Search for: All records

We investigate aspects of the spherical squirmer model employing both large-scale numerical simulations and asymptotic methods when the squirmer is placed in weakly elastic fluids. The fluids are modelled by differential equations, including the upper-convected Maxwell (UCM)/Oldroyd-B, finite-extensibility nonlinear elastic model with Peterlin approximation (FENE-P) and Giesekus models. The squirmer model we examine is characterized by two dimensionless parameters related to the fluid velocity at the surface of the micro-swimmer: the slip parameter $$\xi $$ and the swirl parameter $$\zeta $$ . We show that, for swimming in UCM/Oldroyd-B fluids, the elastic stress becomes singular at a critical Weissenberg number, Wi , that depends only on $$\xi$$ . This singularity for the UCM/Oldroyd-B models is independent of the domain exterior to the swimmer, or any other forces considered in the momentum balance for the fluid – we believe that this is the first time such a singularity has been explicitly demonstrated. Moreover, we show that the behaviour of the solution at the poles is purely extensional in character and is the primary reason for the singularity in the Oldroyd-B model. When the Giesekus or the FENE-P models are utilized, the singularity is removed. We also investigate the mechanism behind the speed and rotation rate enhancement associated with the addition of swirl in the swimmer's gait. We demonstrate that, for all models, the speed is enhanced by swirl, but the mechanism of enhancement depends intrinsically on the rheological model employed. Special attention is paid to the propulsive role of the pressure and elucidated upon. We also study the region of convergence of the perturbation solutions in terms of Wi . When techniques that accelerate the convergence of series are applied, transformed solutions are derived that are in very good agreement with the results obtained by simulations. Finally, both the analytical and numerical results clearly indicate that the low- Wi region is more important than one would expect and demonstrate all the major phenomena observed when swimming with swirl in a viscoelastic fluid. 

Microorganisms are commonly found swimming in complex biological fluids such as mucus and these fluids respond elastically to deformation. These viscoelastic fluids have been previously shown to affect the swimming kinematics of these microorganisms in non-trivial ways depending on the rheology of the fluid, the particular swimming gait and the structural properties of the immersed body. In this report we put forth a previously unmentioned mechanism by which swimming organisms can experience a speed increase in a viscoelastic fluid. Using numerical simulations and asymptotic theory we find that significant swirling flow around a microscopic swimmer couples with the elasticity of the fluid to generate a marked increase in the swimming speed. We show that the speed enhancement is related to the introduction of mixed flow behind the swimmer and the presence of hoop stresses along its body. Furthermore, this effect persists when varying the fluid rheology and when considering different swimming gaits. This, combined with the generality of the phenomenon (i.e. the coupling of vortical flow with fluid elasticity near a microscopic swimmer), leads us to believe that this method of speed enhancement could be present for a wide range of microorganisms moving through complex fluids. 

Microorganisms often move through viscoelastic environments, as biological fluids frequently have a rich microstructure owing to the presence of large polymeric molecules. Research on the effect of fluid elasticity on the swimming kinematics of these organisms has usually been focused on those that move via cilia or flagellum. Experimentally, Shen (X. N. Shen et al. , Phys. Rev. Lett. , 2011, 106 , 208101) reported that the nematode C. elegans , a model organism used to study undulatory motion, swims more slowly as the Deborah number describing the fluid's elasticity is increased. This phenomenon has not been thoroughly studied via a fully resolved three-dimensional simulation; moreover, the effect of fluid elasticity on the swimming speed of organisms moving via euglenoid movement, such as E. gracilis , is completely unknown. In this study, we discuss the simulation of the arbitrary motion of an undulating or pulsating swimmer that occupies finite volume in three dimensions, with the ability to specify any differential viscoelastic rheological model for the surrounding fluid. To accomplish this task, we use a modified version of the Immersed Finite Element Method presented in a previous paper by Guido and Saadat in 2018 (A. Saadat et al. , Phys. Rev. E , 2018, 98 , 063316). In particular, this version allows for the simulation of deformable swimmers such that they evolve through an arbitrary set of specified shapes via a conformation-driven force. From our analysis, we observe several key trends not found in previous two-dimensional simulations or theoretical analyses for C. elegans , as well as novel results for the amoeboid motion. In particular, we find that regions of high polymer stress concentrated at the head and tail of the swimming C. elegans are created by strong extensional flow fields and are associated with a decrease in swimming speed for a given swimming stroke. In contrast, in two dimensions these regions of stress are commonly found distributed along the entire body, likely owing to the lack of a third dimension for polymer relaxation. A comparison of swim speeds shows that the calculations in two-dimensional simulations result in an over-prediction of the speed reduction. We believe that our simulation tool accurately captures the swimming motion of the two aforementioned model swimmers and furthermore, allows for the simulation of multiple deformable swimmers, as well as more complex swimming geometries. This methodology opens many new possibilities for future studies of swimmers in viscoelastic fluids.