Inertial squirmers

EUGENIA S. RÓDRÍGUEZ CACIK; GASTÓN MIÑO; SEBASTIÁN UBAL

Ciudad Autónoma de Buenos Aires

Congreso; III Brazil-Argentine Microfluidics Congress. VI Congreso de Microfluídica Argentina; 2022

Centro Atómico Consituyentes, CNEA. Facultad de Ingeniería, UBA

Liquids naturally include a variety of microorganisms: viruses, bacteria, and protozoa. Some of them are called microswimmers because they can swim in the fluid to reach areas with higher concentration of nutrients, or in response to other physicochemical cues.Lighthill and Blake developed the squirmer model, which can be used to study the dynamics of those swimmers. In this model, the microorganisms are represented as mobile spheres with an imposed tangential velocity on their surface, which allows us to model swimmers with their propulsion mechanisms at the rear of the sphere (called pushers) or in the front of it (pullers). Because of the microscopic size of the biological swimmers, the squirmer model was originally designed for Stokes flow. Nevertheless, in some cases (in larger phoretic particles, for example), the inertial effect must be taken into account.In this work we use the original squirmer model (called type I) and a variant (type II), where the imposed tangential velocity is replaced by a tangential force, which is equivalent to the tangential velocity defined in 1. In both models, we examine the effect of inertia on the velocity of a squirmer swimming in an unbounded fluid, but also in a cylindrical tube with a diameter of the same order as that of the squirmer. We led our study by solving numerically the axisymmetric Navier-Stokes and continuity equations, along with the equations accounting for the conservation of linear momentum of the squirmer. All the equations were solved using a commercial software which implements the Finite Elements Method.When the squirmer is in an unbounded fluid and inertia is negligible, the results show that both models (type I and II) are equivalent. Departure from this behavior is observed when either the squirmer swims in a confined fluid or inertia begins to be more important. For a type I squirmer swimming in an unbounded fluid at a Reynolds number Re>10, the translational velocity increases with increasing Re, for both pushers and pullers. However, if we study a type II inertial squirmer, we observe that pushers (pullers) swim faster (slower) than a squirmer in Stokes regime. For a viscous fluid, increasing the confinement of the squirmer leads to a decrease in the translational velocity compared to an unbounded squirmer. This trend is for both pushers and pullers of types I and II. If we combine the confinement and the effect of inertia, pushers (pullers) move faster (slower) than swimmers in the Stokes regime without confinement.