It is known that some microorganisms such as bacteria and spermatozoa accumulate near a boundary, which has been recently considered to be a phenomenon driven by non-linear hydrodynamic interaction between the cel and the boundary, whereby the time-reversal symmetry highlighted by the scallop theorem of the low Reynolds number flow still holds even in presence of boundaries.

In this talk, swimming stability of (i) a squirmer and (ii) a model spermatozoon near a boundary will be discussed after a brief review of the hydrodynamics of swimming microorganism.

The squirmer is a simple mathematical model of a swimming microorganism that propel with surface deformation. The stability behaviour can be characterised by boundary conditions at the surface as well as cell geometry and swimming morphology. The swimming dynamics of the model spermatozoon illustrates the stable planar beat near a no-slip boundary, though the dynamics can be unstable for abnormal cell morphology, implying biological significance of the swimming stability for mammalian spermatozoa in female reproductive tract.

(Joint work with Dr. E. A. Gaffeny at University of Oxford)