Vector plot of flow fields generated by pusher and puller squirmers in a Newtonian fluid. Left: co-moving frame. Right: laboratory frame. On each panel, the data for the pusher are displayed on the left, and those for the puller on the right. The large arrow (blue) indicates the swimming direction and the background color scheme indicates the velocity magnitudes.
Nondimensional swimming speed, U, of the swimmer as a function of the Weissenberg number, We, for pusher α = −5 (squares, green), puller α = 5 (triangles, blue) and neutral squirmer α = 0 (circles, red). The swimming speed is scaled by its corresponding value in the Newtonian fluid, U New.
Distribution of the component of the polymeric stress for the neutral squirmer and three values of the Weissenberg number, We = 0.1, 2, and 6. (Left: We = 0.1 and 2. Right: We = 6 and 2.)
Distribution of the component of the polymeric stress for the pusher (left) and puller (right) swimming in the viscoelastic fluid. For both gaits, We = 0.1 and We = 2 are chosen for comparison. The inset plots show regions with high value of .
Distribution of the component of the polymeric stress along the symmetry axis. Shaded circles and arrows indicate the squirmer and its swimming direction. Data for the pusher are shown in the top whereas the neutral squirmer and the puller are reported at the bottom. The solid and short-dashed lines correspond to We = 0.1, the long-dashed and dotted-dashed lines to We = 2.
Distribution of the and components of the polymeric stress for pullers in the viscoelastic fluid with We = 0.5. Both the and components lead to a net polymeric (elastic) force indicated by the gray arrows, hindering locomotion. The location of this elastic forces is right above the vortex ring, implying that they are generated by the elongational flow.
Swimming power, , for pusher (squares, green), puller (triangles, blue) and neutral (circles, red) squirmers, nondimensionalized by the swimming power in the Newtonian case, . The power consumption of swimming in the Newtonian fluid are equal to (neutral squirmer) and (both pusher and puller).
Contributions to the total power expended by swimming, , versus Weissenberg number We, β = 0.5, for neutral squirmer (left) and puller (right). The three contributions are defined as: , , and .
Polymeric power density, D P , for pushers in fluids with We = 0.1 (left) and We = 2 (right). Dotted elliptical circles mark areas with negative values of D P . The values of D P along the swimmer surface are displayed in Fig. 10.
Spatial distribution of polymeric power density, D P , along the surface of pushers in viscoelastic fluids with We = 0.1 (solid line, red) and 2 (dashed line, blue); θ is defined in Sec. II, as the angle between the swimming direction and the position vector of each point.
Swimming speed , scaled to ensure locomotion at constant power, versus Weissenberg number, We, for β = 0.5. Nondimensional form is plotted for the three swimming gaits: neutral (circles, red), puller (triangles, blue), and pusher (squares, green).
Swimming efficiency, η, normalized by the corresponding value for Newtonian swimming, ηNew, versus Weissenberg number, We. The efficiencies of swimming in the Newtonian fluid are equal to ηNew = 0.5 (neutral squirmer) and ηNew = 0.037 (both pusher and puller).
Power law exponent, γ, for spatial decay of the axial velocity along the axis of the domain (r = 0) (|u| ∼ r −γ, see text), as a function of the Weissenberg number, We. The inset plot highlights the difference between pusher and puller.
Stresslets induced by swimmers in viscoelastic fluids: rr and zz components of the tensor S, Eq. (21), for different swimming gaits. Left: pusher (α = −5) and puller (α = 5). Right: neutral squirmer (α = 0).
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