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In isotropic fluids like water, micrometer-scale swimmers have evolved swim strokes to translate despite their tiny size. As described by Purcell in his Scallop Theorem, reciprocal motions, like those performed by a scallop, cannot drive…

One of the principal mechanisms by which surfaces and interfaces affect microbial life is by perturbing the hydrodynamic flows generated by swimming. By summing a recursive series of image systems we derive a numerically tractable…

Soft Condensed Matter · Physics 2016-10-12 Arnold J. T. M. Mathijssen , Amin Doostmohammadi , Julia M. Yeomans , Tyler N. Shendruk

Efficient locomotion is important for the evolution of complex life, yet the physical principles selecting specific swimming strokes often remain entangled with biological constraints. In viscous fluids, the scallop theorem constrains the…

Biological Physics · Physics 2026-03-11 Takahiro Kanazawa , Kenta Ishimoto , Kyogo Kawaguchi

Robotic swimmers are currently a subject of extensive research and development for several underwater applications. Clever design and planning must rely on simple theoretical models that account for the swimmer's hydrodynamics in order to…

Fluid Dynamics · Physics 2018-11-21 Evgenia Virozub , Oren Wiezel , Alon Wolf , Yizhar Or

Swimming in circles occurs in a variety of situations at low Reynolds number. Here we propose a simple model for a swimmer that undergoes circular motion, generalising the model of a linear swimmer proposed by Najafi and Golestanian (Phys.…

Soft Condensed Matter · Physics 2012-07-16 Rodrigo Ledesma-Aguilar , Hartmut Loewen , Julia M. Yeomans

Locomotion in Stokes flow is an intensively-studied problem because it describes important biological phenomena such as the motility of many species' sperm, bacteria, algae and protozoa. Numerical computations can be challenging,…

Fluid Dynamics · Physics 2018-05-15 Meurig T. Gallagher , David J. Smith

As technological advances allow us to fabricate smaller autonomous self-propelled devices, it is clear that at some point directed propulsion could not come from pre-specified deterministic periodic deformation of the swimmer's body and we…

Soft Condensed Matter · Physics 2015-05-13 Ramin Golestanian , Armand Ajdari

Microswimmers in turbulent flows often navigate complex, heterogeneous, and obstacle-rich environments, where they exhibit intricate behaviors such as trapping at and escape from obstacles. We generalize recent $\mathcal{Q}-$learning…

Fluid Dynamics · Physics 2026-04-14 Vaishnavi Gajendragad , Akanksha Gupta , Nadia Bihari Padhan , Rahul Pandit

The aim of this paper is to describe the self-propulsion of a micro-robot (or micro-swimmer) consisting of $N$ spheres moving along a fixed line. The spheres are linked to each other by arms with the lengths changing periodically. For the…

Fluid Dynamics · Physics 2015-06-11 Vladimir A. Vladimirov

Hydrodynamic interactions in systems comprised of self-propelled particles, such as swimming microorganisms, and passive tracers have a significant impact on the tracer dynamics compared to the equivalent "dry" sample. However, such…

Fluid Dynamics · Physics 2017-05-17 Joost de Graaf , Joakim Stenhammar

We discuss a locomotion of a three-sphere microswimmer in a viscoelastic medium and propose a new type of active microrheology. We derive a relation which connects average swimming velocity and frequency-dependent viscosity of the…

Soft Condensed Matter · Physics 2017-03-30 Kento Yasuda , Ryuichi Okamoto , Shigeyuki Komura

The swimming of a sphere immersed in a viscous incompressible fluid with inertia is studied for surface modulations of small amplitude on the basis of the Navier-Stokes equations. The mean swimming velocity and the mean rate of dissipation…

Fluid Dynamics · Physics 2016-12-20 B. U. Felderhof , R. B. Jones

The current study presents a systematic investigation of the locomotion performance of a swimmer with a wide range of parameter settings. Two-dimensional simulations with the immersed boundary method are employed for the fluid-structure…

Fluid Dynamics · Physics 2023-12-21 Wenkang Wang , Xu Chu

The paper is about the parking 3-sphere swimmer ($\text{sPr}_3$). This is a low-Reynolds number model swimmer composed of three balls of equal radii. The three balls can move along three horizontal axes (supported in the same plane) that…

Optimization and Control · Mathematics 2016-10-18 François Alouges , Giovanni Di Fratta

The spatiotemporal dynamics in systems of active self-propelled particles is controlled by the propulsion mechanism in combination with various direct interactions, such as steric repulsion, hydrodynamics, and chemical fields. Yet, these…

Soft Condensed Matter · Physics 2024-06-03 Mario Theers , Elmar Westphal , Kai Qi , Roland G. Winkler , Gerhard Gompper

Swimming microorganisms often self propel in fluids with complex rheology. While past theoretical work indicates that fluid viscoelasticity should hinder their locomotion, recent experiments on waving swimmers suggest a possible…

Biological Physics · Physics 2014-11-25 Emily E. Riley , Eric Lauga

We study the three-dimensional dynamics of a spherical microswimmer in cylindrical Poiseuille flow which can be mapped onto a Hamiltonian system. Swinging and tumbling trajectories are identified. In 2D they are equivalent to oscillating…

Soft Condensed Matter · Physics 2012-06-18 Andreas Zöttl , Holger Stark

The locomotion of microorganisms and spermatozoa in complex viscoelastic fluids is of critical importance in many biological processes such as fertilization, infection, and biofilm formation. Depending on their propulsion mechanisms,…

Soft Condensed Matter · Physics 2021-09-14 Gaojin Li , Eric Lauga , Arezoo M. Ardekani

A matrix formulation is derived for the calculation of the swimming speed and the power required for swimming of an assembly of rigid spheres immersed in a viscous fluid of infinite extent. The spheres may have arbitrary radii and may…

Soft Condensed Matter · Physics 2014-09-18 B. U. Felderhof

Many microswimmers are able to swim through viscous fluids by employing periodic non-reciprocal deformations of their appendages. Here we use a simple microswimmer model inspired by swimming biflagellates which consists of a spherical cell…

Soft Condensed Matter · Physics 2025-08-22 Sridhar Bulusu , Andreas Zöttl