# A Review on the Some Issues of Multiphase Flow with Self-Driven Particles
## 1 Introduction  
Previous investigations on multiphase flows were mainly focused on the passive particles which are just driven by fluid and external force. However, in the multiphase flow with self-driven particles, the particles are mainly driven by internal force together with some influence of fluid and external force. Meanwhile, self-driven particles inject energy into fluid so as to change the motion of the fluid and then change its own motion in turn. Multiphase flows with self-driven particles exist in natural and engineering applications. In nature, cells (e.g., Spermatoza, Leucocyte), bacteria (e.g., Coccus, bacillus, Spirillum, Vibrio), fungus (e.g., Ascomycota), algae (e.g., Diatom, Dinoflagellates), protozoa (e.g., Entamoeba histolytica, Paramecium), movement proteins, etc., are all self-driven particles (as shown in Figure 1). Situations including when spermatozoa pass through the mucus to fuse with an egg [1], when Escherichia coli moves to high nutrient areas inside the human body, etc., all belong to the multiphase flow with self-driven particles [2]. In practice, synthesized self-driven particles contain artificial cell tissues, phosphorus-containing colloidal particles, soft field-responsive gel, catalytic particles for biodegradation, biomarkers and contrast media, miniature swimming devices and robots, etc. (as shown in Figure 2). In the presence of external fields, artificial particles become self-driven  
Figure 1: Self-driven particles in nature. (**a**) Spermatoza and _E. coli_; (**b**) Spirillum; (**c**) Dinoflagellates. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([[https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/)]([https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/))). and obtain the abilities of targeted drug delivery, precise surgery, self-assembly, environmental modification, and water treatment; such situations also belong to the multiphase flow with self-driven particles. When compared with multiphase flow with passive particles, the multiphase flow with self-driven particles involves more complex properties [3]. Firstly, the system is in a non-equilibrium state. Brownian motion of self-driven particles is caused by the interaction between random collision of fluid molecules and particles, which cannot satisfy the fluctuation-dissipation theorem that relies on the assumption that the response of a system in equilibrium to a small applied force is the same as its response to a spontaneous fluctuation, while the system consisting of fluid molecules and particles does not satisfy this assumption because of the interaction between small applied force and self-driving force. Secondly, there is a great diversity of self-driving modes which include gravity, torque, flagella driving, cilia shaking, surface deformation, chemical reaction, bubble release, electromagnetic light energy and actin aggregation and so on. Different driving modes lead to different stresses and patterns of flow, which will affect the particle motion in turn. Thirdly, there exist some abnormal characteristics such as turbulence with small Reynolds number [4], abnormal shear viscosity, weak shear hydrodynamic diffusion, biological convection, cluster structure, non-equilibrium phase transition between disordered and ordered phases, orientational ordering of quasi-liquid crystal and so on [5]. Moreover, the translational and rotational velocities of particles will deviate from the Maxwell distribution [6]. The study of multiphase flow with self-driven particles plays an important role in exploring the laws of nature and practical applications. Firstly, research on the moving mode and efficiency of a natural organism as well as the effect of environment on its kinematic characteristics can deepen the understanding of the tropism and rationality of natural selection in organisms.