Micro–macro discrepancies in nonlinear microrheology: II. Effect of probe shape

Abstract

In this second article devoted to ‘computational experiments’ of nonlinear microrheology, we examine the effect that changing the probe shape or motion has upon the three sources of discrepancy that we previously examined for spheres. In particular, prolate ellipsoidal probes have relatively long regions of relatively constant strain rate, giving predominantly shear and relative Lagrangian steadiness. The micro–macro discrepancy is shown not to arise from Lagrangian unsteadiness, but largely from the non-viscometric nature of the flows. Second, an oblate ellipsoidal probe exacerbates the extensional regions in front of and behind the probe. However, the relatively low extensional rates around such ‘disks’ would require them to be pulled at much higher rates through the fluid in order to excite the extensional deformations. Because our model material thickens under uniaxial extension, but thins under biaxial extension, the contribution of each to the total drag is partially negated by the other. Finally, we examine a rotating spherical probe, which is Lagrangian steady and pure shear. We show that the apparent viscosity thus recovered is close to the true shear viscosity, and furthermore that the true shear viscosity can be extracted quantitatively from the apparent microviscosity.