Effect of viscous and thermal forcings on dynamical features of swimming of microorganisms in nanofluids

As a practical dynamical system approach to analyse microorganisms, we have used the system identification approach to develop a framework that is capable of introducing external forcing on a time series data. For this goal, a two-equation deferential equation system for time evolution of the experimental parallel velocity values of head of a bull spermatozoon during circular swimming [1] is reconstructed. The planar movement of the sperm is shown to be modelled well with this deferential system for three different cases. We also present a least-squares analysis on a system with more sampled data with fewer points used in the time marching of the deferential system and show how the system can represent the real pattern approximately. Following this idea we bring a linearized model of the system and investigate it near its equilibrium points on a Trace-Determinant chart. Finally, we show how this straightforward system can be employed where external viscous and/or thermal forcings due to swimming in a nanofluid is a dominant phenomenon. We bring a phase portrait demonstration of the time evolution of the system to highlight the main modifications in the dynamics