A computer simulation framework for vesicles reproduced mesh-only equilibrium branches and characteristic neck-forming and pear-like shapes. But the predicted motion and morphology varied among the membrane bending models. One case produced a deeply constricted, dumbbell-like vesicle nearing pinch-off, while other cases produced grooved, slipper-like shapes or a neck that thinned toward rupture.
One solver, four membrane descriptions
The arXiv preprint, dated 26 August 2026, couples a multiphase SPH fluid solver to a triangulated membrane representation. It places four bending descriptions in one framework: a minimal model, a spontaneous-curvature model, a bilayer-couple model and an area-difference-elasticity model, known as ADE.
The method tracked membrane vertices on the interface marked by the inner and outer fluids' color functions. It omitted particle reflection or bounce-back conditions and used weakly compressible SPH to preserve enclosed volume.
The calculations placed a single vesicle in a rectangular box measuring 16R by 8R by 8R. Walls at y = +/-4R imposed shear, while x and z had periodic boundaries. The inner and outer fluids had equal density and viscosity, and all simulations used Re = 0.1.
Reference tests set the baseline
A resolution check for the minimal model at Ca = 1 compared a standard run with 1,280 membrane triangles and particle spacing of 0.2R with a high-resolution run using 5,120 triangles and 0.1R spacing. The morphologies were virtually indistinguishable, and differences in inclination angle and revolution frequency stayed within measurement scatter. The finding supports convergence under that reported condition, but not across every model and parameter combination.
In equilibrium tests, the coupled solver's steady shapes had direct counterparts in mesh-only calculations. The same shape branches, neck-forming and pear-like morphologies, and transition locations appeared in both. This was a qualitative comparison, with no quantitative error metric reported.
For dynamics, the minimal model's simulated inclination and revolution frequency agreed with theory at large reduced volumes. At Ca = 1 and Vr below 0.75, deviations appeared alongside oblong, centrally indented shapes that fell outside the theory's ellipsoidal-shape assumption. No confidence intervals or formal error estimates were reported.
When the membrane rules disagree
The contrast between orientation and motion became clearer in the spontaneous-curvature test with H0 = 1.2. Its inclination angle stayed in close agreement with the minimal model across the tested reduced-volume range and increased monotonically with Vr. At lower reduced volumes, however, its revolution frequency was higher than the minimal model's and strongly non-monotonic. Near Vr = 0.577 at Ca = 10, the vesicle formed a deeply constricted, dumbbell-like shape approaching pinch-off.
The bilayer-couple model followed a different shape sequence. At a preferred reduced area difference of 1 and Ca = 1, near-spherical vesicles remained smooth and convex. With lower reduced volume, they developed a central groove and then an asymmetric slipper-like shape with an off-center dimple.
In the ADE case, using Ca = 1, H0 = 0, Vr = 0.65 and a preferred reduced area difference of 1.34, the vesicle tilted and elongated. Its inner cavity became a slender pouch, and the connecting neck thinned toward rupture. The fixed-connectivity simulation stopped before breakup.
Where the calculation stops
The mesh's fixed connectivity is the clearest boundary on the result: it cannot represent completed topological changes such as membrane rupture, budding or fission. The spontaneous-curvature case approached pinch-off, and the ADE case stopped before breakup. The authors propose a particle-based membrane as a future extension.
The validation checks were narrow. They compared shapes and motion with mesh-only calculations and theory, while the reported analysis provided no formal uncertainty intervals or quantified error bounds.
The calculation also covered a restricted setup: one vesicle per simulation, matched inner and outer fluid properties, and Re = 0.1. Resolution convergence was demonstrated for the minimal model at one capillary number, Ca = 1, rather than across all models and conditions.
Paper details
The work was supported by the National Key R&D Program of China and the National Natural Science Foundation of China, with grant numbers 2022YFA1203200 and 12172330. The authors declared no potential conflict of interest. Data supporting the findings are available from the corresponding author upon reasonable request.
Paper data and sources
Original title: An SPH--mesh Coupling for Vesicle Dynamics in Shear Flow
Authors: Kuiliang Wang, Xinwei Cai, Ting Ye et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text