Definition sketch for the prolate probe. Here, the aspect ratio . The circle of radius unity represents a bath particle, which is contacting the probe. The probe moves at constant velocity along its axis of revolution, the axis. The excluded-volume surface (broken curve) is formed by “rolling” the bath particle over the probe’s surface.
Definition sketch for the oblate probe. Here, the aspect ratio , and the legend is the same as in Fig. 1. Again, the probe moves along its axis of revolution (the axis) at constant velocity.
Plot of the mobility factors versus probe aspect ratio . The broken line is the oblate factor and the solid line is the prolate factor .
Microviscosity increments at small as a function of probe’s aspect ratio . The broken line is the oblate increment and the solid line is the prolate increment .
Sketch of the microstructure around an oblate probe at large .
Sketch of the microstructure around an prolate probe at large .
Microviscosity increments at large as a function of probe’s aspect ratio . The legend is the same as in Fig. 4.
Difference in microviscosity increments at small and large as a function of probe aspect ratio . The broken(solid) line is the difference in the oblate(prolate) increment
Sample finite difference grid for a prolate probe. Here, ; there are grid points; and . Note the high density of mesh points near the excluded-volume surface.
Microstructural deformation, , in the symmetry plane of the prolate probe as a function of . Here, and the probe moves from left to right. The excluded-volume surface is shown with zero deformation, ; darker regions imply accumulation, ; and lighter regions represent depletion, . The closed curve inside the excluded-volume surface is the probe itself.
Microstructural deformation, , in the symmetry plane of the oblate probe as a function of . Here, and the probe moves from left to right. The shading scheme is the same as in Fig. 10.
Microviscosity increment for a prolate probe, , as a function of for different : circles, ; squares, ; and triangles, . The filling pattern indicates the method of numerical solution: filled, Legendre expansion; and empty, finite differences. The solid line is the microviscosity increment for a spherical probe, [Squires and Brady (2005)].
Microviscosity increment for an oblate probe, , as a function of for different . The legend is the same as in Fig. 12.
Comparison of microviscosity increments from prolate and oblate probes with the macroviscosity [Bergenholtz et al. (2002)] and the microviscosity from a spherical probe [Squires and Brady (2005)]. Symbol legend: diamonds, oblate ; squares, oblate ; triangles, prolate ; circles, prolate . A sketch of the probe for each case is also shown. The solid line is the macroviscosity and the broken line is the microviscosity for a spherical probe, . For the microviscosity , and for the macroviscosity (with the shear rate).
Sketch of a prolate probe translating at angle to its symmetry axis: (a) near-longwise motion, ; and (b) near-broadside motion, . Note, the axis is directed out of the page.
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