Experimental and theoretical studies of the fluid elasticity on the motion of macroscopic models of active helical swimmers

Abstract

This work presents experimental and theoretical studies on the locomotion of helical artificial swimmers at low Reynolds number in both Newtonian and viscoelastic ambient liquids. We examine the effect of fluid elasticity on the propulsive force and torque on the body and speed velocity of the swimmer in terms of two physical parameters: Deborah number ( De) and Strouhal number ( Sh). For this end, some experiments with prototype microorganisms in creeping flow motion are conducted. In the experiments, a macroscopic swimmer that propels itself by mimicking helical flagella are developed and tested. Three swimming models propelled by a helical tail with different wavelengths are investigated, and their motions examined for both cases: when the ambient solvent is a pure Newtonian viscous fluid and when the base fluid is an elastic polymeric solution. In addition, we also apply the slender body theory and the method of regularized Stokeslet in order to calculate theoretically the force and torque, as function of the Strouhal number ( Sh), produced by the helical swimmer moving in a Newtonian fluid. The theoretical results are compared with experimental data, and a very good agreement is observed especially for higher values of Sh within the error bars of the experimental data. In the case of a non-Newtonian base fluid, the flow problem of an Oldroyd-B elastic fluid is solved numerically using a computational code based on a finite element method. The helical swimmer propulsive velocity is calculated in terms of the elastic parameter Deborah number and also compared with the experimental observation when the base fluid is non-Newtonian. It is shown experimentally that the swimming speed increases as the elastic effect in the base fluid increases until a critical Deborah number O(1), when the velocity saturates for a constant value within the experimental error bars. The velocity anisotropy measured experimentally by the ratio of the swimmer speed in two different directions is insensitive to the elastic effect in the base fluids. We complete our discussion on the helical swimmers motion in creeping flow by presenting a comparison between predictions of the speed velocity given by finite elements simulations using an Oldroyd-B model for the base elastic fluid and experimental data. The agreement between the two sets of results is very good within the experimental error bars for the elastic parameter varying from 0 to 2. It may be remarked, however, that while the experimental data tend to saturate at larger De, the simulations results seem to have a continuous increase according to the constitutive model used to describe the base elastic liquid.