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Swimming at the microscale has recently garnered substantial attention due tothe fundamental biological significance of swimming microorganisms and the widerange of biomedical applications for artificial microswimmers. Thesemicroswimmers invariably find themselves surrounded by different confiningboundaries, which can impact their locomotion in significant and diverse ways.In this work, we employ a widely used three-sphere swimmer model to investigatethe effect of confinement on swimming at low Reynolds numbers. We conducttheoretical analysis via the point-particle approximation and numericalsimulations based on the finite element method to examine the motion of theswimmer along the centerline in a capillary tube. The axisymmetricconfiguration reduces the motion to one-dimensional movement, which allows usto quantify how the degree of confinement affects the propulsion speed in asimple manner. Our results show that the confinement does not significantlyaffect the propulsion speed until the ratio of the radius of the tube to theradius of the sphere is in the range of $\mathcal{O}(1)-\mathcal{O}(10)$, wherethe swimmer undergoes substantial reduction in its propulsion speed as theradius of the tube decreases. We provide some physical insights into howreduced hydrodynamic interactions between moving spheres under confinement mayhinder the propulsion of the three-sphere swimmer. We also remark that thereduced propulsion performance stands in stark contrast to the enhanced helicalpropulsion observed in a capillary tube, highlighting how the manifestation ofconfinement effects can vary qualitatively depending on the propulsionmechanisms employed by the swimmers.

The effect of axisymmetric confinement on propulsion of a three-sphere microswimmer