Simulating the motion of a self-propelled dumbbell in fluids

The fluid mechanics of micro swimmers at low Reynolds number has attracted considerable attention due to its potential of biomedical applications. For a dumbbell formed by two balls of different sizes, the effects of asymmetric shape and inertia make it move in Newtonian fluids when rotating about its axis of symmetry at finite Reynolds number. This dumbbell moves in the direction of its axis of symmetry with the larger ball ahead. But, for such rotating asymmetric dumbbell in an Oldroyd-B fluid at the Stokes regime, numerical and experimental works showed that it moves with the small ball ahead. In this article, we first discuss the generalization of Lagrange multiplier based fictitious domain (DLM/FD) methods for simulating the motion of a neutrally buoyant asymmetric dumbbell in fluids. Then we have studied its propulsion in Newtonian fluids (resp., Oldroyd-B viscoelastic fluids) in different configurations computationally at low Reynolds number regime (resp., Stokes regime) and some quasi-optimal configurations are obtained. Also, for such a dumbbell, the competition between the inertia and elastic forces on its motion in Oldroyd-B fluids is studied at low Reynolds numbers.