Nonlinear Microrheology of Wormlike Micelle Solutions using Ferromagnetic Nanowire Probes:
N. Cappallo, C. Lapointe, D. H. Reich, and R. L. Leheny

We have investigated the application of ferromagnetic nanowires to nonlinear microrheology, focusing on wormlike micelle solutions as model non-Newtonian fluids.  Fig. 1(a) displays the effective drag viscosity h_d in 8.5 mM equimolar cetylpyridinium chloride/sodium salicylate (CPCl/NaSal) wormlike micelle solution determined by rotating a nanowire suspended in a solution, as a function of rotation rate w_R.  For comparison, the macroscopic shear viscosity h of the fluid is shown as a function of shear rate in Fig. 1(b).  At low w_R, h_d is independent of rate and mirrors the zero-shear-rate viscosity measured macroscopically.  Above a critical rate w_c, h_d becomes rate dependent and decreases as a power law with w_R.  While this decreasing h_d appears similar to the shear thinning observed macroscopically at large shear rate, a number of differences in the nonlinear regime also emerge.  For example, the onset of the nonlinear drag is characterized by a peak in h_d that has no counterpart in the macroscopic shear viscosity and that we associate with contributions to the drag from extensional flow.  Also, above w_c, h_d at different temperatures collapse onto a single curve, in contrast to h, which remains temperature dependent in the nonlinear regime.  These differences illustrate how the correspondence between microrheology and macroscopic shear rheology breakdown outside the linear regime and highlight unique perspectives afforded by nonlinear microrheology as a result.  Indeed, the collapse of h_d at different temperatures at large w_R demonstrates a temperature invariance of the nonlinear state of the wormlike micelle solutions that is obscured in the macroscopic measurements.

Above w_c, the rotating wires experience an additional force that highlights the anisotropic nature of the fluid's nonlinear state.  Specifically, the fluid imparts a torque G_^ perpendicular to the drag torque that seeks to tilt the wires out of the rotation plane. The onset of this out-of-plane torque is very sharp as a function of w_R and coincides with w_c, resembling a signature of a first order phase transition.  We identify the torque with a transition to nematic order among the micelles in the shear-induced state that has been proposed in previous studies.  Within this interpretation, the nonlinear shear of the rotating wire induces a nematic alignment in the form of a vortex.  The wire, having created this nematic order, is also an impurity that distorts the order.  Hence, we speculate that the out-of-plane torque results from a thermodynamic driving force that seeks to place the wire in the region of suppressed nematic order at the vortex core to reduce the free energy cost of its presence. The out-of-plane torque follows an approximate power-law dependence on w_R for w_R > w_c.  (G_^ = 0 for w_R < w_c.)  Rotation of the wire in response to this torque reveals directly the anisotropy of the drag in the nonlinear state, highlighting again the unique measurement capabilities afforded by nonlinear microrheology using these nanowire probes.

Fig. 1:  (a) Drag viscosity of 8.5 mM equimolar  (CPCl/NaSal) wormlike micelle solution determined from the rotation of a nanowire of length 21.7 mm as a function of rotation frequency at several temperatures.  (b) Shear viscosity of the solution determined using a stress-controlled rheometer with a cone-and-plate geometry as a function of shear rate.

N. Cappallo, C. Lapointe, D. H. Reich, and R. L. Leheny, “Nonlinear microrheology of wormlike micelle solutions using ferromagnetic nanowire probes,” Phys. Rev. E 76, 031505 (2007).

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