Modeling a spheroidal squirmer through a complex fluid

We simulate a spheroidal swimmer through a complex fluid, modeled by the Giesekus constitutive equation incorporating fluid inertia. We develop a spheroidal swimmer model and exert it in a direct-forcing fictitious domain method framework. This model extends the conventional spherical “squirmer,” representing a microswimmer generating self-propulsion through tangential surface waves at its boundaries. We vary the swimmer's aspect ratio (AR) and Weissenberg number (Wi; the ratio of fluid elastic force to viscous force), respectively, in the range of $1.5\le \mathrm{AR}\le 8$ and $0.5\le \mathrm{Wi}\le 10$. Our results show that, an inertial spheroidal puller with a small $\left|\beta \right|$ (a swimming intensity parameter) swims faster than the counterpart subjected to the Stokes flow regime—a departure from the observed pattern in spherical pullers. Within the Giesekus fluid medium, an augmented mobility factor α correlates with an increased squirmer velocity, while a larger AR contributes significantly to the speed enhancement of a neutral squirmer in the presence of fluid inertia. Meanwhile, we explore the squirmer's energy expenditure and hydrodynamic efficiency, finding that a slenderer, inertial squirmer with a vigorous swimming intensity expends more energy, contrasting with the reduced energy expenditure associated with a smaller intensity. Notably, a larger AR positively correlates with squirmer efficiency, displaying an advantageous relationship with swimming speed.