## Microrheology

### Microrheology of complex fluids

While measuring with great care the correlated motion of tracer particles in entangled F-actin networks, we came across a new regime in the decay of the response of a complex fluid to a perturbation. At this intermediate regime the response decays as \(1/r^3\) instead of the asymptotic decay of \(1/r\) (see figure). This behavior persists up to a very large distance of several microns away from the perturbation source. Together with Prof. Haim Diamant we have been able to account for this effect, and show that it is inherent to any complex fluid, and that it may appear at significantly large distances, over ten times the typical length-scale of the fluid (mesh size in our case), if the ratio between local and bulk viscosity is large. Deriving the response within the two-fluid model, we were able to compare experiment to theory, thereby measuring the dynamic correlation length of F-actin networks, as well as their bulk and local viscoelastic properties. In second figure the cross-over distance of many networks differing in mesh size \(\xi_s\), and measured with different tracer particle sizes \(a\), is plotted as a function of the ratio of local viscosity to bulk viscosity, \(H\). By rescaling the cross-over length and presenting it as a function of the ratio \(\xi_s/a\), all the experimental data collapses to the single master curve which was theoretically predicted.
This work is significant for extending the characterization of any complex fluid, and as a new tool to characterize the structure of complex fluids. Moreover, there are cases in which the intermediate regime response is the only contribution to the fluid's response, for example, on a thin film near a rigid wall, or for fluids in a stiff porous medium. A particularly important system to consider is the biological cell, whose size is comparable to the crossover distance measured here. Cell viscoelasticity, therefore, should be reconsidered with the intermediate regime response in mind.( Phys. Rev. Lett. 112, 088301 (2014), Soft Matter, Vol. 10, pp. 8324-8329 (2014) ).