An optimal waving device utilized in micro swimmer/PUMP: Analytical, numerical and experimental analysis

This paper describes a unique non-vibratory traveling wave generator, which performs as a propulsion mechanism or pump in low Reynolds number (Re) environments, i.e. in highly viscous fluids or in micro scales. In low Re numbers the dynamics of a moving body is governed mainly by fluid drag effects, therefore mobility must rely on non-inertial, non-time reversible trajectories, e.g., traveling waves. The proposed device generates axisymmetric transverse traveling waves along an elastic cylindrical shell. The waving surface induces a vorticity and pressure fields in the adjacent fluid, which result in propagation of the swimmer opposite to the wave direction, or alternatively, in pumping fluid in the wave propagation direction. The dynamics of the mechanical multi-cam device ensures, assuming negligible friction, zero actuation shaft torque, while for non-negligible friction it is demonstrated that torque oscillations are dramatically decreased, yielding a small non-zero mean torque. These properties are achieved by choosing a specific angular phase between successive cams, so that the ratio of the number of wavelengths times a harmonic index, over the number of cams is non-integer. The effects of wave discretization on the tempo-spatial frequency content of the cylindrical envelope are also studied. The analytical analysis is accompanied by numerical examples, and demonstrated with an experimental working prototype.