A marker-and-cell approach to free surface 2-D multiphase flows

This work describes a methodology to simulate free surface incompressible multiphase flows. This novel methodology allows the simulation of multiphase flows with an arbitrary number of phases, each of them having different densities and viscosities. Surface and interfacial tension effects are also included. The numerical technique is based on the GENSMAC front-tracking method. The velocity field is computed using a finite-difference discretization of a modification of the NavierStokes equations. These equations together with the continuity equation are solved for the two-dimensional multiphase flows, with different densities and viscosities in the different phases. The governing equations are solved on a regular Eulerian grid, and a Lagrangian mesh is employed to track free surfaces and interfaces. The method is validated by comparing numerical with analytic results for a number of simple problems; it was also employed to simulate complex problems for which no analytic solutions are available. The method presented in this paper has been shown to be robust and computationally efficient. Copyright (c) 2012 John Wiley & Sons, Ltd.

Interpolation estimate for a finite-element space with embedded discontinuities

We consider a recently proposed finite-element space that consists of piecewise affine functions with discontinuities across a smooth given interface Γ (a curve in two dimensions, a surface in three dimensions). Contrary to existing extended finite element methodologies, the space is a variant of the standard conforming Formula space that can be implemented element by element. Further, it neither introduces new unknowns nor deteriorates the sparsity structure. It is proved that, for u arbitrary in Formula, the interpolant Formula defined by this new space satisfies Graphic where h is the mesh size, Formula is the domain, Formula, Formula, Formula and standard notation has been adopted for the function spaces. This result proves the good approximation properties of the finite-element space as compared to any space consisting of functions that are continuous across Γ, which would yield an error in the Formula-norm of order Graphic. These properties make this space especially attractive for approximating the pressure in problems with surface tension or other immersed interfaces that lead to discontinuities in the pressure field. Furthermore, the result still holds for interfaces that end within the domain, as happens for example in cracked domains.

Numerical assessment of stability of interface discontinuous finite element pressure spaces

The stability of two recently developed pressure spaces has been assessed numerically: The space proposed by Ausas et al. [R.F. Ausas, F.S. Sousa, G.C. Buscaglia, An improved finite element space for discontinuous pressures, Comput. Methods Appl. Mech. Engrg. 199 (2010) 1019-1031], which is capable of representing discontinuous pressures, and the space proposed by Coppola-Owen and Codina [A.H. Coppola-Owen, R. Codina, Improving Eulerian two-phase flow finite element approximation with discontinuous gradient pressure shape functions, Int. J. Numer. Methods Fluids, 49 (2005) 1287-1304], which can represent discontinuities in pressure gradients. We assess the stability of these spaces by numerically computing the inf-sup constants of several meshes. The inf-sup constant results as the solution of a generalized eigenvalue problems. Both spaces are in this way confirmed to be stable in their original form. An application of the same numerical assessment tool to the stabilized equal-order P-1/P-1 formulation is then reported. An interesting finding is that the stabilization coefficient can be safely set to zero in an arbitrary band of elements without compromising the formulation's stability. An analogous result is also reported for the mini-element P-1(+)/P-1 when the velocity bubbles are removed in an arbitrary band of elements. (C) 2012 Elsevier B.V. All rights reserved.

A new enrichment space for the treatment of discontinuous pressures in multi-fluid flows

In this work, a new enrichment space to accommodate jumps in the pressure field at immersed interfaces in finite element formulations, is proposed. The new enrichment adds two degrees of freedom per element that can be eliminated by means of static condensation. The new space is tested and compared with the classical P1 space and to the space proposed by Ausas et al (Comp. Meth. Appl. Mech. Eng., Vol. 199, 10191031, 2010) in several problems involving jumps in the viscosity and/or the presence of singular forces at interfaces not conforming with the element edges. The combination of this enrichment space with another enrichment that accommodates discontinuities in the pressure gradient has also been explored, exhibiting excellent results in problems involving jumps in the density or the volume forces. Copyright (c) 2011 John Wiley & Sons, Ltd.

Hofmeister effects on the colloidal stability of poly(ethylene glycol)-decorated nanoparticles

The colloidal stability of poly(ethylene glycol)-decorated poly(methyl methacrylate), PMMA/Tween-20, particles was investigated by means of phase separation measurements, in the presence of sodium fluoride (NaF), sodium chloride, sodium bromide, sodium nitrate, or sodium thiocyanate (NaSCN) at 1.0 mol L-1. Following Hofmeister's series, the dispersions of PMMA/Tween-20 destabilized faster in the presence of NaF than with NaSCN. After the phase separation, the systems were homogenized and except for the dispersions in NaF, re-dispersed particles took longer to destabilize, indicating that anions adsorbed on the particles, creating a new surface. Except for F- ions, the adsorption of anions on the polar outmost shell was evidenced by means of tensiometry and small-angle X-ray scattering measurements. Fluoride ions induced the dehydration of the polar shell, without affecting the polar shell electron density, and the formation of very large aggregates. A model was proposed to explain the colloidal behavior in the presence of Hofmeister ions.

Comparison of physical properties of two exogenous surfactants: new parameter.

The pulmonary surfactant has essential physical properties for normal lung function. The most important property is the surface tension. In this work, it was evaluated the surface tension of two commercial exogenous surfactants used in surfactant replacement therapy, poractant alfa (Curosurf, Chiesi Farmaceuticals, Italy) and beractant (Survanta, Abbott Laboratories, USA) using new parameters. A Langmuir film balance (Minitrough, KSV Instruments, Finland) was used to measure surface tension of poractant alfa and beractant samples. For both samples, we prepared a solution of 1 mg/m dissolved in chloroform (100π`), which was applied over a subphase of milli-Q water (175 ml) in the chamber of the balance. The chamber has two moving barriers that can change its surface area between a maximal value of 112.5 cm 2 , and a minimal value of 22.5 cm 2, defining a balance cycle. Each surfactant had its surface tension evaluated during 20 balance cycles for three times. Four quantities were calculated from the experiment: Minimum Surface Tension (MTS), defined as the surface tension at minimal surface area during the first cycle; Mean Work Cycle (MWC), defined as the mean hysteresis area of the measured surface tension curve of the last 16 balance cycles; Critical Active Surface Area in Compression (CASAC) or in Expansion (CASAE), defined as the maximal chamber area where the surfactant is active on the surface in compression or expansion. The t-test was applied to verify for statistical significance of the results. Comproved with the MST is the same reported in literature, the differences between MWC, CASAC, and CASAE were statistically significant (p<0.001). The MWC, CASAC and CASAE were higher for poractant alfa than for beractant. A higher MWC for poractant alfa means higher elastic recoil of the lung in comparison with beractant. Using a different methodology, our results showed that poractant alfa is probably more effective in a surfactant replacement therapy than beractant due the use of poractant alfa in relation to the use of beractant in preterm infants with Respiratory Distress Syndrome (RDS).

Mechanical Measurements Of Two Exogenous Surfactants Using A Langmuir Film Balance:A Comparative Study

Rationale: The primary function of surfactant is to reduce the surface tension at air-liquid interface. In this study, the surface tension behavior of two commercial surfactants, poractant alfa (ChiesiFarmaceuticals,ltaly) and beractant (Abbott Laboratories,USA), were evaluated,using new parameters. Methods: We used a Langmuir film balance (Minitrough,KSV lnstruments,Finland) to measure of surface tension of both poractant alfa and beractant samples. For both samples,we prepared a solution of 1 mg/mdl dissolved in chloroform. The solution (1uL) was applied over a subphase of milli-Q water (175 ml) in the chamber of the balance. The chamber has two moving barriers that can change its surface area between a maximum value of 112.5 cm2 anda minimum value of 22.5 cm2, defining a balance cycle.lhree sample's films were evaluated for each sample, during 20 balance cycles. Here quantify two new variables, which is the mean hysteresis area of the measured curve surface tension of the last 16 balance cycles,defined here as Mean Work Cycle (MWC), and the moment that the surfactant is active in the surface, this measure is defined here as Active Surface Area Critical in the compression (ASACC) and the expansion (ASACE). The test was applied to compare the statistical significance of the results.