Axisymmetric flows on the torus geometry

Busuioc, Sergiu; Kusumaatmaja, Halim; Ambruş, Victor E.

doi:10.1017/jfm.2020.440

Cited by 1 publication

(7 citation statements)

References 43 publications

(46 reference statements)

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“…Furthermore, the approach to equilibrium configuration through a damped harmonic motion is investigated in Subsec. III C. We show that we recover the damping coefficient and the angular frequency as derived in [11]. Finally, we contrast the drift dynamics of fluid stripes with droplets on the torus in section III D. While the former drift to the inside of the torus, the latter move to the outside of the torus.…”

Section: Drift Dynamics Of Fluid Stripes and Dropletssupporting

confidence: 60%

“…This pressure difference is often termed the Laplace pressure. This pressure difference was recently derived analytically on a torus and the result is [11]…”

Section: B Laplace Pressure Testmentioning

confidence: 96%

“…III B. The Laplace pressure takes a different form on a curved torus geometry compared to that on a flat geometry [11]. Furthermore, the approach to equilibrium configuration through a damped harmonic motion is investigated in Subsec.…”

Section: Drift Dynamics Of Fluid Stripes and Dropletsmentioning

confidence: 99%

“…where the damping coefficient α = α ν + α µ receives contributions from the viscous damping due to the fluid [11]…”

Section: Approach To Equilibriummentioning

confidence: 99%

“…a sphere). For the stripes, analytical results are available for their equilibrium configuration, Laplace pressure, and relaxation dynamics [11], thus providing an excellent platform to systematically examine the accuracy of our method. We demonstrate that these predictions are accurately captured in our simulations.…”

Section: Introductionmentioning

confidence: 99%

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Multicomponent flow on curved surfaces: A vielbein lattice Boltzmann approach

et al. 2019

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We develop and implement a novel lattice Boltzmann scheme to study multicomponent flows on curved surfaces, coupling the continuity and Navier-Stokes equations with the Cahn-Hilliard equation to track the evolution of the binary fluid interfaces. Standard lattice Boltzmann method relies on regular Cartesian grids, which makes it generally unsuitable to study flow problems on curved surfaces. To alleviate this limitation, we use a vielbein formalism to write down the Boltzmann equation on an arbitrary geometry, and solve the evolution of the fluid distribution functions using a finite difference method. Focussing on the torus geometry as an example of a curved surface, we demonstrate drift motions of fluid droplets and stripes embedded on the surface of a torus. Interestingly, they migrate in opposite directions: fluid droplets to the outer side while fluid stripes to the inner side of the torus. For the latter we demonstrate that the global minimum configuration is unique for small stripe widths, but it becomes bistable for large stripe widths. Our simulations are also in agreement with analytical predictions for the Laplace pressure of the fluid stripes, and their damped oscillatory motion as they approach equilibrium configurations, capturing the corresponding decay timescale and oscillation frequency. Finally, we simulate the coarsening dynamics of phase separating binary fluids in the hydrodynamics and diffusive regimes for tori of various shapes, and compare the results against those for a flat two-dimensional surface. Our lattice Boltzmann scheme can be extended to other surfaces and coupled to other dynamical equations, opening up a vast range of applications involving complex flows on curved geometries.

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Section: Drift Dynamics Of Fluid Stripes and Dropletssupporting

confidence: 60%

“…This pressure difference is often termed the Laplace pressure. This pressure difference was recently derived analytically on a torus and the result is [11]…”

Section: B Laplace Pressure Testmentioning

confidence: 96%

Section: Drift Dynamics Of Fluid Stripes and Dropletsmentioning

confidence: 99%

“…where the damping coefficient α = α ν + α µ receives contributions from the viscous damping due to the fluid [11]…”

Section: Approach To Equilibriummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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