Continuum Modeling and Numerical Simulation of Active Suspensions

Active suspensions consist of self-propelled particles, called active particles, suspended in a fluid. These particles exert an active stress on the fluid. We present a continuum-based model that uses mixture theory to simulate an active suspension. The active particles are assumed to have a uniform orientation in the direction of motion, which is particularly relevant for suspensions of magnetotactic bacteria, where an external magnetic field can control the orientation of the bacteria. The focus of this work is to propose a continuum mechanical model for the partial stress tensor of the particle phase and the interaction forces between the particle and fluid phases, such as drag and lift. The flow of an active suspension in an annular channel of rectangular cross-section is then solved numerically. A stable secondary flow pattern, consisting of a pair of Dean vortices, is formed in the cross-section of the channel. The effect of Reynolds number, channel curvature, and cross-section aspect ratio on the secondary flow is studied. Key physical quantities, including the distribution of the particle volume fraction and the partial velocities of both phases, are also discussed.