# A Review on the Some Issues of Multiphase Flow with Self-Driven Particles
## 4 Influence of Rheological Properties on the Motion of Squirmers  
The fluid in which the microorganism lives frequently has non-Newtonian properties, e.g., Escherichia coli swims in the gastric juice, bacterium passes through the viscous-elastic barriers which are used to protect epithelia. The non-Newtonian properties of fluid contain the dependence of viscosity on shear strain rate, viscoelasticity and yield stress, etc. [37]. These characteristics make the motion of self-driven particles in non-Newtonian fluid different from that in Newtonian fluid. For example, the viscoelasticity will change the swimming stoke of particles, and elastic stress may affect the swimming velocities of particles. The existence of high molecular weight and macromolecules will increase the viscosity and further reduce the velocities of particles [38], while the interaction between driving property of self-driven particles and rheology of fluid may improve the velocities  
Figure 7: (**a**) Escherichia coli with honeycomb structure; (**b**) Breivbacterium with rafted structure. of particles [39; 40; 41]. Understanding the influence of rheological properties on the motion of self-driven particles is helpful to manipulate drugs to wipe out germs and control infection. When squirmers swim in a fluid with viscosity varying with shear rate, the velocity and hydrodynamic efficiency, which is defined as the value of the useful to the total work, are related to the change of viscosity and driving mode caused by fluid shear. In the shear-thinning fluid, the non-local effect caused by the change of flow is more important than that of local viscosity reduction on its swimming [42]. The change of squirmer velocity depends on its starting velocity [43]. Compared with swimming in Newtonian fluid, although squirmers swim slowly, they swim more efficiently [44]. The power consumption of squirmer swimming decreases with the increase in Reynolds number, and the hydrodynamic efficiency is the same at a small Reynolds number for pullers and pushers [45]. The squirmers near the wall collide periodically with the wall with a constant period [46] and will change its trajectory due to rotation in parallel and opposite motion collisions [47]. Another property of non-Newtonian fluid is viscoelasticity. In the viscoelastic fluid, self-driven particles can not only paddle, but also move by the elasticity of fluid [48]. The change of squirmer motion caused by viscoelasticity is related to the driving mode. Whether the pullers and pushers move towards the wall depends on their initial position, while the neutral squirmer does not depend on the initial position [49]. The residence time of a squirmer in the near-wall region depends on the fluid elasticity and the initial position [50]. The elasticity of the fluid makes it easier for a squirmer to move towards the wall [51]. The degree of drift caused by viscoelasticity depends on the Deborah number, and ratio of driving velocity to flow velocity and driving mode [52]. The velocity of a squirmer decreases with the addition of Brinkman medium, but the hydrodynamic efficiency increases [53]. Viscoelasticity of fluid strengthens the rotational diffusion [54]. Squirmers move faster in a third-order viscoelastic fluid than in a Giesekus fluid [55]. Viscoelasticity of fluid slows down and speeds up the pullers and pushers, respectively, but it has no effect on neutral squirmers [56]. Squirmers consume more energy in Newtonian fluid and has higher hydrodynamic efficiency in viscoelastic fluid. For squirmers swimming in upper-convected Maxwell/Oldroyd-B fluids, the elastic stress becomes singular at a critical Weissenberg number [57]. However, the singularity is removed when the exponential Phan-Thien and Tanner model is utilized [58]. The above research was based on the Stokes flow with zero or minimum Reynolds number, i.e., the inertia effect is neglected. In fact, many flows are beyond the range of the Stokes flow [59].