Mechanisms of Elastic Enhancement and Hindrance for Finite-Length Undulatory Swimmers in Viscoelastic Fluids

A computational model of finite-length undulatory swimmers is used to examine the physical origin of the effect of elasticity on swimming speed. We explore two distinct target swimming strokes: one derived from the motion of Caenorhabditis elegans, with large head undulations, and a contrasting stroke with large tail undulations. We show that both favorable stroke asymmetry and swimmer elasticity contribute to a speed-up, but a substantial boost results only when these two effects work together. We reproduce conflicting results from the literature simply by changing relevant physical parameters.

Figure 1

(a),(b) The ratio of average swimmer speed to that of the Newtonian swimmer as a function of De, varying stroke type and bending stiffness.

Figure 2

(a) Contour plots of the polymer stress energy at two times during a period for $\mathrm{De}=1$: (i),(ii) soft kicker, (iii),(iv) soft burrower (head on the right). (b),(c) The location of the horizontal component of the swimmer center of mass is plotted over one period at $t=10$ for $\mathrm{De}=0,1$; markers correspond to local maxima in front (circles) and back (squares) stress. (d),(e) Back-front stress asymmetry ratio (time-averaged ratio of back stress to front stress) for $0\le \mathrm{De}\le 5$.

Figure 3

(a) Kicker shapes at times evenly spaced within a half-period: stiff at $\mathrm{De}=0$, soft at $\mathrm{De}=0,1$. (b) Non-normalized average speed for stiff kickers and burrowers for different De (see markers) as a function of ${\mathrm{Stroke}}_{\mathrm{De}}$, where changes in this parameter correspond with passive dynamic stroke changes for soft swimmers indexed by De.

Figure 4

(a) The ratio of average swimmer speed to that of the Newtonian swimmer as a function of De, varying stroke type, bending stiffness on a short time scale. (b) Time evolution of maximum polymer stress energy for $1\le \mathrm{De}\le 5$, soft kicker.