低雷诺数流体中颗粒的受限输运在科学和工程中有着重要应用。近年来，封闭腔内低雷诺数流体中的颗粒输运受到广泛关注，研究其中颗粒的运动，有助于微纳米材料中颗粒的制备和控制，化学反应中纳米颗粒催化剂的研究，揭示细胞内生命活动和药物输运的物理机理，能为药物输运、芯片实验室中生物材料的分析、微液滴和微胶囊中颗粒输运等应用提供科学依据。由于三维封闭腔内颗粒-壁面之间通过流体互相作用，颗粒的输运特征和机理十分复杂。为探索限域效应和水动力相互作用对封闭腔内颗粒输运的影响，本文运用数值模拟，研究了单个颗粒在封闭腔内低雷诺数流体中的运动。

本文首先计算了立方腔内球形颗粒沿x、y和z方向的迁移率随腔内空间位置的变化，得到了立方体内迁移率的分布规律，找到了可以表示整个立方体腔中迁移率的最小四面体单元。颗粒在立方体中呈现出垂直于外力方向的漂移运动，研究了漂移速度的大小与沿外力方向的速度之间的关系，并研究了漂移速度随颗粒位置和颗粒-腔体尺寸比的变化关系。本文还观察和分析了立方体中由颗粒运动引起的涡流，发现了涡旋数量转变的临界位置与颗粒-立方体半边长之比近似成线性关系。

在球形腔体限制下，计算了球体、长球和扁球的回转轴平行和垂直于颗粒-球腔连心线时的迁移率。得到了颗粒纵横比越大，径向迁移率越大横向迁移率越小的规律，并探索了颗粒形状各向异性和受限程度对迁移率的影响。研究了颗粒为长球和扁球时，颗粒的迁移率随颗粒回转轴和颗粒-腔体连心线之间角度的变化规律。分析了球腔内归一化漂移速度与颗粒的位置、大小、形状、非球形颗粒方位角的关系。发现球腔内椭球迁移率和漂移速度与椭球方位角均满足正弦函数关系。

本文还研究了非中性悬浮颗粒在球腔内旋转流中受外力作用的运动，以及球腔限域效应对颗粒运动驻点的影响。分析了外力、由旋转流引起且作用在颗粒上的离心力或向心力以及颗粒-壁面水动力相互作用力的共同作用对颗粒运动模式的影响。长球和扁球在向心力和离心力作用下会受到力矩作用，研究了此力矩对长球和扁球运动状态（稳态或亚稳态）的影响。

Particulate transport in confined low-Reynolds-number fluids has important applications in science and engineering. Recently, particle dynamics under total confinement has received much attention. Studying particle motion within fully enclosed cavities helps preparation and control of particles in micro and nano materials, researching of nanoparticle catalysts in chemical reactions, reveal physical mechanisms involved in intracellular activities and drug transport processes, which has important roles in areas such as drug transport, biomaterials analyzation in the lab-on-a-chip, microdroplets, and microcapsules. Particle-wall hydrodynamic interaction mediated by the low-Reynolds-number fluid in the cavity can lead to complex particle motion, and the mechanism of particle motion confined by the three-dimensional cavity is poorly understood. To explore the effect of confinement and particle-wall hydrodynamic interaction on the particle motion, in this paper, we used numerical simulations to investigate the single-particle dynamics within closed cavities.

Specifically, dynamics of a single particle suspended in a low-Reynolds-number fluid under cubic and spherical confinement was studied numerically. Under the cubic confinement, the mobility of spherical particles at different locations within the cavity along the x-, y- and z-directions were calculated. And the distribution pattern of mobility within the cube was obtained. It was found that the mobility in the entire cubic cavity can be determined by the smallest set of unit tetrahedra. The particle can exhibit drift motion perpendicular to the direction of the external force. The relationship between the magnitude of the drift velocity and the velocity along the direction of the external force was studied, as well as the variation of the drift velocity with particle position and particle-to-cavity size ratio. Fluid vortices caused by particle motion in the cavity are observed and analyzed. The critical position of the vortex number transition was found to be approximately linearly related to the ratio of particle-cavity sizes ratio.

 Similar to the cubic situation, under spherical confinement, mobilities of a sphere, a prolate spheroid, and an oblate spheroid parallel and transverse to particle-cavity line of center were calculated. The larger the aspect ratio of the particles, the larger the radial mobility and the smaller the lateral mobility was obtained, and the relationship between the effect of particle anisotropy on mobility and the degree of cavity closure to the particles was investigated. The variation of the particle mobility with the angle between the particle rotation axis and the particle-cavity centreline was examined when the particles were prolate and oblate. The normalised drift velocity in spherical cavity was found to be affected by the position, size, shape and orientation of the non-spherical particles within the cavity. It was also found that both mobilities and the drift velocity of the ellipsoid in the cavity follow sinusoidal relationship with the orientation angle of the ellipsoid.

 The motion of a non-neutrally buoyant particle under external forces in a rotating flow inside the spherical cavity were also studied. The effect of confinement of the spherical cavity on the stagnation point of particle motion was investigated. The combined effects of external forces, centrifugal or centripetal forces acting on the particles caused by rotation, and particle-wall hydrodynamic interactions lead to complex patterns of particle motion. The prolate and oblate are subjected to a rotation-induced torque under centripetal or centrifugal forces respectively, and the influence of the direction of this torque to stable or metastable state of prolate and oblate spheroids was investigated.