2D materials are promising high-performance sheet-like nanomaterials with unique properties. Liquid-phase exfoliation (LPE) is a scalable and cost-effective process to produce 2D materials on large scales. However, the product of LPE is highly polydispersed. An efficient procedure to fractionate 2D materials is the liquid cascade centrifugation (LCC), which is currently done by trial and error. Moreover, 2D materials are easily deformed when processed in liquids because of their low bending rigidities. To exploit the unique properties of 2D materials, it is essential to control the sizes and morphologies of the nanosheets.
To provide insights for the rational design of the LCC procedure and the understanding of deformation of nanosheets in the shear flow, this thesis tackles two relevant fluid dynamics problems: (i) sedimentation of polydisperse suspensions, and (ii) buckling of flexible particles in the shear flow, both in the Stokes flow regime. The approaches adopted in this thesis are mainly numerical, including Stokesian dynamics and boundary integral method, which are efficient methods to simulate particle dynamics in Stokes flow. Moreover, collaborations with experimentalists have been established during this thesis. The code developed has been used to answer practical questions.
Overall, this thesis contributes to the understanding of particle dynamics in Stokes flow, including the settling of polydisperse suspensions and buckling of flexible sheets in the shear flow, utilizing the theories and numerical approaches of microhydrodynamics. Results of this thesis can be used to optimize the procedures of liquid processing of 2D nanomaterials and in other relevant applications.

Settling velocity statistics for dilute, non-Brownian homogeneous suspensions of polydisperse spheres having a log-normal size distribution are generated from Stokesian dynamics simulations, as a function of the total volume fraction and normalised width of the particle size distribution. Several hundred instantaneous configurations are averaged to obtain reliable statistics. The paper reports data for the average and fluctuating settling velocity of each particle class in a suspension that is widely polydisperse - previous work was limited to only two or three classes, and the average settling velocity of each particle class was in most cases not reported - and provides an assessment of the accuracy of the analytical models proposed by Batchelor, Richardson & Zaki, Davis & Gecol and Masliyah-Lockett-Bassoon in predicting the simulation data. A limited comparison with dynamic simulations in which the particle microstructure is allowed to evolve in time is also included.

Buckling induced by viscous flow changes the shape of sheetlike nanomaterial particles suspended in liquids. This instability at the particle scale affects collective behavior of suspension flows and has many technological and biological implications. Here, we investigated the effect of viscous hydrodynamic interactions on the morphology of flexible sheets. By analyzing a model experiment using thin sheets suspended in a shear cell, we found that a pair of sheets can bend for a shear rate ten times lower than the buckling threshold defined for a single sheet. This effect is caused by a lateral hydrodynamic force that arises from the disturbance flow field induced by the neighboring sheet. The lateral hydrodynamic force removes the buckling instability but massively enhances the bending deformation. For small separations between sheets, lubrication forces prevail and prevent deformation. Those two opposing effects result in a nonmonotonic relation between distances and shear rate for bending. Our study suggests that the morphology of sheetlike particles in suspensions is not purely a material property but also depends on particle concentration and microstructure.