Note on the dynamics of a spherical magnetotactic bacterium swimmer
In this work, we consider a model of spherical bacterium, such as cocci, for which the orientation in a simple shear flow is modified by magnetotaxis phenomenon. The problem has been studied (in different context) by Hall and Busenberg [J. Chem. Phys. 11, 137 (1969)] and Brenner [J. Colloid Inter. Sci. 32, 141 (1970), and Annu. Rev Fluid Mech. 2, 137 (1970)].
The goal here is to derive, for the first time, an explicit analytical solution for the bacterium orientation, with particular attention to periodic (tumbling) motions, via a simple mathematical treatment.