High quality (Q) factor whispering gallery modes (WGMs) can induce nonlinear effects in liquid droplets through mechanisms such as radiation pressure, light scattering, thermocapillarity, Kerr nonlinearity, and thermal effect. However, such nonlinear effects have yet to be thoroughly investigated and compared in the literature. In this study, we first investigate a micron-sized liquid spherical resonator and present an approximated solution for the resonator interface deformation due to the radiation pressure. We then derive an analytical approach that can exactly calculate the droplet deformation induced by the radiation pressure. The accuracy of the analytical solution is confirmed through numerical analyses based on the boundary element method. We show that the nonlinear optofluidic effect induced by the radiation pressure is stronger than the Kerr effect and the thermal effect under a large variety of realistic conditions. Using liquids with ultra-low and experimentally attainable interfacial tension, we further confirm the prediction that it may only take a few photons to produce measurable WGM resonance shift through radiation pressure induced droplet deformation. Similar to the radiation pressure, the scattering force in the droplet can induce a rotational fluid motion which also leads to the interface deformation. The interface deformation can also be produced by the thermocapillarity as a result of the WGM energy absorption and temperature increase. In this study, we provide a numerical scheme to calculate the fluid motion and quantify the nonlinearity induced by the optical scattering force and thermocapillarity. The magnitude of the optofluidic nonlinearities induced by the radiation pressure, thermocapillary effect, light scattering and Kerr effect are compared. We show that the radiation pressure due to the WGM produces the strongest nonlinear optofluidic effect. / Ph. D.

A diffuse-interface finite-element method has been applied to simulate the flow of two-component rheologically complex fluids. It treats the interfaces as having a finite thickness with a phase-field parameter varying continuously from one phase to the other. Adaptive meshing is applied to produce fine grid near the interface and coarse mesh in the bulk. It leads to accurate resolution of the interface at modest computational costs. An advantage of this method is that topological changes such as interfacial rupture and coalescence happen naturally under a short-range force resembling the van der Waals force. There is no need for manual intervention as in sharp-interface model to effect such event. Moreover, this energy-based formulation easily incorporates complex rheology as long as the free energy of the microstructures is known. The complex fluids considered in this thesis include viscoelastic fluids and nematic liquid crystals. Viscoelasticity is represented by the Oldroyd-B model, derived for a dilute polymer solution as linear elastic dumbbells suspended in a Newtonian solvent. The Leslie-Ericksen model is used for nematic liquid crystals，which features distortional elasticity and viscous anisotropy. The interfacial dynamics of such complex fluids are of both scientific and practical significance. The thesis describes seven computational studies of physically interesting problems. The numerical simulations of monodisperse drop formation in microfluidic devices have reproduced scenarios of jet breakup and drop formation observed in experiments. Parametric studies have shown dripping and jetting regimes for increasing flow rates, and elucidated the effects of flow and rheological parameters on the drop formation process and the final drop size. A simple liquid drop model is used to study the neutrophil, the most common type of white blood cell, transit in pulmonary capillaries. The cell size, viscosity and rheological properties are found to determine the transit time. A compound drop model is also employed to account for the cell nucleus. The other four cases concern drop and bubble dynamics in nematic liquid crystals, as determined by the coupling among interfacial anchoring, bulk elasticity and anisotropic viscosity. In particular, the simulations reproduce unusual bubble shapes seen in experiments, and predict self-assembly of microdroplets in nematic media.

A diffuse-interface finite-element method has been applied to simulate the flow of two-component rheologically complex fluids. It treats the interfaces as having a finite thickness with a phase-field parameter varying continuously from one phase to the other. Adaptive meshing is applied to produce fine grid near the interface and coarse mesh in the bulk. It leads to accurate resolution of the interface at modest computational costs. An advantage of this method is that topological changes such as interfacial rupture and coalescence happen naturally under a short-range force resembling the van der Waals force. There is no need for manual intervention as in sharp-interface model to effect such event. Moreover, this energy-based formulation easily incorporates complex rheology as long as the free energy of the microstructures is known. The complex fluids considered in this thesis include viscoelastic fluids and nematic liquid crystals. Viscoelasticity is represented by the Oldroyd-B model, derived for a dilute polymer solution as linear elastic dumbbells suspended in a Newtonian solvent. The Leslie-Ericksen model is used for nematic liquid crystals，which features distortional elasticity and viscous anisotropy. The interfacial dynamics of such complex fluids are of both scientific and practical significance. The thesis describes seven computational studies of physically interesting problems. The numerical simulations of monodisperse drop formation in microfluidic devices have reproduced scenarios of jet breakup and drop formation observed in experiments. Parametric studies have shown dripping and jetting regimes for increasing flow rates, and elucidated the effects of flow and rheological parameters on the drop formation process and the final drop size. A simple liquid drop model is used to study the neutrophil, the most common type of white blood cell, transit in pulmonary capillaries. The cell size, viscosity and rheological properties are found to determine the transit time. A compound drop model is also employed to account for the cell nucleus. The other four cases concern drop and bubble dynamics in nematic liquid crystals, as determined by the coupling among interfacial anchoring, bulk elasticity and anisotropic viscosity. In particular, the simulations reproduce unusual bubble shapes seen in experiments, and predict self-assembly of microdroplets in nematic media.

A diffuse-interface finite-element method has been applied to simulate the flow of two-component rheologically complex fluids. It treats the interfaces as having a finite thickness with a phase-field parameter varying continuously from one phase to the other. Adaptive meshing is applied to produce fine grid near the interface and coarse mesh in the bulk. It leads to accurate resolution of the interface at modest computational costs. An advantage of this method is that topological changes such as interfacial rupture and coalescence happen naturally under a short-range force resembling the van der Waals force. There is no need for manual intervention as in sharp-interface model to effect such event. Moreover, this energy-based formulation easily incorporates complex rheology as long as the free energy of the microstructures is known. The complex fluids considered in this thesis include viscoelastic fluids and nematic liquid crystals. Viscoelasticity is represented by the Oldroyd-B model, derived for a dilute polymer solution as linear elastic dumbbells suspended in a Newtonian solvent. The Leslie-Ericksen model is used for nematic liquid crystals，which features distortional elasticity and viscous anisotropy. The interfacial dynamics of such complex fluids are of both scientific and practical significance. The thesis describes seven computational studies of physically interesting problems. The numerical simulations of monodisperse drop formation in microfluidic devices have reproduced scenarios of jet breakup and drop formation observed in experiments. Parametric studies have shown dripping and jetting regimes for increasing flow rates, and elucidated the effects of flow and rheological parameters on the drop formation process and the final drop size. A simple liquid drop model is used to study the neutrophil, the most common type of white blood cell, transit in pulmonary capillaries. The cell size, viscosity and rheological properties are found to determine the transit time. A compound drop model is also employed to account for the cell nucleus. The other four cases concern drop and bubble dynamics in nematic liquid crystals, as determined by the coupling among interfacial anchoring, bulk elasticity and anisotropic viscosity. In particular, the simulations reproduce unusual bubble shapes seen in experiments, and predict self-assembly of microdroplets in nematic media. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

No description available.

<p>Ferrofluids are remarkable materials composed of magnetic nanoparticles dispersed in a carrier liquid. These suspensions exhibit fluid-like behavior in the absence of a magnetic field, but when exposed to a magnetic field, they can respond and deform into a variety of patterns. This responsive behavior of ferrofluids makes them an excellent material for applications such as drug delivery for targeted therapies and soft robots. In this thesis, we will focus on the interfacial dynamics of ferrofluids in Hele-Shaw cells. The three major objectives of this thesis are: understanding the pattern evolution, unraveling the underlying nonlinear dynamics, and ultimately achieving passive control of ferrofluid interfaces. First, we introduce a novel static magnetic field setup, under which a confined circular ferrofluid droplet will deform and spin steadily like a `gear’, driven by interfacial traveling waves. This study combines sharp-interface numerical simulations with weakly nonlinear theory to explain the wave propagation. Then, to better understand these interfacial traveling waves, we derive a long-wave equation for a ferrofluid thin film subject to an angled magnetic field. Interestingly, the long-wave equation derived, which is a new type of generalized Kuramoto--Sivashinsky equation (KSE), exhibits nonlinear periodic waves as dissipative solitons and reveals fascinating issues about linearly unstable but nonlinearly stable structures, such as transitions between different nonlinear periodic wave states. Next, inspired by the low-dimensional property of the KSE, we simplify the original 2D nonlocal droplet problem using the center manifold method, reducing the shape evolution to an amplitude equation (a single local ODE). We show that the formation of the rotating `gear’ arises from a Hopf bifurcation, which further inspires our work on time-dependent control. By introducing a slowly time-varying magnetic field, we propose strategies to effectively control a ferrofluid droplet's evolution into a targeted shape at a targeted time. The final chapter of this thesis concerns our ongoing research into the interfacial dynamics under the influence of a fast time-varying and rotating magnetic field, which induces a nonsymmetric viscous stress tensor in the ferrofluid, requiring the balance of the angular momentum equation. As a consequence, wave propagation on a ferrofluid interface can be now triggered by magnetic torque. A new thin-film long-wave equation is consistently derived taking magnetic torque into account.</p>

No description available.

Ce travail présente une étude de la dynamique interfaciale de gouttes oscillantes dans une plage étendue de fréquences, en particulier dans le domaine des hautes fréquences. Nous avons développé une méthode de caractérisation de la dynamique des oscillations de gouttes, en présence d’un forçage externe imposé, sous la forme de variations de volume périodiques de faible amplitude sur une goutte attachée à l’extrémité d’un capillaire. Cette méthode permet d’identifier les modes d’oscillation des gouttes et d’en mesurer les fréquences et les taux d’amortissement. Cette méthode a été appliquée à différents systèmes liquide-liquide, en l’absence ou en présence de surfactants. Dans ce dernier cas, elle permet d’évaluer l’effet du comportement viscoélastique des interfaces sur la dynamique des oscillations. Ainsi 3 types d’interfaces ont été identifiés. Pour les interfaces de premier type (heptane/eau sans ajout de surfactant), chaque mode propre est modélisé par un oscillateur linéaire peu amorti. Les fréquences propres et les taux d’amortissement sont bien prédits par la théorie linéaire. Les interfaces de types 2 et 3 sont obtenues en ajoutant du pétrole brut à la phase dispersée. Les surfactants naturellement présents dans le pétrole (asphaltènes, résines) s’adsorbent à l’interface et lui confèrent des propriétés viscoélastiques. Pour les interfaces jeunes (type 2, moins de 20 minutes de vieillissement), les fréquences propres mesurées restent bien prédites par la théorie, qui considère des interfaces non contaminées, tandis que les taux d’amortissement sont de loin supérieurs aux valeurs théoriques. D’autre part, les interfaces vieillies (type 3) présentent des modes propres différents avec des fréquences de résonance supérieures à celles des interfaces jeunes. Dans ce cas, la dynamique de l’interface à haute fréquence est régie par l’élasticité du réseau formé par les espèces amphiphiles du pétrole brut. Les oscillations libres d’une goutte en ascension dans une phase externe stagnante, pour un système liquide-liquide sans ajout de surfactants, ont été étudiées. Les valeurs mesurées de la fréquence d’oscillation des 4 premiers modes sont en adéquation avec la théorie linéaire. Cependant les valeurs mesurées du taux d’amortissement sont très élevées par rapport aux valeurs théoriques, pour une interface non contaminée. En effet, des espèces résiduelles adsorbées à l’interface provoquent l’apparition d’un gradient de tension interfaciale par effet Marangoni et par suite une production de vorticité plus intense dans les couches-limites, ce qui conduit à l’augmentation de l’amortissement des oscillations. / We present an experimental study of oscillating drop interfacial dynamics at a wide frequency range, especially at high frequency. A characterization method of drops oscillation dynamics has been developed. The oscillations are generated by imposing low amplitude periodic variation of volume to a drop which is attached to a capillary tip. The present method is based on the identification of the drop eigenmodes and the determination of their frequencies and damping rates. It has been applied to characterize several liquid-liquid systems. Three types of interface have been identified. For interfaces of type 1 (heptane/water without added surfactant), each eigenmode is modelled by a weakly damped linear oscillator. Eigenfrequencies and damping rates are well predicted by the linear theory. Interfaces of Types 2 and 3 are obtained by adding crude oil to the disperse phase. Oil native surfactants (asphaltenes, resins) adsorb on the drop interface and provide the latter with viscoelastic behaviour. For young interfaces (type 2 with aging time below 20 minutes), eigenfrequencies remain well predicted by the theory, which deals with non contaminated interfaces, whereas the measured damping rates are significantly higher than the theoretical values. On the other hand, aged interfaces (type 3) exhibit different eigenmodes, of which eigenfrequencies are much higher than the resonance frequencies measured for the young interfaces. At high frequency, the dynamics of aged interfaces are governed by the elasticity of the network constituted by the crude oil amphiphilic species, while the dynamics of young interfaces are governed by interfacial tension. Freely decaying oscillations of a rising drop in a liquid at rest without added surfactant were also considered. Measured frequencies for the first four eigenmodes are in good agreement with the linear theory. However, measured damping rates are much higher than the theoretical rates for non contaminated interfaces. In fact, residual adsorbed species at the heptane/water interface induce Marangoni effects and thus gradients of interfacial tension. Therefore, vorticity production within the boundary layers is enhanced, which explains the observed increase of the oscillation damping rates.