A comparative study of transient capillary rise using direct numerical simulations

Gründing, Dirk; Smuda, Martin; Antritter, Thomas; Fricke, Mathis; Rettenmaier, Daniel; Kummer, Florian; Stephan, Peter; Marschall, Holger; Bothe, Dieter

doi:10.1016/j.apm.2020.04.020

Cited by 26 publications

(13 citation statements)

References 61 publications

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“…We note that the refined simulations exhibit a more dynamic behavior, so the simulation for

Eo = 5

is performed on a larger domain with

Ω = [- 4 r_{0}, 4 r_{0}] \times [0, 2 r_{0}]

in order to prevent the contact line to touch the outer boundaries. However, the terminal thickness

e^{*}

and shapes remain unchanged (compare mesh study for the capillary rise in Gründing et al 27 ).…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Therefore, we follow the formulation by Reusken et al 21 Thus, no additional adaption of the original level-set evolution algorithm is needed. Note that this method was already used for a comparative study of the transient capillary rise, see Gründing et al 27 The outline of this work is as follows. In Section 2, the continuous problem statement for the transient incompressible two-phase flow with moving contact lines is given.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, we follow the formulation by Reusken et al 21 Thus, no additional adaption of the original level‐set evolution algorithm is needed. Note that this method was already used for a comparative study of the transient capillary rise, see Gründing et al 27 …”

Section: Introductionmentioning

confidence: 99%

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The extended discontinuous Galerkin method adapted for moving contact line problems via the generalized Navier boundary condition

Smuda

Kummer

2021

Numerical Methods in Fluids

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In this work, an extended discontinuous Galerkin (extended DG/XDG also called unfitted DG) solver for two‐dimensional flow problems exhibiting moving contact lines is presented. The generalized Navier boundary condition is employed within the XDG discretization for the handling of the moving contact lines. The spatial discretization is based on a symmetric interior penalty method and the numerical treatment of the surface tension force is done via the Laplace–Beltrami formulation. The XDG method adapts the approximation space conformal to the position of the interface and allows a sub‐cell accurate representation within the sharp interface formulation. The interface is described as the zero set of a signed‐distance level‐set function and discretized by a standard DG method. No adaption of the level‐set evolution algorithm is needed for the extension to moving contact line problems. The developed solver is validated against typical two‐dimensional contact line driven flow phenomena including droplet simulations on a wall and the two‐phase Couette flow.

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“…We note that the refined simulations exhibit a more dynamic behavior, so the simulation for

Eo = 5

is performed on a larger domain with

Ω = [- 4 r_{0}, 4 r_{0}] \times [0, 2 r_{0}]

in order to prevent the contact line to touch the outer boundaries. However, the terminal thickness

e^{*}

and shapes remain unchanged (compare mesh study for the capillary rise in Gründing et al 27 ).…”

Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The extended discontinuous Galerkin method adapted for moving contact line problems via the generalized Navier boundary condition

Smuda

Kummer

2021

Numerical Methods in Fluids

Self Cite

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“…Several techniques exist to access the time evolution of interfaces. On the one hand, they include tracking methods based on Lagrangian coordinates such as front tracking [ 49 ] and Lagrangian–Eulerian methods [ 50 ]. On the other hand, there also exist capturing methods based on Eulerian coordinates such as the volume-of-fluid [ 51 ], the diffuse [ 52 ] or sharp [ 53 ] interface level-set, and the phase-field [ 54 ] method.…”

Section: Problem Setup and Numerical Methodologymentioning

confidence: 99%

Instability of a liquid sheet with viscosity contrast in inertial microfluidics

Patel

Stark

2021

Eur. Phys. J. E

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Flows at moderate Reynolds numbers in inertial microfluidics enable high throughput and inertial focusing of particles and cells with relevance in biomedical applications. In the present work, we consider a viscosity-stratified three-layer flow in the inertial regime. We investigate the interfacial instability of a liquid sheet surrounded by a density-matched but more viscous fluid in a channel flow. We use linear stability analysis based on the Orr–Sommerfeld equation and direct numerical simulations with the lattice Boltzmann method (LBM) to perform an extensive parameter study. Our aim is to contribute to a controlled droplet production in inertial microfluidics. In the first part, on the linear stability analysis we show that the growth rate of the fastest growing mode $$\xi ^{*}$$ ξ ∗ increases with the Reynolds number $$\text {Re}$$ Re and that its wavelength $$\lambda ^{*}$$ λ ∗ is always smaller than the channel width w for sufficiently small interfacial tension $$\Gamma $$ Γ . For thin sheets we find the scaling relation $$\xi ^{*} \propto mt^{2.5}_{s}$$ ξ ∗ ∝ m t s 2.5 , where m is viscosity ratio and $$t_{s}$$ t s the sheet thickness. In contrast, for thicker sheets $$\xi ^{*}$$ ξ ∗ decreases with increasing $$t_s$$ t s or m due to the nearby channel walls. Examining the eigenvalue spectra, we identify Yih modes at the interface. In the second part on the LBM simulations, the thin liquid sheet develops two distinct dynamic states: waves traveling along the interface and breakup into droplets with bullet shape. For smaller flow rates and larger sheet thicknesses, we also observe ligament formation and the sheet eventually evolves irregularly. Our work gives some indication how droplet formation can be controlled with a suitable parameter set $$\{\lambda ,t_{s},m,\Gamma ,\text {Re}\}$$ { λ , t s , m , Γ , Re } . Graphical Abstract

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“…The interTrackFoam solver is described in Tuković & Jasak (2012), and was validated against several test cases in that article. It has also been used (sometimes in a modified form) to study the motion of free-rising bubbles (Pesci et al 2018;Charin et al 2019), Taylor bubbles (Marschall et al 2014) and transient capillary rise (Gründing et al 2020). It has been validated against other numerical methods (Gründing et al 2020;Marschall et al 2014), as well as experimental measurements (Marschall et al 2014), and good agreement has been obtained.…”

Section: The Intertrackfoam Solvermentioning

confidence: 99%

Vortex ring connection to a free surface

2022

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We perform numerical simulations of the interaction between a vortex ring and a free surface, and provide a new interpretation of the mechanism by which the vortex ring connects to the free surface. Large vorticity gradients at the free surface result in the diffusion of surface-tangential vorticity out of the fluid. This is accompanied by the diffusion of opposite-signed surface-normal vorticity away from the connection line, along the free surface, which results in the attachment of the vortex ring to the free surface. Compared to existing descriptions, this interpretation explains better how the solenoidal property that vortex lines do not end in the fluid is maintained. By including an interface vortex sheet at the free surface, the important property of vorticity conservation is maintained throughout the interaction. The upper part of the vortex ring simply diffuses out of the fluid, and into the interface vortex sheet, with the total circulation remaining constant.

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A comparative study of transient capillary rise using direct numerical simulations

Cited by 26 publications

References 61 publications

The extended discontinuous Galerkin method adapted for moving contact line problems via the generalized Navier boundary condition

The extended discontinuous Galerkin method adapted for moving contact line problems via the generalized Navier boundary condition

Instability of a liquid sheet with viscosity contrast in inertial microfluidics

Vortex ring connection to a free surface

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