Mechanics of Undulatory Swimming in a Frictional Fluid
Figure 2
The empirical resistive force relations for the granular medium.
The empirical force relations were obtained by dragging a rod with square cross-section (width = height = 16 mm, length = 40 mm) through 3 mm glass particles in simulation, at constant depth of 7.6 cm. The perpendicular () and parallel (
) components of the surface forces are plotted as a function of the angle between the velocity direction and the rod axis (
), see inset. See text for the analytical expressions for
and
. For comparison,
and
are calculated for a long thin ellipsoid in a low Re fluid by choosing a viscosity that gives comparable magnitude of
; the low Re forces are plotted as dashed gray lines. Figure adapted from [21].