Kenta Ishimoto

The boundary behavior of axisymmetric microswimming squirmers is theoretically explored within an inertialess Newtonian fluid for a no-slip interface and also a free surface in the small capillary number limit, preventing leading-order surface deformation. Such squirmers are commonly presented as abridged models of ciliates, colonial algae, and Janus particles and we investigate the case of low-mode axisymmetric tangential surface deformations with, in addition, the consideration of a rotlet dip

How does a sperm find its way? The study of guidance cues has fascinated sperm biologists and in particular the prospect of rheotaxis, that is a fluid flow orienting the direction of sperm swimming, has been the subject of extensive recent study, as readily motivated by the prospect that such guidance may be active in the mammalian female reproductive tract. For instance, it has been hypothesized that helical sperm flagellar beating is necessary for such guidance, whereas there is an extensive d

The flagellar beat is extracted from human sperm digital imaging microscopy and used to determine the flow around the cell and its trajectory, via boundary element simulation. Comparison of the predicted cell trajectory with observation demonstrates that simulation can predict fine-scale sperm dynamics at the qualitative level. The flow field is also observed to reduce to a time-dependent summation of regularized Stokes flow singularities, approximated at leading order by a blinking force triple

Remarkably, mammalian sperm maintain a substantive proportion of their progressive swimming speed within highly viscous fluids, including those of the female reproductive tract. Here, we analyse the digital microscopy of a human sperm swimming in a highly viscous, weakly elastic mucus analogue. We exploit principal component analysis to simplify its flagellar beat pattern, from which boundary element calculations are used to determine the time-dependent flow field around the sperm cell. The sper

We reconsider fluid dynamics for a self-propulsive swimmer in Stokes flow. With an exact definition of deformation of a swimmer, a coordinate-based proof is first given to Purcell's scallop theorem including the body rotation.

We have numerically investigated sperm clustering behaviours, modelling cells as superpositions of regularised flow singularities, coarse-grained from experimentally obtained digital microscopy of human sperm, both in watery medium and a highly viscous-weakly elastic, methylcellulose medium. We find that the cell yaw and cell pulling dynamics inhibit clustering in low viscosity media. In contrast clustering is readily visible in simulations modelling sperm within a methylcellulose medium, in lin

The great mammalian sperm race encounters numerous microenvironments to which sperm must adapt and a fundamental sperm response is the change in its waveform owing to both fluid rheology and capacitation, with the latter associated with a hyperactivated beat pattern. Hence, in this modelling study, we examine the effect of different flagellar waveforms for sperm behaviour near adhesive substrates, which are representative of epithelia in female tract sperm reservoirs and the zona pellucida (ZP),

The motions of an unsteady circular-disk squirmer and a spherical squirmer have been investigated in the presence of a no-slip infinite wall and a background shear flow in order to clarify the similarities and differences between two- and three-dimensional motions. Despite the similar bifurcation structure of the dynamical system, the stability of the fixed points differs due to the Hamiltonian structure of the disk squirmer. Once the unsteady oscillating surface velocity profile is considered,

We theoretically investigate self-oscillating waves of an active material, which were recently introduced as a nonsymmetric part of the elastic moduli, termed odd elasticity. Using Purcell's three-link swimmer model, we reveal that an odd-elastic filament at low Reynolds number can swim in a self-organized manner and that the time-periodic dynamics are characterized by a stable limit cycle generated by elastohydrodynamic interactions. Also, we consider a noisy shape gait and derive a swimming fo

Eukaryotic cell swimming is frequently actuated via the flagellum, which is a slender flexible appendage driven by waves of internal couples generated by dynein molecular motors. Here we adapt a regularized elastohydrodynamic model of flagella by Simons et al. (2015, A fully three-dimensional model of the interaction of driven elastic filaments in a Stokes flow with applications to sperm motility, J. Biomech., 48(9, SI), 1639--1651) to consider active filament models of sperm swimming given the

Nonreciprocal shape deformations can drive inertialess cellular swimming, as first explored by Taylor and Lighthill in the 1950s, for the small-amplitude squirming of a planar and a spherical surface, respectively. Lighthill's squirmer, in particular, has been extensively studied for large wave numbers in the context of ciliated microbes. The maximal power efficiency for small-amplitude planar squirming motility is well characterized and degenerate, with nonunique optimal swimming strokes. We ex

Abstract The motion of a spherical squirmer in unsteady Stokes flow is investigated for a deeper understanding of unsteady inertial effects on swimming micro-organisms and differences of swimming strokes between a wave pattern and a flapping motion. An asymptotic analysis with respect to the small amplitude and the small inertia is performed, and the average swimming velocity after a long period of time under an assumption of a time-periodic stroke is obtained. This analysis shows that the scall

The consideration of viscoelasticity within fluid dynamical boundary element methods has traditionally required meshing over the whole flow domain. In turn, a major advantage of the boundary element method is lost, namely the need to consider only surface boundary integrals. Here, using a generalised reciprocal relation and viscoelastic force singularities, a boundary element method is developed for linear viscoelastic flows. We proceed to explore finite-deformation microswimming in a linear Max