It is well known that the reversibility of Stokes flow makes it difficult for small microorganisms to swim. Inertial effects break this reversibility, allowing new mechanisms of propulsion and feeding. Therefore it is important to estimate the effect of unsteady and fluid inertia on the dynamics of microorganisms in flow. In this work, we show how to translate known inertial effects for non-motile organisms to motile ones, from passive to active particles. The method relies on a trick used earlier by Legendre and Magnaudet to deduce inertial corrections to the lift force on a bubble from Saffmans results for a solid sphere, using the fact that small inertial effects are determined by the far field of the disturbance flow. The method allows to compute the inertial effect of unsteady fluid accelerations on motile organisms, and the inertial forces they experience in steady shear flow. We explain why the method fails to describe the effect of convective fluid inertia.
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