Probing linear and nonlinear microrheology of viscoelastic fluids

Bulk rheological properties of viscoelastic fluids have been extensively studied in macroscopic shearing geometries. However, little is known when an active microscopic probe is used to locally perturb them far from the linear-response regime. Using a colloidal particle dragged periodically by scanning optical tweezers through a viscoelastic fluid, we investigate both, its linear and nonlinear microrheological response. With increasing particle velocity, we observe a transition from constant viscosity to a thinning regime, where the drag force on the probe becomes a nonlinear function of the particle velocity. We demonstrate that this transition is only determined by the ratio of the fluid’s equilibrium relaxation time and the period of the driving. Introduction. – Most soft materials of industrial and biological importance are viscoelastic and have nonNewtonian behavior under applied stress. For example, at sufficiently high strain rates, the deformation of their microscopic structure gives rise to nonlinear rheological response, e.g. shear thinning or shear thickening [1]. The flow properties of such materials are usually investigated by means of controlled stress or strain rheometers in macroscopic shear geometries. These techniques provide bulk quantities (e.g. complex shear moduli and viscosities) averaged over the entire volume of the sample, typically millilitres. However, one is often interested in local instead of bulk rheological properties of micron-sized flows, e.g. in new synthesised materials and biological fluids, for which conventional rheological techniques are inapplicable. In such cases, colloidal probe-based techniques (microrheology) are more adequate to study flow properties in a non-invasive manner. One example is passive microrheology, where the complex shear modulus of viscoelastic materials can be determined from the mean square displacement of embedded colloidal particles using a Generalized Stokes-Einstein relation (GSER) [2]. Due to its simple implementation and straightforward interpretation, passive microrheology is nowadays a standard technique to investigate linear rheological properties of microlitre samples of soft matter in thermal equilibrium. Less well understood is active microrheology, where a microscopic probe is driven through the sample by an external field, e.g. by optical tweezers, in order to directly measure the local rheological response of the fluid [3]. Unlike bulk rheology, where the entire sample is uniformily sheared, in active microrheology, strain is only applied to a small fluid volume around the probe. Therefore, instead of shear rate-stress flow curves, one usually determines velocity-force relations of the probe [4], which comprise memory effects of the surrounding viscoelastic fluid. Active microrheology has been exploited to measure linearresponse properties in out-of-equilibrium matter, where the GSER breaks down and passive microrheology is not applicable [5–10]. More recently, it has been proposed that active probes can be also utilized to create sufficiently strong strain and stress in complex fluids, thus providing a way to investigate nonlinear rheology at mesoscopic scales [11]. Indeed, nonlinear microrheological behavior has been induced by moving microscopic probes through dense colloidal suspensions [12,13] micellar fluids [14,15], gels [16], and polymer solutions [17,18]. However, it is not obvious to what extent the threshold for the nonlinear behavior is determined by the specific flow geometry of the probe rather than the properties of the investigated fluid [19]. This is important e.g. to understand flow properties of complex fluids in confined microscopic geometries such as in microfluidic devices [20] and porous media [21], or the motion of microswimmers in viscoelastic media [22,23]. In this letter, we investigate local linear and nonlinear microrheological response of a worm-like micellar solution by means of an active probe. Since the bulk rheology of