Breakup of liquid jets: the capillary retraction
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Why and how does a falling stream of fluid break up into droplets? It is well known that the major driving mechanism is the fluid surface tension, but other variables such as viscosity and environmental instabilities are also known to affect the breakup. In this thesis, the capillary retraction of liquid filaments is studied through experimental, theoretical and numerical methods. Previous works have established that a liquid filament can either recoil into a single sphere or break up into multiple droplets. Its fate depends on the Ohnesorge number Oh, a parameter that measures the relative importance of viscous to capillary forces, and the initial size aspect ratio Γ (length/thickness). According to the state-of-the-art, a critical aspect ratio Γc should exist and depend on the Ohnesorge number, such that longer filaments break up and shorter ones collapse into a single drop. The results in this thesis demonstrate that the breakup/no-breakup boundary is complex and not as simple as originally pro- posed. A transitional regime exists in which there are multiple Γc thresholds: breakup and no-breakup behaviours alternate. These observations are explained through a model based on the interaction of capillary waves that originate at both ends of the filament and travel inwards along its surface. Additionally, an asymptotic analysis is used to derive a long-time steady state expansion for the retracting filament profile. This analysis results in three distinct regions with different characteristic length and time scales: a growing spherical rim, a cylindrical section and an intermediate matching zone. The analytical model shows that capillary waves escape from the rim travelling on the fluid interface. The key critical values of the problem are discussed: conditions to form a neck between the rim and the cylindrical filament, its minimal thickness, the waves’ asymptotic wavelength and decay length. Interestingly, the wavelength of the capillary ripples is found to be approximately 3.6 times the filament’s radius at the inviscid limit. Finally, the theoretical model is verified by numerical simulations and past works obtaining a good agreement.
AuthorsConto, Francesco Paolo
- Theses