Modeling diffusion of nonspherical particles presents an unsolved and considerable challenge, despite its importance for the understanding of crowding effects in biology, food technology and formulation science. A common approach in experiment and simulation is to map nonspherical objects on effective spheres to subsequently use the established predictions for spheres to approximate phenomena for nonspherical particles. Using numerical evaluation of the hydrodynamic mobility tensor, we show that this so-called effective sphere model fundamentally fails to represent the self-diffusion in solutions of ellipsoids as well as rod-like assemblies of spherical beads. The effective sphere model drastically overestimates the slowing down of self-diffusion down to volume fractions below 0.01. Furthermore, even the linear term relevant at lower volume fraction is inaccurate, linked to a fundamental misconception of effective sphere models. To overcome the severe problems related with the use of effective sphere models, we suggest a protocol to predict the short-time self-diffusion of rod-like systems, based on simulations with hydrodynamic interactions that become feasible even for more complex molecules as the essential observable shows a negligible system-size effect.

尽管非球形粒子的扩散模型对于理解生物学、食品技术和配方科学中的拥挤效应很重要，但它仍然是一个未解决且相当大的挑战。实验和模拟中的一种常见方法是将非球形物体映射到有效球体上，然后使用已建立的球体预测来近似非球形粒子的现象。使用流体动力学流动张量的数值评估，我们表明这种所谓的有效球体模型根本无法表示椭球体溶液以及球形珠的棒状组件中的自扩散。有效球体模型极大地高估了自扩散减慢到低于 0.01 的体积分数。此外，即使是与较低体积分数相关的线性项也不准确，这与对有效球体模型的基本误解有关。为了克服与使用有效球体模型相关的严重问题，我们提出了一个协议来预测棒状系统的短时自扩散，基于流体动力学相互作用的模拟，即使对于更复杂的分子也是可行的。 observable 显示了可以忽略不计的系统规模效应。