**1. Introduction**

Many of the diverse material properties of soft materials (polymer solutions, gels, filamentous proteins in cells, etc.) stem from their complex structures and dynamics with multiple characteristic length and time scales. A wide variety of technologies, from paints to foods, from oil recovery to processing of plastics, all heavily rely on the understanding of how complex fluids flow (Larson, 1999).

Rheological measurements on complex materials reveal viscoelastic responses which depend on the time scale at which the sample is probed. In order to characterize the rheological response one usually measures the shear or the Young modulus as a function of frequency by applying a small oscillatory strain of frequency ω. Typically, commercial rheometers probe frequencies up to tens of Hz, the upper range being limited by the onset of inertial effects, when the oscillatory strain wave decays appreciably before propagating throughout the entire sample. If the strain amplitude is small, the structure is not significantly deformed and the material remains in equilibrium; in this case the affine deformation of the material controls the measured stress, and the time-dependent stress is linearly proportional to the strain (Riande et al., 2000).

Even though standard rheological measurements have been very useful in characterizing soft materials and complex fluids (e.g. colloidal suspensions, polymer solutions and gels, emulsions, and surfactant solutions), they are not always well suited for all systems because milliliter samples are needed thus precluding the study of rare or precious materials, including many biological samples that are difficult to obtain in large quantities. Moreover, conventional rheometers provide an average measurement of the bulk response, and do not allow for local measurements in inhomogeneous systems. To address these issues, a new methodology, microrheology, has emerged that allows to probe the material response on micrometer length scales with microliter sample volumes. Microrheology does not correspond to a specific experimental technique, but rather a number of approaches that attempt to overcome some limitations of traditional bulk rheology (Squires & Mason, 2010; Wilson & Poon, 2011). Advantages over macrorheology include a significantly higher range of frequencies available without time-temperature superposition (Riande et al., 2000), the capability of measuring material inhomogeneities that are inaccessible to macrorheological methods, and rapid thermal and chemical homogeneization that allow the transient rheology of evolving systems to be studied (Ou-Yang & Wei, 2010). Microrheology methods typically use embedded micron-sized probes to locally deform the sample, thus allowing one to use this type of rheology on very small volumes, of the order of a microliter. Macro-

Microrheology of Complex Fluids 147

contains dilational (or extensional) and shear contributions. For more complex interfaces, such as thicker ones, other dynamic modes (bending, splaying) have to be considered (Miller & Liggieri, 2009). Moreover, the coupling of the abovementioned modes with adsorption/desorption kinetics may be very relevant for interfaces that contain soluble or partially soluble surfactants, polymers or proteins (Miller & Liggieri, 2009; Muñoz et al., 2000; Díez-Pascual et al. 2007). In the case of surface shear rheology, most of the information available has been obtained using macroscopic interfacial rheometers which in many cases work at low Boussinesq numbers (Barentin et al., 2000; Gavranovic et. al., 2005; Miller & Liggieri, 2009; Maestro et al., 2011.a). Microrheology has been foreseen as a powerful method to study the dynamics of interfaces. In spite that the measurement of diffusion coefficients of particles attached to the interface is relatively straightforward with modern microrheological techniques, many authors have relied on hydrodynamic models of the viscoelastic surroundings traced by the particles in order to obtain variables such as interfacial elasticity or shear viscosity. The more complex the structure of the interface the stronger are the assumptions of the model, and therefore it is more difficult to check their validity. In the present work we will briefly review modern microrheology experimental techniques, and some of the recent results obtained for bulk and interfacial systems. Finally, we will summarize the theoretical models available for calculating the shear microviscosity of fluid monolayers from particle tracking experiments, and discuss the results for some systems.

For studying the viscoelasticity of the probe environment there are two broad types of experimental methods: active methods, which involve probe manipulation, and passive methods, that relay on thermal fluctuations to induce motion of the probes. Because thermal driving force is small, no sample deformation occurs that exceeds equilibrium thermal fluctuations. This virtually guarantees that only the linear viscoelastic response of the embedding medium is probed (Waigh, 2005). On the contrary, active methods allow the nonlinear response to be inferred from the relationship between driving force and probe velocity, in such cases the microstructure itself can be deformed significantly so that the material response differs from the linear case (Squires, 2008). As a consequence, passive techniques are typically more useful for measuring low values of predominantly viscous moduli, whereas active techniques can extend the measurable range to samples with significant elasticity modulus. Figure 1 shows the typical ranges of frequencies and shear

This is the oldest implementation of an active microrheology technique, and it has been recently reviewed by Conroy (Conroy, 2008). A modern design has been described by Keller et al. (2001). The method combines the use of strong magnets to manipulate embedded super-paramagnetic or ferromagnetic particles, with video microscopy to measure the displacement of the particles upon application of constant or time-dependent forces. Strong magnetic fields are required to induce a magnetic dipole in the beads and magnetic field gradients are applied to produce a force. The force exerted is typically in the range of 10 pN to 10 nN depending on the experimental details (Keller et al. 2001). The spatial resolution is typically in the range of 10-20 nm, and the frequency range is 0.01 – 1000 Hz. Three modes

moduli that can be studied with the different microrheological techniques.

**2. Experimental techniques** 

**2.1 Active techniques 2.1.1 Magnetic tweezers** 

and microrheology probe different aspects of the material: the former makes measurements over extremely long (macroscopic) length scales using a viscometric flow field, whereas the latter effectively measures material properties on the scale of the probe itself (Squires & Mason, 2010; Breedveld & Pine, 2003). As the probe increases in size, one might expect that micro- and macrorheology would converge, however, as it has been suggested, it is possible that macro- and microrheology techniques do not probe exactly the same physical properties because - even in the continuum (large probe) limit - one experiment uses a viscometric flow whereas the other does not (Kahir & Brady, 2005; Lee et al., 2010; Schmidt et al., 2000; Oppong & de Bruyn, 2010).

One can distinguish two main families of microrheological experiments: One type of experiments focuses on the object itself; for example, the study of motor proteins aims at understanding the mechanical motions of the protein associated with enzymatic activities on the molecular level (Ou-Yang & Wei, 2010). The other type of experiment aims at understanding the local environment of the probe by observing changes in its random movements (Crocker & Grier, 1996; MacKintosh & Schmidt, 1999). Fundamentally different from relaxation kinetics, microrheology measures spontaneous thermal fluctuations without introducing major external perturbations into the systems being investigated. Other wellestablished methods in this family are dynamic light scattering (Dasgupta et al., 2002; Alexander & Dalgleish, 2007; Tassieri et al. 2010), and fluorescence correlation spectroscopy (Borsali & Pecora, 2008; Wöll et al., 2009). With recent advancement in spatial and temporal resolution to subnanometer and submillisecond, particle tracking experiments are now applicable to study of macromolecules (Pan et al., 2009) and intracellular components such as cytoskeletal networks (Cicuta & Donald, 2007). Detailed descriptions of the methods and applications of microrheology to the study of bulk systems have been given in review articles published in recent years (Crocker & Grier 1996; MacKintosh & Schmidt, 1999; Mukhopadhyay & Granick, 2001; Waigh, 2005; Gardel et al., 2005; Cicuta & Donald, 2007).

Interfaces play a dominant role in the behavior of many complex fluids. Interfacial rheology has been found to be a key factor in the stability of foams and emulsions, compatibilization of polymer blends, flotation technology, fusion of vesicles, etc. (Langevin, 2000). Also, proteins, lipids, phase-separated domains, and other membrane-bound objects diffuse in the plane of an interface (Cicuta et al., 2007). Particle-laden interfaces have attracted much attention in recent years because of the tendency of colloidal particles to become (almost irreversibly) trapped at interfaces and their behavior once there has lead to their use in a wide variety of systems including drug delivery, stabilization of foams and emulsions, froth, flotation, or ice cream production. There still is a need to understand the colloidal interactions to have control over the structure and therefore the properties of the particle assemblies formed, specially because it has been pointed out that the interactions of the particles at interfaces are far more complex than in the bulk (Binks & Horozov, 2006; Bonales et al., 2011). In recent years books and reviews of particles at liquid interfaces have been published (Kralchewski & Nagayama, 2001). The dynamic properties of particle-laden interfaces are strongly influenced by direct interparticle forces (capillary, steric, electrostatic, van der Waals, etc.) and complicated hydrodynamic interactions mediated by the surrounding fluid. At macroscopic scales, the rheological properties of particle-laden fluid interfaces can be viewed as those of a liquidliquid interface with some effective surface viscoelastic properties described by effective shear and compressional complex viscoelastic moduli.

A significant fact is that for the simplest fluid-fluid interface, different dynamic modes have to be taken into account: the capillary (out of plane) mode, and the in-plane mode, which

and microrheology probe different aspects of the material: the former makes measurements over extremely long (macroscopic) length scales using a viscometric flow field, whereas the latter effectively measures material properties on the scale of the probe itself (Squires & Mason, 2010; Breedveld & Pine, 2003). As the probe increases in size, one might expect that micro- and macrorheology would converge, however, as it has been suggested, it is possible that macro- and microrheology techniques do not probe exactly the same physical properties because - even in the continuum (large probe) limit - one experiment uses a viscometric flow whereas the other does not (Kahir & Brady, 2005; Lee et al., 2010; Schmidt

One can distinguish two main families of microrheological experiments: One type of experiments focuses on the object itself; for example, the study of motor proteins aims at understanding the mechanical motions of the protein associated with enzymatic activities on the molecular level (Ou-Yang & Wei, 2010). The other type of experiment aims at understanding the local environment of the probe by observing changes in its random movements (Crocker & Grier, 1996; MacKintosh & Schmidt, 1999). Fundamentally different from relaxation kinetics, microrheology measures spontaneous thermal fluctuations without introducing major external perturbations into the systems being investigated. Other wellestablished methods in this family are dynamic light scattering (Dasgupta et al., 2002; Alexander & Dalgleish, 2007; Tassieri et al. 2010), and fluorescence correlation spectroscopy (Borsali & Pecora, 2008; Wöll et al., 2009). With recent advancement in spatial and temporal resolution to subnanometer and submillisecond, particle tracking experiments are now applicable to study of macromolecules (Pan et al., 2009) and intracellular components such as cytoskeletal networks (Cicuta & Donald, 2007). Detailed descriptions of the methods and applications of microrheology to the study of bulk systems have been given in review articles published in recent years (Crocker & Grier 1996; MacKintosh & Schmidt, 1999; Mukhopadhyay & Granick, 2001; Waigh, 2005; Gardel et al., 2005; Cicuta & Donald, 2007). Interfaces play a dominant role in the behavior of many complex fluids. Interfacial rheology has been found to be a key factor in the stability of foams and emulsions, compatibilization of polymer blends, flotation technology, fusion of vesicles, etc. (Langevin, 2000). Also, proteins, lipids, phase-separated domains, and other membrane-bound objects diffuse in the plane of an interface (Cicuta et al., 2007). Particle-laden interfaces have attracted much attention in recent years because of the tendency of colloidal particles to become (almost irreversibly) trapped at interfaces and their behavior once there has lead to their use in a wide variety of systems including drug delivery, stabilization of foams and emulsions, froth, flotation, or ice cream production. There still is a need to understand the colloidal interactions to have control over the structure and therefore the properties of the particle assemblies formed, specially because it has been pointed out that the interactions of the particles at interfaces are far more complex than in the bulk (Binks & Horozov, 2006; Bonales et al., 2011). In recent years books and reviews of particles at liquid interfaces have been published (Kralchewski & Nagayama, 2001). The dynamic properties of particle-laden interfaces are strongly influenced by direct interparticle forces (capillary, steric, electrostatic, van der Waals, etc.) and complicated hydrodynamic interactions mediated by the surrounding fluid. At macroscopic scales, the rheological properties of particle-laden fluid interfaces can be viewed as those of a liquidliquid interface with some effective surface viscoelastic properties described by effective shear

A significant fact is that for the simplest fluid-fluid interface, different dynamic modes have to be taken into account: the capillary (out of plane) mode, and the in-plane mode, which

et al., 2000; Oppong & de Bruyn, 2010).

and compressional complex viscoelastic moduli.

contains dilational (or extensional) and shear contributions. For more complex interfaces, such as thicker ones, other dynamic modes (bending, splaying) have to be considered (Miller & Liggieri, 2009). Moreover, the coupling of the abovementioned modes with adsorption/desorption kinetics may be very relevant for interfaces that contain soluble or partially soluble surfactants, polymers or proteins (Miller & Liggieri, 2009; Muñoz et al., 2000; Díez-Pascual et al. 2007). In the case of surface shear rheology, most of the information available has been obtained using macroscopic interfacial rheometers which in many cases work at low Boussinesq numbers (Barentin et al., 2000; Gavranovic et. al., 2005; Miller & Liggieri, 2009; Maestro et al., 2011.a). Microrheology has been foreseen as a powerful method to study the dynamics of interfaces. In spite that the measurement of diffusion coefficients of particles attached to the interface is relatively straightforward with modern microrheological techniques, many authors have relied on hydrodynamic models of the viscoelastic surroundings traced by the particles in order to obtain variables such as interfacial elasticity or shear viscosity. The more complex the structure of the interface the stronger are the assumptions of the model, and therefore it is more difficult to check their validity. In the present work we will briefly review modern microrheology experimental techniques, and some of the recent results obtained for bulk and interfacial systems. Finally, we will summarize the theoretical models available for calculating the shear microviscosity of fluid monolayers from particle tracking experiments, and discuss the results for some systems.
