  Since their development in 2001, regularised stokeslets have become a popular
numerical tool for low-Reynolds number flows since the replacement of a point
force by a smoothed blob overcomes many computational difficulties associated
with flow singularities (Cortez, 2001, \textit{SIAM J. Sci. Comput.}
\textbf{23}, 1204). The physical changes to the flow resulting from this
process are, however, unclear. In this paper, we analyse the flow induced by
general regularised stokeslets. An explicit formula for the flow from any
regularised stokeslet is first derived, which is shown to simplify for
spherically symmetric blobs. Far from the centre of any regularised stokeslet
we show that the flow can be written in terms of an infinite number of
singularity solutions provided the blob decays sufficiently rapidly. This
infinite number of singularities reduces to a point force and source dipole for
spherically symmetric blobs. Slowly-decaying blobs induce additional flow
resulting from the non-zero body forces acting on the fluid. We also show that
near the centre of spherically symmetric regularised stokeslets the flow
becomes isotropic, which contrasts with the flow anisotropy fundamental to
viscous systems. The concepts developed are used to { identify blobs that
reduce regularisation errors. These blobs contain regions of negative force in
order to counter the flows produced in the regularisation process, but still
retain a form convenient for computations.
