Since the proposal of inertial microfluidics in 2007, it has been widely used for particle focusing and separation with superior performances. The particle migration behaviour in microchannel is extremely complicated involving various parameters. Recently, computational approaches have been utilized to obtain better insights into the underlying physics, which facilitates a comprehensive and intuitive understanding of particle migration in inertial flow. The numerical methods are ideal ways for assessing the effects of various parameters on particle focusing. In this review, numerous theories and models proposed to systematically explore the effects on migration of particles are summed concisely, especially numerical methods. Besides, latest research advances in direct numerical simulation of diverse particle motion and migration, whether rigid or deformable, spherical or non-spherical, suspended in simple or complex channel, are introduced comprehensively. Then, numerical simulations for microfluidic devices design are provided and discussed to facilitate the optimization of microchannel and the design of coupling microfluidic device for real- particles separation. Finally, we further discuss the remaining challenges in the modeling of inertial particle microfluidics and provide several suggestions for future investigators.

自2007年惯性微流控技术提出以来，以其优越的性能广泛应用于粒子聚焦和分离。微通道中的粒子迁移行为极其复杂，涉及各种参数。最近，计算方法已被用于更好地了解基础物理学，这有助于全面和直观地理解惯性流中的粒子迁移。数值方法是评估各种参数对粒子聚焦影响的理想方法。在这篇综述中，简明扼要地总结了为系统探索粒子迁移影响而提出的众多理论和模型，尤其是数值方法。此外，各种粒子运动和迁移的直接数值模拟的最新研究进展，无论是刚性的还是可变形的，球形的还是非球形的，悬浮在简单的还是复杂的通道中，都得到了全面的介绍。然后，提供并讨论了微流控装置设计的数值模拟，以促进微通道的优化和用于实际颗粒分离的耦合微流控装置的设计。最后，我们进一步讨论了惯性粒子微流体建模中剩余的挑战，并为未来的研究人员提供了一些建议。