Publications

2024

1. Orientation of inertialess spheroidal particles in turbulent channel flow with spanwise rotation

   Dongming Chen, Zhiwen Cui, Wenjun Yuan^*, Lihao Zhao, and Helge I. Andersson

   Journal of Fluid Mechanics, Nov 2024

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   The orientation dynamics of inertialess prolate and oblate spheroidal particles in a directly simulated spanwise-rotating turbulent channel flow has been investigated by means of an Eulerian–Lagrangian point-particle approach. The channel rotation and the particle shape were parameterized using a rotation number Ro and the aspect ratio λ, respectively. Eleven particle shapes 0.05 ≤ λ ≤ 20 and four rotation rates 0 ≤ Ro ≤ 10 have been examined. The spheroidal particles retained their almost isotropic orientation in the core region of the channel, despite the significant mean shear rate set up by the Coriolis force. Irrespective of channel rotation rate Ro, rod-like spheroids tend to align in the streamwise direction, while disk-like particles are oriented in the wall-normal direction. These trends were accentuated with increasing departure from sphericity λ = 1. The changeover from the isotropic orientation mode in the centre to the highly anisotropic near-wall orientation mode commenced further away from the suction-side wall with increasing Ro, whereas the particle orientations on the pressure side of the rotating channel remained essentially unaffected by Ro. We observed that the alignments of the fluid rotation vector with the Lagrangian stretching direction were similarly unaffected by the imposed system rotation, except that the de-alignment set in deeper into the core at high Ro. This contrasts with the well-known substantial impact of system rotation on the velocity and vorticity fields. Similarly, slender rods and flatter disks were aligned with the Lagrangian stretching and compression directions, respectively, for all Ro considered, except in the vicinity of the walls. The typical near-wall de-alignment extended considerably further away from the suction-side wall at high Ro. We conjecture that this phenomenon reflects a change in the relative importance of mean shear and small-scale turbulence caused by the Coriolis force. Preferential particle alignment with Lagrangian stretching and compression directions are known from isotropic and anisotropic turbulence in inertial reference systems. The present results demonstrate the validity of this principle also in a non-inertial system.

2. Temperature statistics of settling particles in homogeneous isotropic turbulence

   Shuojin Li, Zhiwen Cui, Chunxiao Xu, and Lihao Zhao^*

   International Journal of Heat and Mass Transfer, Aug 2024

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   Heat transfer of settling particles in homogeneous isotropic turbulence is investigated in one-way coupled Eulerian–Lagrangian direct numerical simulations. In the absence of gravity, our observations highlight that there was a correlation between particles concentration and temperature fronts, which are characterized by high-temperature gradients. The particle clustering is mainly influenced by the preferential concentration and the non-local effect, the latter being the memory of their interaction with the flow along their trajectories. Nevertheless, gravity significantly affects the clustering of particles, which further influence the heat transfer of particles with the fluid. We find that the heat transfer of particles is intricately related to particle dynamic inertia and thermal inertia, which can be quantified by the particle Stokes number St and particle thermal Stokes number Stθ, respectively. In this study, we observe that the variance of particle temperature rate of change is independent of Stθ at small thermal inertia but inversely proportional to Stθ2 for large thermal inertia. In the presence of gravity, the variance converges to Stθ−1 for particles with negligible thermal inertia. Our findings reveal that the second-order structure function of the particle temperature, indicating the enhancement of Lagrangian scalar intermittency, adheres to a power-law behavior with limited thermal inertial particles in the dissipation region, denoted as r2. However, as Stθ increases, the power law of the structure function of the particle temperature is disrupted leading to ‘thermal caustics’. The present findings of the heat transfer behavior of settling particles advance the understanding of gravity effect, and are valuable for the modeling of heat transfer in particle-laden turbulent flows.

3. Alignment of inertialess spheroidal particles in flow-structure-dominated regions of turbulent channel flow: shape effect

   Zhiwen Cui, and Lihao Zhao^*

   Acta Mechanica Sinica, Jun 2024

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   The alignment of elongated fibers and thin disks is known to be significantly influenced by the presence of fluid coherent structures in near-wall turbulence (Cui et al. 2021). However, this earlier study is confined to the spheroids with infinitely large or small aspect ratio, and the shape effect of finite aspect ratio on the alignment is not considered. The current study investigates the shape-dependent alignment of inertialess spheroids in structure-dominated regions of channel flow. With utilizing an ensemble-averaged approach for identifying the structure-dominated regions, we analyze the eigensystem of the linear term matrix in the Jeffery equation, which is governed by both particle shape and local fluid velocity gradients. In contrast to earlier conventional analysis based on local vorticity and strain rate, our findings demonstrate that the eigensystem of the Jeffery equation offers a convenient, effective, and universal framework for predicting the alignment behavior of inertialess spheroids in turbulent flows. By leveraging the eigensystem of the Jeffery equation, we uncover a diverse effect of fluid coherent structures on spheroid alignment with different particle shapes. Furthermore, we provide explanations for both shape-independent alignments observed in vortical-core regions and shape-dependent alignments around near-wall streamwise vortices.

4. Clustering of settling microswimmers in turbulence

   Jingran Qiu, Zhiwen Cui, Eric Climent, and Lihao Zhao^*

   Nonlinear Processes in Geophysics, May 2024

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   Clustering of plankton plays a vital role in several biological activities, including feeding, predation, and mating. Gyrotaxis is one of the mechanisms that induces clustering. A recent study (Candelier et al., 2022) reported a fluid inertial torque acting on a spherical microswimmer, which has the same effect as a gyrotactic torque. In this study, we model plankton cells as microswimmers that are subject to gravitational sedimentation as well as a fluid inertial torque. We use direct numerical simulations to obtain the trajectories of swimmers in homogeneous isotropic turbulence. We also investigate swimmers’ clustering using Voronoï analysis. Our findings indicate that fluid inertial torque leads to notable clustering, with its intensity depending on the swimming and settling speeds of swimmers. Using Voronoï analysis, we demonstrate that swimmers preferentially sample downwelling regions where clustering is more prevalent.

5. Effect of slip-induced fluid inertial torque on the angular dynamics of spheroids in a linear shear flow

   Zhiwen Cui, Huancong Liu, Jingran Qiu, and Lihao Zhao^*

   Physics of Fluids, Mar 2024

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   The angular dynamics of tiny spheroidal particles in shear flows have been widely investigated, but most of the studies mainly focus on the effect of strong shear, while the combined effect of both shear and slip velocity at the center of the particle has been less considered. Actually, the fluid inertial torque induced by the slip velocity between particle and fluid plays a significant role in spheroid angular dynamics. However, it is difficult to investigate these dynamics theoretically until the analytical expression of the fluid inertial torque at a small Reynolds number was derived by Dabade et al. [J. Fluid Mech. 778, 133–188 (2015)]. In this study, the effect of the fluid inertial torque on the particle rotations is considered in a linear shear flow with a small streamwise slip velocity at the center of the particle. We find that as the fluid inertial torque dominates, the prolate spheroids tend to logroll while oblate ones have a tendency to tumble or align to a direction with a relative angle to the streamwise direction. These results are opposite to the earlier results in the absence of the fluid inertial torque. Different ultimate rotation modes of spheroids are dependent on the relative importance between the fluid inertial torque and the particle inertia, as well as the initial orientations. This reflects a non-trivial effect of fluid inertial torque on the angular dynamics of inertial spheroidal particles.

2023

1. Effect of fluid inertial torque on the rotational and orientational dynamics of tiny spheroidal particles in turbulent channel flow

   Zhiwen Cui, Jingran Qiu, Xinyu Jiang, and Lihao Zhao^*

   Journal of Fluid Mechanics, Dec 2023

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   Rotation and orientation of non-spherical particles in a fluid flow depend on the hydrodynamic torque they experience. However, little is known about the effect of the fluid inertial torque on the dynamics of tiny inertial spheroids in turbulent channel flows, as only Jeffery torque has been considered in previous studies by point-particle direct numerical simulations. In this study, we investigate the rotation and orientation of tiny spheroids with both fluid inertial torque and Jeffery torque in a turbulent channel flow. By comparing with the case in the absence of fluid inertial torque, we find that the rotational and orientational dynamics of spheroids is significantly affected by the fluid inertial torque when the Stokes number, which is non-dimensionalized by fluid viscous time scale, is larger than the critical value Stc≈2, indicating that the fluid inertial torque is non-negligible for most particle cases considered in earlier studies. In contrast to the earlier findings considering only Jeffery torque (Challabotla et al., J. Fluid Mech., vol. 776, 2015, p. R2), we find that prolate (oblate) spheroids with a large Stokes number tend to tumble (spin) in the streamwise–wall-normal plane in a thinner region near the wall due to the presence of the fluid inertial torque. Approaching the channel centre, the flow shear gradually vanishes, but the velocity difference between local fluid and particles is still pronounced and increasing as particle inertia grows. As a result, in the core region, fluid inertial torque is dominant and drives the particles to align with its broad side normal to the streamwise direction rather than a random orientation observed in earlier studies without fluid inertial torque. Meanwhile, the presence of fluid inertial torque enhances the tumbling rates of spheroids in the core region. In addition, the effect of fluid inertial force on the dynamics of spheroids is also examined in this study, but the results indicate the effect of fluid inertial force is weak. Our findings imply the importance of fluid inertial torque in modelling the dynamics of inertial non-spherical particles in turbulent channel flows.

2. Bifunctional Activated Carbon Ultrathin Fibers: Combining the Removal of VOCs and PM in One Material

   Haiyang Wang^†, Di Zu^†, Xinyu Jiang^†, Yong Xu, Zhiwen Cui, Peng Du, Zekun Cheng , and 12 more authors

   Advanced Fiber Materials, Aug 2023

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   Volatile organic compounds (VOCs) and particulate matter (PM) are both frequently present in air as contaminants, posing serious health and environmental hazards. The current filtration of VOCs utilizes entirely different materials compared with PM filtration, adding complexity to air cleaning system. Herein, we design a pitch-based activated carbon ultrathin fibers (PACUFs) for bifunctional air purification. The PACUFs, with fiber diameter of ∼1.2 µm and specific surface area of 2341 m2 g−1, provide both high VOCs adsorption capacity (∼706 mg g−1) and excellent efficiency of ∼97% PM0.3 filtration with low pressure drop. In contrast, traditional activated carbon fibers exhibit VOCs adsorption capacity of ∼448 mg g−1 and PM0.3 removal efficiency of only ∼36% at an equal area density of ∼190 g m−2. Theoretical investigations reveal the filtration mechanism of the high-performance bifunctional fibrous PACUFs, considering full advantages of the high surface area, small pore size, and significant micropore volume.

3. Particle dynamics in compressible turbulent vertical channel flows

   Tingting Li, Zhiwen Cui^*, Xianxu Yuan, Ying Zhang, Qiang Zhou, and Lihao Zhao^*

   Physics of Fluids, Aug 2023

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   In this work, we carry out direct numerical simulations of particle suspensions in the compressible turbulent vertical channel (TVC) flows with Mach number Ma = 1.5 and particle Stokes number St = 1–100. The compressibility effect is considered in the particle dynamic model for the first time in the study of compressible particle-laden wall turbulence. We find that in both incompressible and compressible flow, gravity weakens the wall-normal and spanwise fluctuations of particle velocities as the Stokes number increases. However, compared to the incompressible flow case, the compressible effect amplifies the mean velocity, fluctuations of velocity, and slip velocity of particle in the streamwise direction. The wall-normal and spanwise fluctuations of particle velocities are augmented by the compressible effect in the channel core region. Moreover, in the core region, the effect of fluid compressibility on the wall-normal and spanwise fluctuations of particle velocities attenuates as the Stokes number increases, indicating a competition between the compressible effect and the particle inertia effect. We, furthermore, conduct the quadrant analysis of the local fluctuation velocities of fluid at particle positions and observe preferential distributions in the second and the fourth quadrants at y+ = 12.5–13.5. For compressible TVC flows, the pattern of probability distributions is more elongated, and the percentage is slightly higher in the second and fourth quadrants than that of incompressible flows. This observation implies that more particles locate in the ejection and sweep events in compressible flows than that in incompressible flows, which is anticipated to influence the particle wall-normal transport.

2022

1. Shape-dependent regions for inertialess spheroids in turbulent channel flow

   Zhiwen Cui, and Lihao Zhao^*

   Physics of Fluids, Dec 2022

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   The alignment between the inertialess spheroids and the directions of the fluid Lagrangian stretching or compression is sensitive to the particles shape near the wall but not near the center of the channel [Cui et al. “Alignment statistics of rods with the Lagrangian stretching direction in a channel flow,” J. Fluid Mech. 901, A16 (2020)]. This observation is further investigated in the current study to uncover the mechanism of particle alignment behavior in different regions of channel flows at Reτ≈180 and 1000. Meanwhile, by using the probability distributions of the sign of the discriminant of the linear term in the Jeffery equation, we find that the turbulent channel flow can be distinctly divided into strong and weak shape-dependent regions. In the weak shape-dependent region, the slender (flat) particles have extraordinarily similar alignments with the directions of fluid Lagrangian stretching (compression). However, in the strong shape-dependent region, the alignments of these inertialess particles are sensitive to the particles shape, especially with the particle positions approaching the wall. The ranges of these shape-dependent regions rely on the Reynolds number, but the probability distributions of the sign of the discriminant of the linear term in the Jeffery equation are a useful tool to distinguish these shape-dependent regions in the wall turbulence regardless of the Reynolds number.

2. Gyrotactic mechanism induced by fluid inertial torque for settling elongated microswimmers

   Jingran Qiu, Zhiwen Cui, Eric Climent, and Lihao Zhao^*

   Physical Review Research, May 2022

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   Marine plankton are usually modeled as settling elongated microswimmers. We consider the torque induced by fluid inertia on such swimmers, and we discover that they spontaneously swim in the direction opposite to gravity. We analyze the equilibrium orientation of swimmers in quiescent fluid and the mean orientation in turbulent flows using direct numerical simulations. Similar to well-known gyrotaxis mechanisms, the effect of fluid inertial torque can be quantified by an effective reorientation timescale. We show that the orientation of swimmers strongly depends on the reorientation timescale, and swimmers exhibit strong preferential alignment in an upward direction when the timescale is of the same order of the Kolmogorov timescale. Our findings suggest that the fluid inertial torque is a different mechanism of gyrotaxis that stabilizes the upward orientation of microswimmers such as plankton.

3. Numerical study of non-spherical particle-laden flows 非球形颗粒两相流的数值模拟研究进展

   Zhiwen Cui 崔智文,  Ze Wang 王泽,  Xinyu Jiang 蒋新宇, and  Lihao Zhao 赵立豪^*

   Advances in Mechanics 力学进展, May 2022

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   Non-spherical particle-laden flows are commonly seen and important in nature and industrial processes. The particle’s rotational and orientational behaviors could affect the forces and torques acting on the particle from ambient fluid flow. To accurately capture the motion of non-spherical particles, especially for angular particle dynamics, most numerical studies of non-spherical particleladen flows are carried out in the Euler-Lagrange frame. There are two most popular numerical approaches: the point-particle method and the particle-resolved method. This paper comprehensively and systematically summarizes these methods and significant recent findings about non-spherical particles in simple and turbulent flows. The mechanism of particle orientation and rotation by suspended nonspherical particles, as well as the modulation effect of particles on turbulent drag reduction, are discussed. Furthermore, the key and unsolved problems of non-spherical particle-laden flows for future study are proposed at the end of the paper.

4. On the existence and formation of multi-scale particle streaks in turbulent channel flows

   Yucheng Jie, Zhiwen Cui, Chunxiao Xu, and Lihao Zhao^*

   Journal of Fluid Mechanics, Mar 2022

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   Direct numerical simulations of particle-laden turbulent channel flows at friction Reynolds number ReτReτRe_}tau from 600 to 2000 have been performed to examine the near-wall particle streaks. Different from the well-observed small-scale particle streaks in near-wall turbulence of low ReτReτRe_}tau, the present results show large-scale particle streaks through the computational domain formed for relatively high-inertia particles at high Reτ. Transferred by large-scale sweep and ejection events (Q-), these high-inertia particles preferentially accumulate in near-wall regions beneath the large-scale low-speed flow streaks observed in the logarithmic region. The corresponding Stokes numbers are associated with the lifetime of large-scale Q- structures, which increases as the Reynolds number grows. The small-scale particle streaks with a typical Stokes number Stν≈30 are mainly driven by the Q^- structures in the buffer layer, whose lifetime is approximately 303030 in viscous time unit. Therefore, we propose a new structure-based Stokes number normalized by the lifetime of Q- structures of different scales. The relevant flow scales that control the formation of the large-scale particle streaks are parameterized by the structure-based Stokes number. The small-scale (large-scale) particle streaks are most prominent when the buffer-layer (large-scale) structure-based Stokes number approaches unity. The present findings reveal that formation of near-wall particle streaks is governed by the Q- structures of different scales, and the particles with different inertia respond efficiently to the Q- structures of corresponding scales with respect to the particle translational motion.

5. High-throughput production of kilogram-scale nanofibers by Kármán vortex solution blow spinning

   Ziwei Li^†, Zhiwen Cui^†, Lihao Zhao^†, Naveed Hussain, Yanzhen Zhao, Cheng Yang, Xinyu Jiang , and 5 more authors

   Science Advances, Mar 2022

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   The interaction between gas flow and liquid flow, governed by fluid dynamic principles, is of substantial importance in both fundamental science and practical applications. For instance, a precisely designed gas shearing on liquid solution may lead to efficacious production of advanced nanomaterials. Here, we devised a needleless Kármán vortex solution blow spinning system that uses a roll-to-roll nylon thread to deliver spinning solution, coupled with vertically blowing airflow to draw high-quality nanofibers with large throughput. A wide variety of nanofibers including polymers, carbon, ceramics, and composites with tunable diameters were fabricated at ultrahigh rates. The system can be further upgraded from single thread to multiple parallel threads and to the meshes, boosting the production of nanofibers to kilogram scale without compromising their quality.

2021

1. Alignment of slender fibers and thin disks induced by coherent structures of wall turbulence

   Zhiwen Cui, Wei-Xi Huang, Chun-Xiao Xu, Helge I. Andersson, and Lihao Zhao^*

   International Journal of Multiphase Flow, Dec 2021

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   The angular dynamics of small rigid fibers and disks in turbulent channel flow has been investigated numerically, focusing on interactions between particles and near-wall coherent vortices. Three distinctly different alignment patterns of fibers and disks around ensemble-averaged vortices were identified. From the wall to the channel center we observed a shear-dominant, a structure-dominant, and an isotropic region, each with its unique alignment pattern. These regions are different from those based on the conventional Reynolds-averaging view. The structure-dominant region, for instance, extends from about 3 to 60 wall units from the channel wall. Unlike the prevailing view that preferential alignment of fibers and disks are more common in the viscous sublayer than in the buffer layer, where the turbulence intensity reaches its maximum, the conditional ensemble-averaged approach revealed that fibers and disks align preferentially in the structure-dominant region. The particles moreover align differently in sweep and ejection events. The physical alignment mechanism we proposed may also be carried over to polymer- and fiber-induced drag reduction in wall-turbulence.

2. A method for long-time integration of Lyapunov exponent and vectors along fluid particle trajectories

   Zhiwen Cui, and Lihao Zhao^*

   Physics of Fluids, Dec 2021

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   Finite-time Lyapunov exponents (FTLEs) and Lyapunov vectors (LVs) are powerful tools to illustrate Lagrangian coherent structures (LCSs) in experiments and numerical simulations of fluid flows. To obtain the FTLEs and LVs with the flow simulation simultaneously, we computed the eigenvectors and eigenvalues of the left Cauchy–Green tensor along the trajectories of fluid particles separately instead of computing deformation gradient tensor directly. The method proposed in the present study not only avoids solving the eigenvalue problem of the singular matrix at each time step but also guarantees a stable simulation for a long time. The method is applied in the computation of FTLEs and LVs in two-/three-dimensional (2D/3D) compressible/incompressible cases. In 2D cases, we found that LCSs are folded as fine filaments induced by vortices, while LCSs are sheet-like structures among the vortices for 3D cases. Meanwhile, the directions of stretching and compression of LVs are tangent and normal to the FTLE ridges (2D)/iso-surfaces (3D), respectively.

3. Reviews on alignment of non-spherical particles in wall-bounded turbulence 近壁湍流中微小非球形颗粒取向行为研究综述

   Zhiwen Cui 崔智文, and  Lihao Zhao 赵立豪^*

   Acta Aerodynamica Sinica 空气动力学学报, Dec 2021

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   The article reviews recent progress on the orientation dynamics of non-spherical particles in wallbounded turbulence, focusing on the numerical methods and physical mechanisms. Due to the presence of solid wall, there is a strong mean shear and near-wall turbulence structures, which lead to anisotropy of wall-bounded turbulence. In previous studies, the prolate particles are found to preferentially align in the streamwise direction while the oblate ones preferentially orient to the wall-normal direction in the vicinity of the wall. The preferential alignments of particles are enhanced with increasing asphericity of particles. In addition, the orientations of the particles have a strong correlation with the directions of Lagrangian fluid stretching and compression. Nevertheless, the correlation between the particle orientation and the Lagrangian stretching and compression near the wall is weaker than that in the core region of the channel or in homogeneous isotropic turbulence. To better understand this observation, prolate particles are investigated to analyze their probability distribution relative to the Lagrangian coordinate frame, which is defined by the three principle axes of the left Cauchy-Green tensor. A two-dimensional model for predicting the particle rotation period was developed based on the ratio of mean shear to the fluctuations of fluid velocity gradient tensor according to the characteristics of wall-bounded turbulence. The model revealed that this ratio plays an important role in the alignments of non-spherical particles relative to the directions of Lagrangian stretching and compression in the shear turbulence.

2020

1. Alignment statistics of rods with the Lagrangian stretching direction in a channel flow

   Z. Cui^†, A. Dubey^†, L. Zhao^*, and B. Mehlig

   Journal of Fluid Mechanics, Oct 2020

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   In homogeneous isotropic turbulence, slender rods are known to align with the Lagrangian stretching direction. However, how the degree of alignment depends on the aspect ratio of the rod is not understood. Moreover, particle-laden flows are often anisotropic and inhomogeneous. Therefore we study the alignment of rods with the Lagrangian stretching direction in a channel flow, which is approximately homogeneous and isotropic near the centre but inhomogeneous and anisotropic near the walls. Our main question is how the distribution of relative angles between a rod and the Lagrangian stretching direction depends on the aspect ratio of the rod and upon the distance of the rod from the channel wall. We find that this distribution exhibits two regimes: a plateau at small angles corresponding to random uncorrelated motion, and power-law tails due to large excursions. We find that slender rods near the channel centre align better with the Lagrangian stretching direction compared with those near the channel wall. These observations are explained in terms of simple statistical models based on Jeffery’s equation, qualitatively near the channel centre and quantitatively near the channel wall. Lastly we discuss the consequences of our results for the distribution of relative angles between the orientations of nearby rods (Zhao et al., Phys. Rev. Fluids, vol. 4, 2019, 054602).

2019

1. On rotational dynamics of a finite-sized ellipsoidal particle in shear flows

   Ru-Yang Li, Zhi-Wen Cui, Wei-Xi Huang, Li-Hao Zhao^*, and Chun-Xiao Xu

   Acta Mechanica, Oct 2019

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   The rotational dynamics of finite-sized ellipsoidal particles with different aspect ratios around their fixed mass centers in shear flows have been investigated by direct numerical simulations. Particles are fully resolved by a revised immersed boundary projection method, and their rotational motion is governed by Euler’s equation which is calculated in the particle-fixed frame. The particle Reynolds number varies from 10 to 300 based on the longest axis of the particle. The steady states of the prolate and oblate spheroids in uniform flow, linear shear flow with the moving top wall and fixed bottom wall, and wall-bounded turbulence are analyzed. It is observed that the longest particle axes are perpendicular to or have a large angle with the local flow direction in the flow-gradient plane, which leads to a large drag force. A linear stability analysis on the rotational motion of a finite-sized particle in uniform flow is also carried out for supporting this finding. In the linear shear flow, the influence of fluid inertia and fluid shear on the inclined angle is examined in detail. In wall-bounded turbulence, it is found that the particles in the buffer region and the outside of the boundary layer behave similarly in the mean sense as in the linear shear flow and uniform flow, respectively. The present results with intermediate to large particle Reynolds numbers can be regarded as a starting point to understand the dynamics of heavy finite-sized particles in viscous flows.

2. Stability analysis of rotational dynamics of ellipsoids in simple shear flow

   Zhiwen Cui, Lihao Zhao^*, Wei-Xi Huang, and Chun-Xiao Xu

   Physics of Fluids, Feb 2019

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   The rotation of anisotropic particles in fluid flow is essential for particle transport and collisions of nearby particles. The earlier studies indicate that both axis-symmetric spheroids and tri-axial ellipsoids in a simple shear flow tend to rotate about their shortest axes in the absence of fluid inertia. However, tri-axial ellipsoids display more complicated behavior with variations of the Stokes number and aspect ratio. In this paper, we theoretically studied the rotation stability of both axis-symmetric spheroids and tri-axial ellipsoids in a simple shear flow with negligible fluid inertia by the Floquet analysis. In the case of axis-symmetric spheroids, we find that tumbling motion of a prolate spheroid is neutrally stable, but logrolling motion is unstable, while logrolling of an oblate spheroid is stable, but tumbling is unstable. A tri-axial ellipsoid rotating about the shortest axis is found to be stable at large Stokes numbers (St > St0.5, where St0.5 is denoted as a critical Stokes number) but becoming unstable with small particle inertia (St < St0.5) for a tri-axial elongated particle. Moreover, stable intermediate-axial rotation is observed for the ellipsoids with small inertia. Meanwhile, small shape variations of slightly tri-axial ellipsoids could result in different stability states. The slightly tri-axial elongated ellipsoids easily reach a chaotic rotation state, while the rotation of slightly tri-axial flat ellipsoids is relatively more stable.