On the kinematics-wave motion of living particles in suspension

This work presents theoretical and experimental analyses on the kinematics-wave motion of suspended active particles in a biological fluid. The fluid is an active suspension of nematodes immersed in a gel-like biological structure, moving at a low Reynolds number. The nematode chosen for the study is Caenorhabditis elegans. Its motion is subjected to the time reversibility of creeping flows. We investigate how this worm reacts to this reversibility condition in order to break the flow symmetry and move in the surrounding fluid. We show that the relationship between the length of an individual nematode and the wavelength of its motion is linear and can be fitted by a theoretical prediction proposed in this work. We provide a deep discussion regarding the propulsion mechanics based on a scaling analysis that identifies three major forces acting on an individual nematode. These forces are a viscous force, a yield stress force due to gelification of agar molecules in the gel-like medium, and a bending force associated with the muscular tension imposed by the nematodes in the medium. By the scalings, we identify the most relevant physical parameters of the nematode's motion. In order to examine and quantify the motion, dynamical system tools such as FFT are used in the present analysis. The motion characterization is performed by examining (or studying) two different populations: (i) in the absence of food with starving nematodes and (ii) with well-fed nematodes. In addition, several kinematic quantities of the head, center of mass, and tail for a sample of nematodes are also investigated: their slip velocities, wavelengths, trajectories, frequency spectra, and mean curvatures. The main findings of this work are the confirmation of a linear relationship between the nematode's physical length and its motion wavelength, the identification of secondary movements in high frequencies that helps breaking the time-reversibility in which the worms are bonded, and the observation and interpretation of a systematic difference between the individual motion of well-fed and starving nematodes.