On the Theory and Computation of Surface Tension: The Elimination of Parasitic Currents through Energy Conservation in the Second-Gradient Method

Jamet, Dominique; Torres, David J.; Brackbill, J. U.

doi:10.1006/jcph.2002.7165

Cited by 174 publications

(133 citation statements)

References 13 publications

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“…Their key ideas in suppressing parasitic currents, usually mentioned in this literature, are (i) improvement of curvature computation, (ii) achievement of discrete balance between surface tension and pressure gradient (iii) adaptive time integration scheme to tackle the stiffness induced by surface tension [25]. In addition, a singular and very promising work is developed by Jamet and coworkers [18]. It relies more on minimal energy consideration and can eliminate parasitic currents down to machine precision.…”

Section: Introductionsupporting

confidence: 41%

“…For low Reynolds, the time step (20) is close to (18) and has been validated in section 4.2, we discuss below a comparison of (52) and (20) with respect to flow characteristics.…”

Section: Comparison With Previous Heuristicsmentioning

confidence: 41%

“…Furthermore, if ρ is increased this value of c 2 also leads to numerically stable simulations as it is predicted by the analysis. For large ρ, note that the stability condition induced by (20) is not optimal and can be relaxed to the one induced by (18).…”

Section: Numerical Confirmation Of the Stability Conditionmentioning

confidence: 45%

“…In the previous paragraph, we have seen that our stability condition suffices for stable simulations and is close to (18).…”

Section: Time Steps Associated To Various Flow Regimesmentioning

confidence: 48%

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On stability condition for bifluid flows with surface tension: Application to microfluidics

Galusinski

Vigneaux

2008

Journal of Computational Physics

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Models for incompressible immiscible bifluid flows with surface tension are here considered. Since Brackbill, Kothe and Zemach (J. Comput. Phys. 100, pp 335-354, 1992) introduced the Continuum Surface Force (CSF) method, many methods involved in interface tracking or capturing are based on this reference work. Particularly, the surface tension term is discretized explicitly and therefore, a stability condition is induced on the computational time step. This constraint on the time step allows the containment of the amplification of capillary waves along the interface and puts more emphasis on the terms linked with the density in the Navier-Stokes equation (i. e. unsteady and inertia terms) rather than on the viscous terms. Indeed, the viscosity does not appear, as a parameter, in this stability condition.We propose a new stability condition which takes into account all fluid characteristics (density and viscosity) and for which we present a theoretical estimation. We detail the analysis which is based on a perturbation study -with capillary wave -for which we use energy estimate on the induced perturbed velocity. We validate our analysis and algorithms with numerical simulations of microfluidic flows using a Level Set method, namely the exploration of different mixing dynamics inside microdroplets.

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Section: Introductionsupporting

confidence: 41%

“…For low Reynolds, the time step (20) is close to (18) and has been validated in section 4.2, we discuss below a comparison of (52) and (20) with respect to flow characteristics.…”

Section: Comparison With Previous Heuristicsmentioning

confidence: 41%

Section: Numerical Confirmation Of the Stability Conditionmentioning

confidence: 45%

“…In the previous paragraph, we have seen that our stability condition suffices for stable simulations and is close to (18).…”

Section: Time Steps Associated To Various Flow Regimesmentioning

confidence: 48%

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On stability condition for bifluid flows with surface tension: Application to microfluidics

Galusinski

Vigneaux

2008

Journal of Computational Physics

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“…Overall, this code takes about 75% longer to run than CSF but has more accurate convergence properties; hence, it makes sense to use PROST when CPUs are available, and use CSF when a rough solution would suffice. An example is drop relaxation upon cessation of applied shear [43], in which small deformations are to be resolved spatially over a long time.…”

Section: Numerical Methodsologymentioning

confidence: 48%

Influence of viscoelasticity on drop deformation and orientation in shear flow. Part 2: Dynamics

Verhulst

Cardinaels

Moldenaers

et al. 2009

Journal of Non-Newtonian Fluid Mechanics

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An experimental study of drop dynamics under shear is conducted for five fluid pairs: a reference Newtonian system, two systems with a viscoelastic drop in a Newtonian matrix, one with a Newtonian drop in a viscoelastic matrix, all at drop to matrix viscosity ratio λ = 1.5, and a separate case at λ = 0.75. The viscoelastic liquids are either a Boger fluid or a shear-thinning viscoelastic fluid satisfying an Ellis model. Deborah numbers in the range 1 to 2 and a range of capillary numbers from low to above breakup conditions are addressed. The results focus on three aspects: relaxation after cessation of shear, a new viscoelastic drop breakup scenario, and the effect of shear flow history on drop breakup. Numerical simulations with the 3D volume-of-fluid PROST method complement the experimental results.

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A unified finite volume framework for phase‐field simulations of an arbitrary number of fluid phases

et al. 2022

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While the phase-field methodology is widely adopted for simulating two-phase flows, the simulation of an arbitrary number (N ≥ 2) of fluid phases at physical fidelity is non-trivial and requires special attention concerning mathematical modelling, numerical discretization, and solution algorithm. We present our most recent work with a focus on validation for multiple immiscible, incompressible, and isothermal phases, enhancing further our library for diffuse interface phase-field interface capturing methods in OpenFOAM (FOAMextend 4.0/4.1). The phase-field method is an energetic variational formulation based on the work of Cahn and Hilliard where the interface is composed of a physical diffuse layer resembling realistic interfaces. The evolution of the phases is then governed by the minimization of the free energy of the system.The accuracy of the method is demonstrated for a number of test problems, including a floating liquid lens, bubble rise in two stratified layers, and drop impact onto thin liquid film.

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On the Theory and Computation of Surface Tension: The Elimination of Parasitic Currents through Energy Conservation in the Second-Gradient Method

Cited by 174 publications

References 13 publications

On stability condition for bifluid flows with surface tension: Application to microfluidics

On stability condition for bifluid flows with surface tension: Application to microfluidics

Influence of viscoelasticity on drop deformation and orientation in shear flow. Part 2: Dynamics

A unified finite volume framework for phase‐field simulations of an arbitrary number of fluid phases

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