microfluidic device (called centipede) which produces microdroplets at a very high rate without relying on any active element to precipitate the detachment of the drops. We clearly show that the drops detach through a Rayleigh-Plateau instability in an otherwise quasi-static flow. We also predict how the throughput and size of the drops are affected by the geometrical parameters of the device.