Study of imbibition in various geometries using phase field method

Phase field method has been widely utilized to study multiphase flow problems, but has seldom been applied to the study of imbibition. Previous methods used to simulate imbibition, such as moving mesh method, need to specify capillary pressure as a boundary condition a priori, whereas phase field method can calculate capillary pressure automatically for various geometries. Therefore, phase field method would be a versatile tool for the study of imbibition in various geometries. In this paper, phase field method is employed to solve dynamical imbibition problem in various geometries, including straight tube, conical tube and structures in which the topology changes. The variation of the imbibition height with respect to time from phase field simulation is verified with theoretical predictions from Lucas-Washburn law in a straight capillary tube with three gravitational scenarios. In addition, the capillary pressure and velocity field are found to be consistent with Laplace-Young equation and Hagen-Poiseuille equation in various geometries. The applicability and accuracy of the phase field method for the study of imbibition in structures with changing topology are also discussed.Cited as: Xiao, J., Luo, Y., Niu, M., Wang, Q., Wu, J., Liu, X., Xu, J. Study of imbibition in various geometries using phase field method. Capillarity, 2019, 2(4): 57-65, doi: 10.26804/capi.2019.04.0

Interface-Resolving Simulations of Gas-Liquid Two-Phase Flows in Solid Structures of Different Wettability

This PhD study is devoted to numerical investigations of two-phase flows on and through elementary and complex solid structures of varying wettability. The phase-field method is developed and implemented in OpenFOAM®. The numerical method/code is verified by a series of test cases of two-phase flows, and then applied to investigate: (1) droplet wetting on solid surfaces; (2) air bubble rising and interacting with cellular structures and (3) gas-liquid interfacial flows in foam structures

Development of a gas–liquid multiphase solver for direct numerical simulation of atomization phenomena

Gas-liquid multiphase flows play an essential role in nature and industry. Understanding the complex dynamics of multiphase flows is fundamental in many technological applications, including metal forming and energy production industries. In aerospace applications, multiphase flows have considerable importance in the atomization and mixing of fuels, as well as in sloshing in fuel tanks. In nature, one of the most complicated and important phenomena is the breaking of waves, in which complex atomization processes occur, leading to the formation of bubbles, droplets, spray, and aerosol. In this thesis work, we develop an efficient solver for direct numerical simulation of the incompressible Navier-Stokes equations to study multiphase flow phenomena as bubble dynamics and formation, and atomization phenomena, in both natural and artificial flows. In the first part of the thesis, we present the basic equations that govern multiphase flow dynamics within the one-fluid formulation approach. The solver relies on the Volume-of-Fluid (VOF) method to account for different phases, and the interface tracking is carried out using novel schemes based on a tailored TVD limiter. A staggered Cartesian mesh is used, and space derivatives approximated with second-order finite-difference formulas to guarantee discrete energy preservation. Moreover, for time integration, Adams-Bashfort extrapolation is used for the convective terms and interface tracking, whereas implicit Crank-Nicolson time integration is used for the viscous terms. Surface tension is accounted for through the continuous surface force (CFS) approach, and the local interface curvature is approximated through a hierarchical approach, whereby the height function method is locally replaced with least-square derivative estimation at critical points. Several validation test cases are then presented. First, capillary wave motion and bubble in a shearing field are studied to validate surface tension discretization. Second, the dynamics of a rising bubble in a liquid tank are presented, and the results are compared with other authors. Finally, we analyze the physics of gas-liquid multiphase flows occurring in natural flows. We consider natural wave breaking phenomena by focusing on the associated energy dissipation and the formation of spray, droplets, and bubbles

Modelling of two-phase flow with surface active particles

Kolloidpartikel die von zwei nicht mischbaren Fluiden benetzt werden, tendieren dazu sich an der fluiden Grenzfläche aufzuhalten um die Oberflächenspannung zu minimieren. Bei genügender Anzahl solcher Kolloide werden diese zusammengedrückt und lassen die fluide Grenzfläche erstarren. Das gesamte System aus Fluiden und Kolloiden bildet dann eine spezielle Emulsion mit interessanten Eigenschaften. In dieser Arbeit wird ein kontinuum Model für solche Systeme entwickelt, basierend auf den Prinzipien der Massenerhaltung und der themodynamischen Konsistenz. Dabei wird die makroskopische Zwei-Phasen-Strömung durch eine Navier-Stokes Cahn-Hilliard Gleichung modelliert und die mikroskopischen Partikel an der fluiden Grenzfläche durch einen Phase-Field-Crystal Ansatz beschrieben. Zur Evaluation des verwendeten Strömungsmodells wird ein Test verschiedener Navier-Stokes Cahn-Hilliard Modelle anhand eines bekannten Benchmark Szenarios durchgeführt. Die Ergebnisse werden mit denen von anderen Methoden zur Simulation von Zwei-Phasen-Strömungen verglichen. Desweiteren wird eine neue Methode zur Simulation von Zwei-Phasen-Strömungen in komplexen Gebieten vorgestellt. Dabei wird die komplexe Geometrie implizit durch eine Phasenfeldvariable beschrieben, welche die charakteristische Funktion des Gebietes approximiert. Die Strömungsgleichungen werden dementsprechend so umformuliert, dass sie in einem größeren und einfacheren Gebiet gelten, wobei die Randbedingungen implizit durch zusätzliche Quellterme eingebracht werden. Zur Einarbeitung der Oberflächenkolloide in das Strömungsmodell wird schließlich die Variation der freien Energie des Gesamtsystems betrachtet. Dabei wird die Energie der Partikel durch die Phase-Field-Crystal Energie approximiert und die Energie der Oberfläche durch die Ginzburg-Landau Energie. Eine Variation der Gesamtenergie liefert dann die Phase-Field-Crystal Gleichung und die Navier-Stokes Cahn-Hilliard Gleichungen mit zusätzlichen elastischen Spannunngen. Zur Validierung des Ansatzes wird auch eine sharp interface Version der Gleichungen hergeleitet und mit der zuvor hergeleiteten diffuse interface Version abgeglichen. Die Diskretisierung der erhaltenen Gleichungen erfolgt durch Finiten Elemente in Kombination mit einem semi-impliziten Euler Verfahren. Durch numerische Simulationen wird die Anwendbarkeit des Modells gezeigt und bestätigt, dass die oberflächenaktiven Kolloide die fluide Grenzfläche hinreichend steif machen können um externen Kräften entgegenzuwirken und das gesamte System zu stabilisieren.Colloid particles that are partially wetted by two immiscible fluids can become confined to fluidfluid interfaces. At sufficiently high volume fractions, the colloids may jam and the interface may crystallize. The fluids together with the interfacial colloids compose an emulsion with interesting new properties and offer an important route to new soft materials. Based on the principles of mass conservation and thermodynamic consistency, we develop a continuum model for such systems which combines a Cahn-Hilliard-Navier-Stokes model for the macroscopic two-phase fluid system with a surface Phase-Field-Crystal model for the microscopic colloidal particles along the interface. We begin with validating the used flow model by testing different diffuse interface models on a benchmark configuration for a two-dimensional rising bubble and compare the results with reference solutions obtained by other two-phase flow models. Furthermore, we present a new method for simulating two-phase flows in complex geometries, taking into account contact lines separating immiscible incompressible components. In this approach, the complex geometry is described implicitly by introducing a new phase-field variable, which is a smooth approximation of the characteristic function of the complex domain. The fluid and component concentration equations are reformulated and solved in larger regular domain with the boundary conditions being implicitly modeled using source terms. Finally, we derive the thermodynamically consistent diffuse interface model for two-phase flow with interfacial particles by taking into account the surface energy and the energy associated with surface colloids from the surface PFC model. The resulting governing equations are the phase field crystal equations and Navier-Stokes Cahn-Hilliard equations with an additional elastic stress. To validate our approach, we derive a sharp interface model and show agreement with the diffuse interface model. We demonstrate the feasibility of the model and present numerical simulations that confirm the ability of the colloids to make the interface sufficiently rigid to resist external forces and to stabilize interfaces for long times

Approximation of phase-field models with meshfree methods: exploring biomembrane dynamics

Las biomembranas constituyen la estructura de separación fundamental en las celulas animales, y son importantes en el diseño de sistemas bioinspirados. Su simulación presenta desafíos, especialmente cuando ésta implica dinámica y grandes cambios de forma o se estudian sistemas micrométricos, impidiendo el uso de modelos atomísticos y de grano grueso. El objetivo principal de esta tesis es el desarrollo de un marco computacional para entender la dinámica de biomembranas inmersas en fluido viscoso usando modelos de campo de fase. Los modelos de campo de fase introducen un campo escalar contínuo que define una interfase difusa, cuya física está codificada en las ecuaciones en derivadas parciales que la gobiernan. Estos modelos son capaces de soportar cambios dramáticos de forma y topología, y facilitan el acoplamiento de distintos fenómenos físicos. No obstante, presentan desafíos numéricos significativos, como el alto orden de las ecuaciones, la resolución de frentes móviles y abruptos, o una eficiente integración en el tiempo. En esta disertación abordamos estos puntos mediante la combinación de una discretización espacial con métodos sin malla usando las funciones base locales de máxima entropía, y una formulación variacional Lagrangiana para acoplamiento elástico-hidrodinámico. La suavidad del método sin malla genera una aproximación precisa del campo de fase y puede lidiar fácilmente con adaptatividad local, la aproximación Lagrangiana extiende de manera natural esta adaptividad a la dinámica, y la formulación variacional permite una integración variacional temporal no linealmente estable y robusta. La implementación numérica de estos métodos en un entorno de computación de alto rendimiento ha motivado el desarrollo de un nuevo código computacional. Este código integra el estado del arte de las librerías en paralelo e incorpora importantes contribuciones técnicas para solventar cuellos de botella que aparecen con el uso de métodos sin malla en computación a gran escala. El código resultante es flexible y ha sido aplicado a otros problemas científicos en varias colaboraciones que incluyen flexoelectricidad, conformado metálico, fluidos viscosos o fractura en materiales con energía de superficie altamente anisotrópica.Biomembranes are the fundamental separation structure in animal cells, and are also used in engineered bioinspired systems. Their simulation is challenging, particularly when large shape changes and dynamics are involved, or micrometer systems are considered, ruling out atomistic or coarse-grained molecular modeling. The main goal of this thesis is to develop a computational framework to understand the dynamics of biomembranes embedded in a viscous fluid using phase-field models. Phase-field models introduce a scalar continuous field to define a diffuse moving interface, whose physics is encoded in partial differential equations governing it. These models can deal with dramatic shape and topological transformations and are amenable to multiphysics coupling. However, they present significant numerical challenges, such as the high-order character of the equations, the resolution of sharp and moving fronts, or the efficient time-integration. We address all these issues through a combination of meshfree spacial discretization using local maximum-entropy basis functions, and a Lagrangian variational formulation of the coupled elasticity-hydrodynamics. The smooth meshfree approach provides accurate approximations of the phase-field and can easily deal with local adaptivity, the Lagrangian approach naturally extend adaptivity to dynamics, and the variational formulation enables nonlinearly-stable robust variational time integration. The numerical implementation of these methods in a high-performance computing framework has motivated the development of a new computer code, which integrates state-of-the-art parallel libraries and incorporates important technical contributions to overcome bottlenecks that arise in meshfree methods for large-scale problems. The resulting code is flexible and has been applied to other scientific problems in a number of collaborations dealing with flexoelectricity, metal forming, creeping flows, or fracture in materials with strongly anisotropic surface energy