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We present an innovative Lagrangian dual-mechanism model for simulating versatile surface tension phenomena, designed to replicate the intricate interplay of liquids with textured solid surfaces and the emergence of gas bubbles. This model ...

We present a numerical model for the approximation of multiphase flows with free surfaces and strong interfacial effects. The model relies on the multiphase incompressible Navier-Stokes equations, and includes surface tension effects on the ...

• A numerical method for 3D incompressible Newtonian multiphase flows.
• A discretization based on an operator splitting algorithm and a two-grid method.
• A mesh cutting adaptive algorithm for the accurate approximation of interfacial ...

We propose a level-set approach to characterize the region occupied by the solid in Stefan problems with and without surface tension, based on their recent probabilistic reformulation. The level-set function is parameterized by a feed-forward ...

• Novel deep level-set method to represent the solid region in Stefan problems.
• Characterization of probabilistic solutions in general Stefan problems.
• Ability to capture surface tension effects, supercooling, and jump in the volume ...

This paper addresses the validation and verification of numerical models for complex multiphase flows involving immiscible fluids. Specifically, the focus is on the dynamics of the interface between the fluids, which remains a challenge in many ...

• Analysis of the advective term discretization in two-phase solver.
• Identify optimal numerical schemes for robustness and energy conservation.
• The role of surface tension in the energy balance is explored.
• Research offers ...

An efficient matrix factorization approach is proposed for simulation of interfacial flows involving surface tension forces within the projection framework. The level set method is used to capture the interface of different phases and a ...

When a thin liquid film flows down on a vertical fiber, one can observe the complex and captivating interfacial dynamics of an unsteady flow. Such dynamics are applicable in various fluid experiments due to their high surface area-to-volume ...

The numerical simulation of surface tension is an active area of research in many different fields of application and has been attempted using a wide range of methods. Our contribution is the derivation and implementation of an implicit cohesion force ...

Numerical modeling of surface tension requires an accurate description of fluid-fluid interfaces as well as an efficient discretization of the governing equations. As a Lagrangian method, smoothed particle hydrodynamics (SPH) is ...

In 1965, B. A. Troesch solved the isoperimetric sloshing problem of determining the container shape that maximizes the fundamental sloshing frequency among two classes of shallow containers: symmetric canals with a given free surface width and ...$\mathrm{}$$\mathrm{}$$\mathrm{}$$\mathrm{}$$\mathrm{}$$\mathrm{}\mathrm{}$$\mathrm{}$

Second-order phase field models have emerged as an attractive option for capturing the advection of interfaces in two-phase flows. Prior to these, state-of-the-art models based on the Cahn-Hilliard equation, which is a fourth-order ...

• Justified using energy-based surface tension model for 2nd order phase field models.

The E(xplicit)I(implicit)N(null) method was developed recently to remove numerical instability from PDEs, adding and subtracting an operator D of arbitrary structure, treating the operator implicitly in one case, and explicitly in the ...

• A new method to solve stiff partial differential equations is described.
• The ...

The impact of liquid droplets on flexible substrates is a common phenomenon in applications, such as plant leaves repelling raindrops and piezoelectric sensors harvest droplet energy. It involves the coupling of free surface flow, elasticity and ...

Pore size distribution of polymeric gel scaffold and the corresponding porosity are key elements influencing their drug release profile in several targeted drug delivery applications. This research aimed to build a network model that can ...

We analyze optimal control problems for two-phase Navier-Stokes equations with surface tension. Based on $L_p$-maximal regularity of the underlying linear problem and recent well-posedness results of the problem for sufficiently small data we show ...${}_{}$

• Axisymmetric governing equations are applied for a particle method.
• Moving ...

It is difficult to accurately simulate axisymmetric free-surface flows with surface tension and topological changes, such as drop formation through a nozzle. A promising numerical method that can achieve this goal is the moving surface ...

In this work, three classes of numerical methods are investigated to evaluate the mean curvature, the unit normal vector and the surface tension on a front tracking interface encountered in the simulation of multiphase flows with ...

• 3 families of methods presented to get surface properties.
• Comparison on a ...

The capillary time-step constraint is the dominant limitation on the applicable time-step in many simulations of interfacial flows with surface tension and, consequently, governs the execution time of these simulations. We propose a ...

• Fully-coupled pressure-based algorithm for interfacial flows with implicitly coupled VOF method.

• A generalized particle shifting technique applicable to both 2D and 3D multiphase flows.

This contribution outlines a multiphase flow solution method developed in conjunction with the incompressible smoothed particle hydrodynamics (SPH) discretization. We present (a) a generalized multiphase particle shifting technique ...

In this work, by extending the Gurtin-Murdoch surface elasticity theory to a surface hydrodynamics theory, we developed an adhesive surface hydrodynamics theory of moving contact line (MCL), which is essentially a hybrid theory of a ...

• We have developed an adhesive Gurtin-Murdoch surface hydrodynamics theory of moving contact line.

• A new lattice Boltzmann model for the one-fluid multiphase flow equations.
• ...

A multiphase lattice Boltzmann model is constructed to numerically solve the one-fluid flow equations for immiscible fluids. The method features one solver for the macroscopic pressure and momentum and another for a scalar field that ...