A Comparison of Cahn–Hilliard and Navier–Stokes–Cahn–Hilliard Models on Manifolds

Olshanskii, Maxim A.; Palzhanov, Yerbol; Quaini, Annalisa

doi:10.1007/s10013-022-00564-5

Cited by 2 publications

(5 citation statements)

References 50 publications

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“…This equilibrium state coincides with the corresponding result for the reduced model without hydrodynamics, see Appendix D. However, without friction γ = 0 the dissipation potential in the reached axisymmetric state is invariant under surface rigid body motion. Such configurations have been explored for one-component fluid deformable surfaces (Reuther et al 2020;Krause & Voigt 2023;Nestler & Voigt 2023b;Olshanskii 2023). Indeed the shown configurations in figures 4 and 5 for κ = 0.5 undergo slight rigid body motions and as the resulting forces interact with the shape and the phase composition also slightly differ.…”

Section: Variation Of Parametersmentioning

confidence: 99%

“…For further numerical and analytical approaches under additional symmetry assumptions we refer to Al-Izzi et al (2020), where a linear stability analysis of a tube geometry is considered, and to Olshanskii (2023), where potential rotational symmetric equilibrium configurations are addressed. For a comparison of different derivations of this model we refer to Reuther & Voigt (2015, 2018a and Brandner, Reusken & Schwering (2022b).…”

Section: One Component Fluid Deformable Surfacementioning

confidence: 99%

“…In the case of γ = 0, the model has been introduced and discussed in Bachini et al (2023b), where it is used to study the influence of surface hydrodynamics on coarsening in multicomponent scaffolded lipid vesicles, see Fonda et al (2018), Fonda et al (2019) and Rinaldin et al (2020). Without the bending terms, the system has already been addressed in Nitschke et al (2012), Ambrus et al (2019) and Olshanskii et al (2022).…”

Section: Two-component Fluid On a Stationary Surfacementioning

confidence: 99%

“…On stationary surfaces these problems are addressed in Nitschke, Voigt & Wensch (2012), Ambrus et al. (2019), Olshanskii, Palzhanov & Quaini (2022) and Bachini, Krause & Voigt (2023 b ) and essentially reveal an enhanced coarsening rate due to hydrodynamic effects, similar to the situation in flat space (Fan et al. 2010; Camlay & Brown 2011).…”

Section: Introductionmentioning

confidence: 96%

“…We follow this simplification and consider only surface two-phase flow problems. On stationary surfaces these problems are addressed in Nitschke, Voigt & Wensch (2012), Ambrus et al (2019), Olshanskii, Palzhanov & Quaini (2022) and Bachini, Krause & Voigt (2023b) and essentially reveal an enhanced coarsening rate due to hydrodynamic effects, similar to the situation in flat space (Fan et al 2010;Camlay & Brown 2011). To consider evolving surfaces under the influence of surface viscosity requires models for so-called fluid deformable surfaces.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Derivation and simulation of a two-phase fluid deformable surface model

Bachini,

Krause,

Nitschke

et al. 2023

J. Fluid Mech.

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To explore the impact of surface viscosity on coexisting fluid domains in biomembranes we consider two-phase fluid deformable surfaces as model systems for biomembranes. Such surfaces are modelled by incompressible surface Navier–Stokes–Cahn–Hilliard-like equations with bending forces. We derive this model using the Lagrange–d’Alembert principle considering various dissipation mechanisms. The highly nonlinear model is solved numerically to explore the tight interplay between surface evolution, surface phase composition, surface curvature and surface hydrodynamics. It is demonstrated that hydrodynamics can enhance bulging and furrow formation, which both can further develop to pinch-offs. The numerical approach builds on a Taylor–Hood element for the surface Navier–Stokes part, a semi-implicit approach for the Cahn–Hilliard part, higher-order surface parametrizations, appropriate approximations of the geometric quantities, and mesh redistribution. We demonstrate convergence properties that are known to be optimal for simplified subproblems.

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Section: Variation Of Parametersmentioning

confidence: 99%

Section: One Component Fluid Deformable Surfacementioning

confidence: 99%

Section: Two-component Fluid On a Stationary Surfacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Derivation and simulation of a two-phase fluid deformable surface model

Bachini,

Krause,

Nitschke

et al. 2023

J. Fluid Mech.

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show abstract

The interplay of geometry and coarsening in multicomponent lipid vesicles under the influence of hydrodynamics

2023

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We consider the impact of surface hydrodynamics on the interplay between membrane curvature and lipid composition in coarsening processes on model systems for biomembranes. This includes the influence on scaling laws and equilibrium configurations, which are investigated by computational studies of a surface two-phase flow problem with additional phase-dependent bending terms. These additional terms geometrically favor specific configurations. We find that the effect of hydrodynamics strongly depends on the composition. In situations where the composition allows a realization of a geometrically favored configuration, hydrodynamics enhances the evolution toward this configuration. We restrict our model and numerics to stationary surfaces of varying curvature and validate the numerical approach with various benchmark problems and convergence studies.

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A Comparison of Cahn–Hilliard and Navier–Stokes–Cahn–Hilliard Models on Manifolds

Cited by 2 publications

References 50 publications

Derivation and simulation of a two-phase fluid deformable surface model

Derivation and simulation of a two-phase fluid deformable surface model

The interplay of geometry and coarsening in multicomponent lipid vesicles under the influence of hydrodynamics

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