# A Review on the Some Issues of Multiphase Flow with Self-Driven Particles
## 5 Characteristics of Suspension Flow of Axisymmetric Squirmers  
Natural and synthetic self-driven particles are not limited to spherical shapes. Axisymmetric shape is a typical shape except for sphere, such as protozoa (e.g., Ciliata), biopolymer (e.g., Myoglobin, movement proteins), Bacillus (e.g., Bacillus subtitles, _Escherichia coli_) in nature and some synthetic self-driven particles (as shown in Figure 8).  
The study of the shape effect on the flow with self-driven particles is helpful to deepen the understanding of the natural selection tendency of some organisms and the design of micro artificial swimming devices. The non-isotropic shape of axisymmetric particles  
Figure 8: (**a**) Ciliata; (**b**) Bacillus; (**c**) miniature artificial swimming devices; (**d**) artificial Janus granules.  
leads to more complex motion modes and abundant self-organization phenomena, e.g., the swimming and feeding changes were found to be more significant in oblate spheroids than prolate spheroids [60]. For spherical squirmers, the self-organization phenomenon is caused by the interference and blocking between squirmers, but the self-organization of axisymmetric squirmers is caused by its array formed by the interactions. For example, Bacillus subtilis forms polar clusters [61]; Bacteroides dendritic moves along the narrow, long and high-density zone [62]; Tubulin-dynamin forms vortex arrays [63]; and Escherichia coli forms long range array [64].  
Axisymmetric particles are more prone to self-organization than spherical particles. Moreover, shape-induced phase separation will occur at low Peclet numbers. However, whether the direct contact between particles or the long-range hydrodynamic effect is the main reason for the self-organization of squirmers has been debated. Based on the Langevin dynamics simulation of columnar [65] and filamentous squirmers [66], it was found that the formation of self-organization is dominated by the interactions between squirmers. Moreover, Brownian dynamics' simulation considering long-range hydrodynamic action [67] also captured the self-organization. However, [PERSON] et al. [68] believed that particle shape and long-range hydrodynamic force were the factors to form the self-organization.  
It has been found that suspension flow of axisymmetric squirmers is more prone to turbulence than that of spherical one [5]. It is generally believed that the turbulence emergence of particle suspension is related to the Peclet number. When the Peclet number is large, i.e., convection is stronger than diffusion, turbulence is more likely to appear. However, it was found that there is no turbulence when the Peclet number in the suspension flow of axisymmetric squirmers is as high as 50 [69]. Therefore, there are other factors at work, e.g., the hydrodynamic interactions, rotating dipoles formed by rotating flagella bundle and a counter-rotating body propulsion of squirmers [70], and induced circular motions [71] on the surface. [PERSON] et al. [72] pointed out that axisymmetric squirmers had a stronger rotation effect than spherical ones; the coupling of rotation and translation made turbulence appear. If the axisymmetric squirmers are asymmetric along the axis, the order of its orientation would be weakened, which also leads to turbulence [73]. Therefore, the factors leading to turbulence of suspension contain Peclet number, squirmer flexibility, hydrodynamic interactions, effects of strong rotation, anteroposterior asymmetry of squirmers, and self-driving modes. Thus, it is important to explore the correlation between various factors and turbulence.