Generalize the effective-particle-size mapping to three dimensions

Establish whether the effective-particle-size mapping and its mean-field geometric calculation can be successfully generalized from two-dimensional rough particles to three-dimensional systems.

Background

The paper demonstrates that the structure and translational dynamics of two-dimensional particles decorated with surface asperities can be mapped onto those of hard disks through an effective radius and effective packing fraction. The authors explicitly leave open whether this framework survives in three dimensions, while noting that the mean-field character of the calculation provides a reason to expect that such a generalization may be possible.

References

Whether the proposed approach can be successfully generalized to 3D systems is at present an open question, but the mean-field nature of the calculation leads to the expectation that this can indeed be done.

— Effective particle size governs structure and dynamics in rough hard-particle fluids  (2609.08699 - Xiao et al., 8 Sep 2026) in Conclusion, final paragraph