Swimming speed for (a) a pusher and (b) a puller squirmer. The inertia of the fluid increases the swimming speed of a pusher; however, the effect is opposite for a puller. This effect is more pronounced as β increases.
Streamlines for (a) a pusher and (c) a puller squirmer are plotted in the frame of reference translating by the squirmer at |β| = 3. Stream functions are shown at 0:-0.5:-3.5 for the pusher and 0:-0.5:-4.5 for the puller. Contours of velocity magnitude for a (b) pusher and (d) puller squirmer in a fixed frame of reference are plotted. The contours are shown at 0.4:0.2:2.0 for both pusher and puller. The solid line (green online) represents the case of Re = 1 and dashed line (red online) represents Re = 0. (x, y, z) are Cartesian coordinates, where z is along the swimming direction and the squirmer is swimming downward.
(a) Stress along the swimming direction as a function of polar angle θ. Vorticity contours around (b) a pusher and (c) a puller squirmer at |β| = 3. The contours are shown at −10:1:10. The solid line (green online) represents the case of Re = 1 and dashed line (red online) represents Re = 0.
Swimming efficiency for pusher and puller squirmers enhances as Reynolds number increases. Data are shown for |β| = 5.
Dimensionless strength of B s for a (a) pusher and (b) puller squirmer. The Stokelet is absent in the limit of the Stokes regime and velocity decays as r −2. In the inertial regime, slowest decaying term scales as r −1 in the inner solution and its magnitude increases with |β| and Reynolds number.
The detection volume of a pusher in the inertial regime normalized by the one in the Stokes regime increases with Reynolds number (shown with squares, red online). However for an inertial puller, the normalized detection volume decreases in the range of Re < 0.5 but it increases at larger Reynolds numbers (black circles). Data are shown for |β| = 5.
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