https://hal.archives-ouvertes.fr/hal-01445445/document

An accurate adaptive solver for surface-tension-driven interfacial flows

Preface.- Preface to the 2nd edition.- Notational conventions.- 1 Preliminary general material.- I Steady-state problems.- 2 Pseudomonotone or weakly continuous mappings.- 3 Accretive mappings.- 4 Potential problems: smooth case.- 5 Nonsmooth problems variational inequalities.- 6. Systems of equations: particular examples.- II Evolution problems.- 7 Special auxiliary tools.- 8 Evolution by pseudomonotone or weakly continuous mappings.- 9 Evolution governed by accretive mappings.- 10 Evolution governed by certain set-valued mappings.- 11 Doubly-nonlinear problems.- 12 Systems of equations: particular examples.- References.- Index.

/pdf/nonlinear-partial-differential-equations-with-applications-204hhsvanv.pdf

Nonlinear partial differential equations with applications

https://ctflab.mae.cornell.edu/papers/Desjardins,%20Moureau,%20Pitsch.%202008.%20An%20accurate%20conservative%20level%20set-ghost%20fluid%20method%20for%20simulating%20turbulent%20atomization.pdf

An accurate conservative level set/ghost fluid method for simulating turbulent atomization

This article presents a comprehensive review of numerical methods and models for interface resolving simulations of multiphase flows in microfluidics and micro process engineering. The focus of the paper is on continuum methods where it covers the three common approaches in the sharp interface limit, namely the volume-of-fluid method with interface reconstruction, the level set method and the front tracking method, as well as methods with finite interface thickness such as color-function based methods and the phase-field method. Variants of the mesoscopic lattice Boltzmann method for two-fluid flows are also discussed, as well as various hybrid approaches. The mathematical foundation of each method is given and its specific advantages and limitations are highlighted. For continuum methods, the coupling of the interface evolution equation with the single-field Navier–Stokes equations and related issues are discussed. Methods and models for surface tension forces, contact lines, heat and mass transfer and phase change are presented. In the second part of this article applications of the methods in microfluidics and micro process engineering are reviewed, including flow hydrodynamics (separated and segmented flow, bubble and drop formation, breakup and coalescence), heat and mass transfer (with and without chemical reactions), mixing and dispersion, Marangoni flows and surfactants, and boiling.

Numerical modeling of multiphase flows in microfluidics and micro process engineering: a review of methods and applications

The beauty and complexity of the shapes and dynamics of bubbles rising in liquid have fascinated scientists for centuries. Here we perform simulations on an initially spherical bubble starting from rest. We report that the dynamics is fully three-dimensional, and provide a broad canvas of behaviour patterns. Our phase plot in the Galilei-Eotvos plane shows five distinct regimes with sharply defined boundaries. Two symmetry-loss regimes are found: one with minor asymmetry restricted to a flapping skirt; and another with marked shape evolution. A perfect correlation between large shape asymmetry and path instability is established. In regimes corresponding to peripheral breakup and toroid formation, the dynamics is unsteady. A new kind of breakup, into a bulb-shaped bubble and a few satellite drops is found at low Morton numbers. The findings are of fundamental and practical relevance. It is hoped that experimenters will be motivated to check our predictions.

/pdf/dynamics-of-an-initially-spherical-bubble-rising-in-1zrsdzjsvo.pdf

Dynamics of an initially spherical bubble rising in quiescent liquid

https://www.math.fsu.edu/~sussman/twofluid.pdf

A sharp interface method for incompressible two-phase flows

The present method combines the advantages of the Cartesian-grid approach, second-order coupled level set and volume-of-fluid approach, and the dynamic adaptive mesh refinement(AMR) procedure to treat complex three-dimensional problems with sharp interfaces. Its accuracy and robustness are demonstrated by its application to bubble dynamics, ship hydrodynamics, and “water crown” computation. It is shown to capture or preserve sharp slip-lines, phase boundaries remarkably well.

A Second-Order Adaptive Sharp-Interface Method for Incompressible Multiphase Flow

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A sharp interface method for incompressible two-phase flows

A Second-Order Adaptive Sharp-Interface Method for Incompressible Multiphase Flow