Drop Formation in a One-Dimensional Approximation of the Navier-Stokes Equation

We consider the viscous motion of a thin, axisymmetric column of fluid with a free surface. A one-dimensional equation of motion for the velocity and the radius is derived from the Navier-Stokes equation. We compare with recent experiments on the breakup of a liquid jet and on the bifurcation of a drop suspended from an orifice. The equations form singularities as the fluid neck is pinching off. The nature of the singularities is investigated in detail

Singularities in droplet pinching with vanishing viscosity

A slender-jet model for the pinching of a liquid column is considered in the limit of vanishing viscosity. We find the model to develop a singularity in the gradients of the local radius and the velocity at a finite thread radius, so it does not describe breakup. However, the observed steepening of the profile corresponds to experiments and simulations with fluids at low viscosity. The singularity has similarity form, which we compute analytically. The result agrees well with numerical simulations of the model equations.Comment: 18 pages including 4 eps figures, revte

Dynamics of complex capillary flows: stability, rupture, and influence of surfactants

Mención Internacional en el título de doctorFluid-fluid interfaces are ubiquitous in nature and everyday life, where they are found across scales and material properties, as for instance in many engineering, biological, and physiological applications and processes. In particular, cylindrical interfaces and, in general, the spontaneous tendency of surface-tension-driven flows to break up into drops, have fascinated naturalists and scientists throughout history; a fascination that lasts to date due to its crucial relevance in many phenomena of fundamental and applied interest. This is the reason for the huge research effort devoted to understand the behavior and dynamics of these filaments, namely elongated vesicles and membranes which are frequent in biological environments, or liquid jets that are routinely used for additive manufacturing applications. In most of these scenarios, the interface is usually populated with surface-active molecules, macromolecules, proteins, or contaminated with particles, which eventually form a complex microstructure that endows the interface with a rheologically complex behavior. The interaction between this structure and the hydrodynamic forces is traduced macroscopically into nonlinear interfacial rheological properties and nontrivial constitutive equations relating the surface stress with the deformation of the surface. An interface that possesses these kinds of properties is usually referred to as a complex interface, and the particular field of study is typically denoted by interfacial rheology. Nonetheless, despite of this complexity, these material cylinders share the same intrinsic instability induced by the interfacial tension known as the Plateau-Rayleigh instability, where disturbances of sufficiently long wavelength trigger the instability by decreasing the surface energy at constant volume. The complex interactions between the bulk fluids and the surface layer complicate the theoretical modelling and the experimental protocols and measurements of the material properties associated with the interface. A vast number of issues regarding the behavior and dynamics of such complex fluid threads are yet not understood. In particular, this thesis aims to unravel fundamental aspects of the linear and nonlinear dynamics of liquid filaments whose interface is endowed with complex surface rheology, which can be elastic and/or viscous. We first deduce the components of the surface stress balance modified by interfacial elastic and viscous forces, which is necessary for the derivation of leading-order and second-order one-dimensional models. The performance of these approximations is then evaluated in the linear regime by comparing their associated growth rate of small perturbations with the one obtained from the complete conservation equations. To this end, we use Rayleigh’s temporal linear stability analysis to deduce the corresponding dispersion relation of a liquid filament with interfacial rheology. Additionally, by performing simulations of the full conservation equations, we then investigate the nonlinear dynamics of these complex filaments. In particular we study the effect of Marangoni and surface viscous stresses on the natural breakup and thinning of threads, and the subsequent formation of satellite droplets. Finally, we study the linear and nonlinear dynamics of a capillary jet injected in the direction of gravity and confined between the nozzle and a bath of the same fluid.This doctoral dissertation was supported by Ministerio de Educación, Cultura, y Deporte through the fellowship FPU16/02562, and its associated program Ayudas a la Movilidad 2017 and 2018 during my stays with the group of Prof. Benoit Scheid (TIPs) at the University of Brussels, and with the group of Prof. Howard A. Stone at Princeton University. This work also had financial support by Ministerio de Economía y Competitividad, Subdirección General de Gestión de Ayudas a la Investigación, under the projects DPI2014-59292-C3-1-P, DPI2014-59292-C3-3-P, DPI2015-71901-REDT, and by Ministerio de Ciencia, Innovación y Universidades-Agencia Estatal de Investigación through the project DPI2017-88201-C3-3-R, partly financed through FEDER European funds. Support from the Red Nacional para el Desarrollo de la Microfluídica, RED2018-102829-T, is also acknowledged.Programa de Doctorado en Mecánica de Fluidos por la Universidad Carlos III de Madrid, la Universidad de Jaén, la Universidad de Zaragoza, la Universidad Nacional de Educación a Distancia, la Universidad Politécnica de Madrid y la Universidad Rovira i VirgiliPresidente: Jens Eggers,.- Secretario: Nicolas Bremond.- Vocal: José M. Gordillo Arias de Saavedr

Description of Jet Breakup

In this article we review recent results on the breakup of cylindrical jets of a Newtonian fluid. Capillary forces provide the main driving mechanism and our interest is in the description of the flow as the jet pinches to form drops. The approach is to describe such topological singularities by constructing local (in time and space) similarity solutions from the governing equations. This is described for breakup according to the Euler, Stokes or Navier-Stokes equations. It is found that slender jet theories can be applied when viscosity is present, but for inviscid jets the local shape of the jet at breakup is most likely of a non-slender geometry. Systems of one-dimensional models of the governing equations are solved numerically in order to illustrate these differences

Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid

In this paper we examine some general features of the time-dependent dynamics of drop deformation and breakup at low Reynolds numbers. The first aspect of our study is a detailed numerical investigation of the ‘end-pinching’ behaviour reported in a previous experimental study. The numerics illustrate the effects of viscosity ratio and initial drop shape on the relaxation and/or breakup of highly elongated droplets in an otherwise quiescent fluid. In addition, the numerical procedure is used to study the simultaneous development of capillary-wave instabilities at the fluid-fluid interface of a very long, cylindrically shaped droplet with bulbous ends. Initially small disturbances evolve to finite amplitude and produce very regular drop breakup. The formation of satellite droplets, a nonlinear phenomenon, is also observed

Development and validation of a two-phase computational model for an alternative fire suppression agent

[ES] Halon1301 se ha utilizado como agente de extinción de incendios en sistemas activos de extinción de incendios en motores de aviones, APU (Unidad de potencia auxiliar) y protección contra incendios de carga durante más de 50 años. En 1987, una investigación realizada por el Protocolo de Montreal muestra que Halon está dañando el medio ambiente debido a sus propiedades que agotan el ozono. Por lo tanto, el uso de gases de halón ha sido prohibido en la industria por el protocolo de Montreal (1994) y Kyoto (1998). Por lo tanto, es el reemplazo de gases de halón lo que es más ecológico. Entre estas alternativas, Novec-1230 es una alternativa sostenible que funciona de manera rápida, limpia y eficiente. El sistema de extinción de incendios requiere que se diluya una concentración específica del agente de extinción de incendios (4-6% para Novec-1230 y 5% para Halon) en el aire para extinguir el fuego. El problema de cambiar la fase de la niebla rápidamente despresurizada de un sistema de extinción de incendios es un tema de gran interés debido al efecto del modelado de estos fenómenos en una simulación exitosa para diseñar estas modificaciones. Debido a la gran diferencia de presiones entre el recipiente y el ambiente, se espera que la descarga a través de la boquilla sea crítica. En este informe, se utilizan dos agentes de supresión de incendios alternativos diferentes y dos boquillas: agua y Novec1230. El objetivo principal de este proyecto es desarrollar un nuevo modelo de subcuadrícula para un U-RANS CFD Euleriano-Euleriano de dos fases que pueda usarse para reducir el costo computacional y aumentar la precisión de los enfoques tradicionales basados en Eulerian-Lagrangian. Estos dos enfoques se realizan con el software comercial CFD (ANSYS Fluent). Como validación, los rendimientos de pulverización como la forma de pulverización, el ángulo del cono de pulverización se comparan con los resultados experimentales.[EN] Halon1301 has been used as a fire suppression agent in active fire extinction systems in aircraft engines, APU (Auxiliary Power Unit) and cargo fire protection for more than 50 years. In 1987, a research carried out by the Montreal Protocol shows that Halon is damaging the environment because of its ozone-depleting properties. Therefore, the use of Halon gases has been banned in the industry by the Montreal (1994) and Kyoto (1998) protocol. So, it is indeed to find replacement of halon gases which is more eco friendly. Among these alternatives, Novec-1230 is a sustainable alternative that works quickly, cleanly and efficiently. The fire suppression system requires a specific concentration of the fire suppression agent (4-6 % for Novec-1230 and 5% for Halon) to be diluted in the air to extinguish the fire. The problem of changing the phase of the rapidly depressurized mist of a fire suppression system is a topic of high interest due to the effect of the modelling of these phenomena in a successful simulation to design these modifications. Due to the high difference of pressures between the container and the ambient, the discharge through the nozzle is expected to be critical. In this report, two different alternative fire suppression agents and two nozzles are used - Water and Novec1230. The main goal of this project is to develop a new sub-grid model for a two-phase Eulerian-Eulerian CFD U-RANS that can be used to reduce the computational cost and increase the accuracy of traditional approaches based on Eulerian-Lagrangian. These two approaches are performed with CFD commercial software (ANSYS Fluent). As validation, spray performances such as spray shape, spray cone angle are compared with experimental results.Shaparia, NR. (2020). Development and validation of a two-phase computational model for an alternative fire suppression agent. Universitat Politècnia de València. http://hdl.handle.net/10251/157474TFG

Reconstruction methods for single-shot diffractive imaging of free nanostructures with ultrashort x-ray and XUV laser pulses

With x-ray and XUV single-shot diffractive imaging on free nanoparticles it is possible to investigate structure and shape of the particles. The scattering image of the nanoparticle only contains the intensity distribution but not the phase of the scattered light. Thus, numerical methods are required to infer information from experimental data. In the thesis, different reconstruction methods are implemented, advanced and applied to different scattering scenarios to characterize diffraction patterns for different laser parameters, reconstruct optical properties and 3d shapes of nanotargets.Mit Einzelschussmessungen an freien Nanoteilchen mit Hilfe von Röntgenstrahlung ist es möglich, die Teilchenstruktur zu untersuchen. Damit die Information aus Experimenten gewonnen werden kann, sind numerische Methoden notwendig, da das Streubild der Nanoteilchen nur die Inensitätsverteilung des gestreuten Lichtes, aber nicht die Phase bereitstellt. Es werden verschiedene Rekonstruktionsmethoden implementiert, weiterentwickelt und auf verschiedene Streuszenarien angewandt, um Streubilder für verschiedene Laserparameter zu charakterisieren, optische Eigenschaften und 3D-Formen zu rekonstruieren

Numerical simulation of the aerobreakup of a water droplet

We present a three-dimensional numerical simulation of the aerobreakup of a spherical water droplet in the flow behind a normal shock wave. The droplet and surrounding gas flow are simulated using the compressible multicomponent Euler equations in a finite-volume scheme with shock and interface capturing. The aerobreakup process is compared with available experimental visualizations. Features of the droplet deformation and breakup in the stripping breakup regime, as well as descriptions of the surrounding gas flow, are discussed. Analyses of observed surface instabilities and a Fourier decomposition of the flow field reveal asymmetrical azimuthal modulations and broadband instability growth that result in chaotic flow within the wake region

Advanced Fluid Dynamics

This book provides a broad range of topics on fluid dynamics for advanced scientists and professional researchers. The text helps readers develop their own skills to analyze fluid dynamics phenomena encountered in professional engineering by reviewing diverse informative chapters herein