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

Popinet, Stéphane

doi:10.1016/j.jcp.2009.04.042

Cited by 1,123 publications

(1,196 citation statements)

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“…Mass conservation is usually very good in Gerris simulations as discussed by Popinet (2009). In our simulations, errors in mass conservation are below 0.01%, as shown in Fig.…”

Section: Appendix a Convergence Of The Numerical Results With The Mesupporting

confidence: 68%

“…As shown in Appendix A, errors in mass (or volume) conservation are very small in the present numerical methods (Popinet 2003(Popinet , 2009. We have checked here that, mass is conserved to better than 0.01% for both air and water for all resolutions tested and better than 0.001% in the highest resolution case (equivalent to 1024 3 , see Appendix A).…”

Section: Interface Reconstruction and Bubble Countingmentioning

confidence: 57%

“…We solve the three-dimensional two-phase incompressible Navier Stokes equations accounting for surface tension and viscous effects using the open source solver Gerris (Popinet 2003(Popinet , 2009), based on a quad/octree adaptive spatial discretization, multilevel Poisson solver. The interface between the high density liquid (water) and the low density gas (air) is reconstructed by a geometric Volume Of Fluid (VOF) method.…”

Section: The Gerris Flow Solvermentioning

confidence: 99%

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Air entrainment and bubble statistics in breaking waves

2016

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We investigate air entrainment and bubble statistics in three-dimensional breaking waves through novel direct numerical simulations of the two-phase air-water flow, resolving the length scales relevant for the bubble formation problem, the capillary length and the Hinze scale. The dissipation due to breaking is found to be in good agreement with previous experimental observations and inertial-scaling arguments. The air-entrainment properties and bubble-size statistics are investigated for various initial characteristic wave slopes. For radii larger than the Hinze scale, the bubble size distribution, can be described by N (r, t) = B(V 0 /2π)(ε(t − ∆τ )/W g)r −10/3 r −2/3 m during the active breaking stages, where ε(t − ∆τ ) is the time dependent turbulent dissipation rate, with ∆τ the collapse time of the initial air pocket entrained by the breaking wave, W a weighted vertical velocity of the bubble plume, r m the maximum bubble radius, g gravity, V 0 the initial volume of air entrained, r the bubble radius and B a dimensionless constant. The active breaking time-averaged bubble size distribution is described bȳ N (r) = B(1/2π)( l L c /W gρ)r −10/3 r −2/3 m , where l is the wave dissipation rate per unit length of breaking crest, ρ the water density and L c the length of breaking crest. Finally, the averaged total volume of entrained air,V , per breaking event can be simply related to l byV = B( l L c /W gρ), which leads to a relationship to a characteristic slope, S, of V ∝ S 5/2 . We propose a phenomenological turbulent bubble break-up model, based on earlier models and the balance between mechanical dissipation and work done against buoyancy forces. The model is consistent with the numerical results and existing experimental results.

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“…Mass conservation is usually very good in Gerris simulations as discussed by Popinet (2009). In our simulations, errors in mass conservation are below 0.01%, as shown in Fig.…”

Section: Appendix a Convergence Of The Numerical Results With The Mesupporting

confidence: 68%

Section: Interface Reconstruction and Bubble Countingmentioning

confidence: 57%

Section: The Gerris Flow Solvermentioning

confidence: 99%

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Air entrainment and bubble statistics in breaking waves

2016

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“…The governing conservation equations for the incompressible and variable-density flow with surface tension are [40] u…”

Section: Appendix A1 Governing Equations and Numerical Methodsmentioning

confidence: 99%

“…Direct numerical simulations (DNS) of the two-phase interfacial flow are also performed using the Gerris flow solver [40] to further understand the droplet dynamics in curved channels. The computational domain is simplified to quarter of circumstance for each curvature (Figure 1(c)).…”

Section: Numericalmentioning

confidence: 99%

Lateral migration of dual droplet trains in a double spiral microchannel

Xue

Chen

Liu

et al. 2016

Sci. China Phys. Mech. Astron.

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Microfluidic droplets have emerged as novel platforms for chemical and biological applications. Manipulation of droplets has thus attracted increasing attention. Different from solid particles, deformable droplets cannot be efficiently controlled by inertia-driven approaches. Here, we report a study on the lateral migration of dual droplet trains in a double spiral microchannel at low Reynolds numbers. The dominant driving mechanism is elucidated as wall effect originated from the droplet deformation. Three types of migration modes are observed with varying Reynolds numbers and the size-dependent mode is intensively investigated. We obtain empirical formulas by relating the migration to Reynolds numbers and droplet sizes. The effect of droplet deformability on the migration and the detailed migration behavior along the double spiral channel are discussed. Numerical simulations are also performed and yielded in qualitative agreement with the experiments. This proposed low Re approach based on lateral migration could be a promising alternative to existing inertia-driven approaches especially concerning deformable entities and susceptible bio-particles.

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Adaptive Mesh Refinement

Löhner

2008

Applied Computational Fluid Dynamics Techniques

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

Cited by 1,123 publications

References 71 publications

Air entrainment and bubble statistics in breaking waves

Air entrainment and bubble statistics in breaking waves

Lateral migration of dual droplet trains in a double spiral microchannel

Adaptive Mesh Refinement

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