Thermocapillary motion of droplets in complex fluid flows

Student thesis: Doctoral Thesis


Understanding how the presence of thermal gradients affects the motion of bubbles and drops is a subject of great relevance both from a theoretical and a practical standpoint, particularly when gravitational effects are minimal or completely uninfluential. In the past half century, considerable progress has been made onthe investigation of the so-called thermocapillary phenomenon in an attempt to clarify the mechanisms at work in multiphase systems with liquid-liquid or liquid-gas interfaces.;Given the complexity of the problem, most of these investigations have been carried out under simplified conditions, assuming unbounded flows or considering relatively simple geometries in which the presence of solid boundaries was not explicitly taken into account. Additionally, even though non-Newtonian fluids are ubiquitous in engineering and science, the majority of these works have been carried out assuming Newtonian phases.;The aim of the present thesis is to study the thermocapillary migration of a droplet in systems exhibiting an added level of complexity, specifically in terms of wall effects, domain shape and rheological properties of the fluids. To accomplish these objectives, we rely on a concerted approach based on well-established numerical strategies and, where possible, we derive analytical solutions.;A thermocapillary solver based on a hybrid Level Set-Volume of Fluid method availablein OpenFOAM has been implemented and validated against previous analytical results, numerical solutions and experimental observations obtained in reduced gravity conditions (Sect. 3.5). In the first part of the study, we investigate the problem of a droplet interacting with the boundaries of a parallelepipedic domain.;The case study has been assessed by releasing the droplet in proximity to the lateral walls of the domain considering both adiabatic and purely conductive boundary conditions. The results showed that the droplet can experience a secondary motion perpendicular to the main direction of motion. In particular, it was observed that the droplet can either move away or towards the walls depending on the thermal boundary conditions at the wall (i.e., whether the wall is adiabatic or purely conductive) and on the extent of convective phenomena.;The investigation was then extended by adopting more complex geometries (converging and diverging channels), which were found to produce distortion of the thermal field distribution with direct consequences on the migration process (Sect. 4.2.1 and 4.2.2). In the second part of the thesis, non-Newtonian effects have been expressly considered. Specifically, the role played by the fluid's elasticity (while neglecting convective transport of energy and momentum) has been accounted for by modelling the continuous phase on the basis of constant-viscosity viscoelastic models, namely the Oldroyd-B model and FENE-CR model.;The numerical simulations were carried out for a specific value of the Capillary number and assuming thesame material properties for both phases. We investigated the effects of the various model parameters (i.e., polymer concentration and extensibility parameter) and Deborah number on the droplet motion. The results showed that the droplet speed, evaluated as a function of the Deborah number, initially decreases following a quadratic trend.;For larger Deborah number, the trend reverts its concavity and eventually reaches a plateau. In terms of shape, the results have shown that under the prescribed conditions the droplet deforms in a prolate manner and, for sufficiently large values of the Deborah number (having fixed the Capillary number), the viscoelastic stresses localised at the rear stagnation point are responsible for the formation of a pointed tail.;The viscoelastic problem was also tackled by means of perturbation techniques under the assumption of absence of confinement and weak viscoelastic effects, which allowed the derivation of corrective formulae for the droplet migration velocity and expressions describing the shape of the deformed drop. The results of the analytical solutions were found to be in fairly good agreement with the outcomes of the computations, both interms of drop shape and migration speed.
Date of Award22 Feb 2019
Original languageEnglish
Awarding Institution
  • University Of Strathclyde
SponsorsUniversity of Strathclyde
SupervisorMonica Oliveira (Supervisor) & Yonghao Zhang (Supervisor)

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