The series above are often truncated at  in the study of far field flow, . Within that approximation, , with squirmer parameter . The first mode  characterizes a hydrodynamic source dipole with decay  (and with that the swimming speed ). The second mode  corresponds to a hydrodynamic stresslet or force dipole with decay . Thus,  gives the ratio of both contributions and the direction of the force dipole.  is used to categorize microswimmers into pushers, pullers and neutral swimmers.
The above figures show the velocity field in the lab frame and in the particle-fixed frame. The hydrodynamic dipole and quadrupole fields of the squirmer model result from surface stresses, due to beating cilia on bacteria, or chemical reactions or thermal non-equilibrium on Janus particles. The squirmer is force-free. On the contrary, the velocity field of the passive particle results from an external force, its far-field corresponds to a "stokeslet" or hydrodynamic monopole. A force-free passive particle doesnt move and doesnt create any flow field.