Multiphase dynamics in liquid mixtures: thermocapillary propulsion of bubbles and instabilities in evaporating layers
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Date
03/07/2019Author
Kalata Nazareth, Robson
Metadata
Abstract
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.