Modified two-grid method for solving coupled Navier-Stokes/Darcy model based on Newton iteration

A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the err...     

A cost‐effective curvature calculation approach for interfacial flows on unstructured meshes

We present a simple and cost‐effective curvature calculation approach for simulations of interfacial flows on structured and unstructured grids. The interface is defined using volume fractions, and the interface curvature is obtained as a function of the gradients of volume fractions. The gradient computation is based on a recently proposed gradient recovery method that mimicks the least squares approach without the need to solve a system of equations and is quite easy to implement on arbitrary polygonal meshes. The resulting interface curvature is used in a continuum surface force formulation within the framework of a well‐balanced finite‐volume algorithm to simulate multiphase flows dominated by surface tension. We show that the proposed curvature calculation is at least as accurate as some of the existing approaches on unstructured meshes while being straightforward to implement on any mesh topology. Numerical investigations also show that spurious currents in stationary problems that are dependent on the curvature calculation methodology are also acceptably low using the proposed approach. Studies on capillary waves and rising bubbles in viscous flows lend credence to the ability of the proposed method as an inexpensive, robust, and reasonably accurate approach for curvature calculation and numerical simulation of multiphase flows.     

Forces between a hard surface and an air–aqueous interface with and without films

The adsorption of particles to air–aqueous interfaces is vital in many applications, such as mineral flotation and the stabilization of food foams. The forces in the system determine whether a particle will attach to an air–aqueous interface. The forces between a particle and an air–aqueous interface are influenced by Derjaguin–Landau–Verwey–Overbeek forces (i.e. van der Waals and electrostatic forces), non–Derjaguin–Landau–Verwey–Overbeek forces (e.g. hydrophobic, hydrodynamic, structural, and capillary forces), liquid drainage, and liquid flow. As an air–aqueous interface can be deformed by a particle, the forces measured between an air–aqueous interface and a particle can differ from those measured between two hard surfaces separated by liquid. The presence of a film at an air–aqueous interface can also change the forces.     

A mass conservative well‐balanced reconstruction at wet/dry interfaces for the Godunov‐type shallow water model

This paper presents a novel mass conservative, positivity preserving wetting and drying treatment for Godunov‐type shallow water models with second‐order bed elevation discretization. The novel method allows to compute water depths equal to machine accuracy without any restrictions on the time step or any threshold that defines whether the finite volume cell is considered to be wet or dry. The resulting scheme is second‐order accurate in space and keeps the C‐property condition at fully flooded area and also at the wet/dry interface. For the time integration, a second‐order accurate Runge–Kutta method is used. The method is tested in two well‐known computational benchmarks for which an analytical solution can be derived, a C‐property benchmark and in an additional example where the experimental results are reproduced. Overall, the presented scheme shows very good agreement with the reference solutions. The method can also be used in the discontinuous Galerkin method. Copyright © 2016 John Wiley & Sons, Ltd.     

Simulating gas–liquid multiphase flow using meshless Lagrangian method

A multiphase flow model has been established based on a moving particle semi‐implicit method. A surface tension model is introduced to the particle method to improve the numerical accuracy and stability. Several computational techniques are employed to simplify the numerical procedure and further improve the accuracy. A particle fraction multiphase flow model is developed and verified by a two‐phase Poiseuille flow. The multiphase surface tension model is discussed in detail, and an ethanol drop case is introduced to verify the surface tension model. A simple dam break is simulated to demonstrate the improvements with various modifications in particle method along with a new boundary condition. Finally, we simulate several bubble rising cases to show the capacity of this new model in simulating gas–liquid multiphase flow with large density ratio difference between phases. The comparisons among numerical results of mesh‐based model, experimental data, and the present model, indicate that the new multiphase particle method is acceptable in gas–liquid multiphase fluids simulation. Copyright © 2014 John Wiley & Sons, Ltd.     

Microscopic Interface Between Two Immiscible Electrolytes: A Parallelism to an Ultramicroelectrode

Abstract

Current-potential response of a small interface formed between two immiscible solutions of electrolytes is examined. The diameter of the contact area made in a thin glass wall separating two solvents is approximately 130 μm. Ion transport across the nitrobenzene-water interface is studied by addition of probe semi-hydrophobic ions such as tetramethylammonium, tetraethylammonium, picrate, choline and dodecylsulfate to either aqueous or nonaqueous phase. The voltammetric behavior observed with the microinterface generally resembles that of a solid microelectrode of a similar radius. The contribution of ohmic drop becomes less significant with decrease of the interface area. This phenomenon permits voltammetric and amperometric measurements without using a potentiostat, and the solvent resistance is of a lesser problem.     

An operator splitting strategy for fluid–structure interaction problems with thin elastic structures in an incompressible Newtonian flow

We present a computational framework based on the use of the Newton and level set methods to model fluid–structure interaction problems involving elastic membranes freely suspended in an incompressible Newtonian flow. The Mooney–Rivlin constitutive model is used to model the structure. We consider an extension to a more general case of the method described in Laadhari (2017) to model the elasticity of the membrane. We develop a predictor–corrector finite element method where an operator splitting scheme separates different physical phenomena. The method features an affordable computational burden with respect to the fully implicit methods. An exact Newton method is described to solve the problem, and the quadratic convergence is numerically achieved. Sample numerical examples are reported and illustrate the accuracy and robustness of the method.     

A sharp‐interface immersed boundary framework for simulations of high‐speed inviscid compressible flows

A new finite‐volume flow solver based on the hybrid Cartesian immersed boundary (IB) framework is developed for the solution of high‐speed inviscid compressible flows. The IB method adopts a sharp‐interface approach, wherein the boundary conditions are enforced on the body geometry itself. A key component of the present solver is a novel reconstruction approach, in conjunction with inverse distance weighting, to compute the solutions in the vicinity of the solid‐fluid interface. We show that proposed reconstruction leads to second‐order spatial accuracy while also ensuring that the discrete conservation errors diminish linearly with grid refinement. Investigations of supersonic and hypersonic inviscid flows over different geometries are carried out for an extensive validation of the proposed flow solver. Studies on cylinder lift‐off and shape optimisation in supersonic flows further demonstrate the efficacy of the flow solver for computations with moving and shape‐changing geometries. These studies conclusively highlight the capability of the proposed IB methodology as a promising alternative for robust and accurate computations of compressible fluid flows on nonconformal Cartesian meshes.     

Weak coupling of a Reynolds model and a Stokes model for hydrodynamic lubrication

The Reynolds model is a reduced Stokes model, valid for narrow lubrication regions. In order to be able to handle locally non‐narrow regions such as pits or grooves, often displaying rapid geometrical variations, there is a need to be able to transit to the more accurate Stokes model. A fundamental problem is how to couple the two models in a numerical simulation, preferably allowing for different meshes in the different domains. In this paper, we present a weak coupling method for Reynolds and Stokes models for lubrication computations, including the possibility of cavitation in the different regions. The paper concludes with a numerical example. Copyright © 2010 John Wiley & Sons, Ltd.     

Adsorption of azacrown ethers at solid–liquid interface. Contact angle and neutron reflectivity study

Adsorption of two alkylated N,N′-diaza-18-crown-6 ethers (decyl- and hexadecyl-derivatives, ACE-10 and ACE-16, respectively) on solid surfaces was studied by using contact angle and neutron reflectivity measurements. The solid substrates used were (a) Si covered with a native oxide layer (Si/SiO₂) and (b) Si with sputtered Pt layer (Si/Pt). The sensitivity of neutron reflectivity was drastically improved by applying the intermediate Pt layer of 150 Å, which gave rise to several Kiessig fringes in the experimentally accessible q-range. The position of the fringes is very sensitive to slight changes of the interfacial composition induced by adsorption of a thin monolayer, otherwise very difficult to detect. Unfortunately, in the studied case this sensitivity is immediately lost due to undesired adsorption of a protonated material on the Pt surface exposed to the lab air. A decrease of surface energy (increase of contact angle) of both Si/SiO₂ and Si/Pt upon exposure to toluene solutions of ACEs suggests that the latter are attached to the surface via the hydrophilic azacrown ether head with alkyl chains standing upright towards the liquid phase.