The environment in which microscopic organisms live in is dominated by viscous forces because of their small length scales. Inertial forces are of little use to them in their propulsion mechanisms. As a consequence of this, an organism such as the scallop which moves through time-reversible deformations of its body would not propel itself in a regime dominated by visocus forces. Hence, microscopic organisms use appendages like cilia and flagella that are not time reversible to move forward. However, inertial effects become important to microscopic organisms at the relevant time and length scales. For example, inertia is used by a microscopic organism such as Paramecium to escape/attack its predator/prey.
The effects of inertia on the model of a spherically ciliated micro-organism are studied numerically using an Immersed Boundary Method (IBM) in the present work. In this model ,the distortions of the envelope that is generated by connecting all the tips of the cilia together, are prescribed. The unsteady Reynolds number which characterizes the influence of unsteady inertia that is generated by the beat of the organism, is varied from 0.025 to 18. The code which uses a Volume Penalization/Volume of Solid IBM to simulate the distorting sphere is validated for several test cases. The mean swimming velocity of the organism that is obtained numerically from the code is in agreement with the analytical model for two cases of the unsteady Reynolds number. The mean swimming velocity is found to decrease at increasing inertia. The flow pattern that is obtained in the near-field as a result of the distorting sphere is significantly different from those obtained with the existing models available in literature.