Inversion transformation of Stokes flows bounded by parallel planes

The positive inversion transformation applied to a two-dimensional Stokes flow around bodies leads alike to a Stokes flow. This fact can be exploited to find new two-dimensional Stokes flow solutions around inverse bodies. Some features of this method, such as the relations between the reference and inverse fluid velocity fields, are presented followed by an application to examples of cellular flow between two parallel plates induced by rotating or translating cylinder. Thus hydrodynamic characteristics of flow around circular bodies obtained by inversion of the plates are straightforward deduced. Typical fluid flow patterns around two circular cylinders in contact placed in the centre of a rotating or a translating circular cylinder are thus illustrated.