Multiphase dynamics in liquid mixtures: thermocapillary propulsion of bubbles and instabilities in evaporating layers
Kalata Nazareth, Robson
Liquid mixtures are ubiquitous in industry and in nature, and demonstrate remarkably more complex behaviour than pure fluids, which is still to be revealed. Particularly, commercial coolants are mixtures and the complexity in their flow behaviour is due to the interplay between phenomena driven by thermal and concentration gradients. This thesis considers predominantly binary mixtures wherein one component is more volatile than the other. The thesis focuses on multiphase dynamics presented in liquid mixtures. Given the volatility difference, there is always phase-change under temperature gradients. A bubble generated in that mixture has dynamics which will be subjected to the surrounding flow, temperature and concentration fields. The bubble will eventually grow until it occupies the entirety of the tube leaving behind a thin evaporating layer of the mixture. Thus the thesis work focusses on i) investigations of the bubble dynamics (during its slow growth phase) and ii) the instabilities in the evaporating layer (once the bubble occupies the whole cross section of the tube). The first part of this thesis investigates the counter/co-current thermocapillary propulsion of bubbles in the so-called self-rewetting liquids by means of direct numerical simulations (DNS) and validated by experiments. In self-rewetting liquids, surface tension presents a peculiar non-monotonic dependence on temperature. A DNS model based on the volume-of-fluid method is developed to study the dynamics of bubbles inside of a horizontal channel with constant flow rate and constant temperature gradient in the flow direction. A parametric study is performed to investigate the influence of the viscous drag and thermocapillary forces on the bubble motion. Four distinct regimes of bubble migration are determined: counter-current propulsion, damped oscillations, sustained oscillations and co-current migration. A map is provided in the parameter space of Reynolds and capillary numbers showing these regimes. Each regime is discussed in detail and the mechanism that leads to sustained oscillations at low capillary numbers is discussed. The results are compared against the theoretical prediction for the bubble equilibrium position and frequency of the oscillations reported in the literature. Next, experiments are performed to investigate the thermocapillary migration of bubbles in self-rewetting liquids inside of a horizontal circular channel with constant flow rate and constant temperature gradient in the flow direction. The motion of the bubbles is recorded with a CCD camera from the top while the temperature at the channel wall is recorded with an IR-camera from the side. The influence of the flow rate and the temperature gradient on the bubble motion is investigated. It has been observed that the flow rate has a decreasing linear relationship with the bubble velocity while the temperature gradient has an increasing linear relationship with the bubble velocity during the countercurrent motion. The experiments validate the numerical findings and these are presented in the flow-regime map. The third part of this thesis is devoted to the study of the stability of the evaporation of a horizontal thin liquid layer which consists of a binary mixture of volatile liquids heated from below by means of linear stability analysis and transient numerical simulations. The effect of vapour recoil, thermo- and solute-capillarity and the van der Waals interactions are considered. The long-wave approximation is used to derive the evolution equations for the free interface and the concentration of the components. A linear stability analysis is performed to derive the growth rate of the instabilities for the case of quasi-equilibrium evaporation and non-equilibrium evaporation. The developed linear theory describes two modes of instabilities: i) a monotonic instability mode where the perturbations simply grow until the liquid layer is ruptured if the thermo-capillary and the solute-capillary force enhance each other and ii) an oscillatory instability mode where perturbations oscillate if the thermo-capillary and the soluto-capillary forces compete with each other. A parametric study is performed to investigate how these modes depend on the ratio between the thermal and solutal Marangoni numbers and on the volatility ratio of the components. The mechanisms of the instabilities are discussed in detail. The linear theory is validated against transient simulations and show a good agreement in the comparison of the growth rates. Lastly, the evolution of the interface for the two instability modes is analysed by means of transient simulations.