Local rheological probes for complex fluids: application to Laponite suspensions

Viscoelastic Properties of ECM-Rich Embryonic Microenvironments

The material properties of tissues and their mechanical state is an important factor in development, disease, regenerative medicine and tissue engineering. Here we describe a microrheological measurement technique utilizing aggregates of microinjected ferromagnetic nickel particles to probe the viscoelastic properties of embryonic tissues. Quail embryos were cultured in a plastic incubator chamber located at the center of two pairs of crossed electromagnets. We found a pronounced viscoelastic behavior within the ECM-rich region separating the mesoderm and endoderm in Hamburger Hamilton stage 10 quail embryos, consistent with a Zener (standard generalized solid) model. The viscoelastic response is about 45% of the total response, with a characteristic relaxation time of 1.3 s.

A mesoscale study of creep in a microgel using the acoustic radiation force

We study the motion of a sphere of diameter 330 μm embedded in a Carbopol microgel under the effect of the acoustic radiation pressure exerted by a focused ultrasonic field. The sphere motion within the microgel is tracked using videomicroscopy and compared to conventional creep and recovery measurements performed with a rheometer. We find that under moderate ultrasonic intensities, the sphere creeps as a power law of time with an exponent α ≃ 0.2 that is significantly smaller than the one inferred from global creep measurements below the yield stress of the microgel (α ≃ 0.4). Moreover, the sphere relaxation motion after creep and the global recovery are respectively consistent with these two different exponents. By allowing a rheological characterization at the scale of the sphere with forces of the order of micronewtons, the present experiments pave the way for acoustic "mesorheology" which probes volumes and forces an intermediate between standard macroscopic rheology and classical microrheology. They also open new questions about the effects of the geometry of the deformation field and of the sphere size and surface properties on the creep behaviour of soft materials.

Microrheology of colloidal systems

Microrheology was proposed almost twenty years ago as a technique to obtain rheological properties in soft matter from the microscopic motion of colloidal tracers used as probes, either freely diffusing in the host medium, or subjected to external forces. The former case is known as passive microrheology, and is based on generalizations of the Stokes-Einstein relation between the friction experienced by the probe and the host-fluid viscosity. The latter is termed active microrheology, and extends the measurement of the friction coefficient to the nonlinear-response regime of strongly driven probes. In this review article, we discuss theoretical models available in the literature for both passive and active microrheology, focusing on the case of single-probe motion in model colloidal host media. A brief overview of the theory of passive microrheology is given, starting from the work of Mason and Weitz. Further developments include refined models of the host suspension beyond that of a Newtonian-fluid continuum, and the investigation of probe-size effects. Active microrheology is described starting from microscopic equations of motion for the whole system including both the host-fluid particles and the tracer; the many-body Smoluchowski equation for the case of colloidal suspensions. At low fluid densities, this can be simplified to a two-particle equation that allows the calculation of the friction coefficient with the input of the density distribution around the tracer, as shown by Brady and coworkers. The results need to be upscaled to agree with simulations at moderate density, in both the case of pulling the tracer with a constant force or dragging it at a constant velocity. The full many-particle equation has been tackled by Fuchs and coworkers, using a mode-coupling approximation and the scheme of integration through transients, valid at high densities. A localization transition is predicted for a probe embedded in a glass-forming host suspension. The nonlinear probe-friction coefficient is calculated from the tracer's position correlation function. Computer simulations show qualitative agreement with the theory, but also some unexpected features, such as superdiffusive motion of the probe related to the breaking of nearest-neighbor cages. We conclude with some perspectives and future directions of theoretical models of microrheology.

Combined passive and active microrheology study of protein-layer formation at an air-water interface

We investigate the mechanical properties of layers of the protein beta-lactoglobulin during their formation at the air-water interface using a combination of passive and active microrheological techniques. The passive microrheology, which employs multiple particle tracking measurements using spherical colloids, indicates that the interfacial rheology evolves over time through three stages as protein adsorbs at the interface: (i) an increase in viscosity, (ii) a period of spatial heterogeneity in which the interface contains elastic and viscous regions, and (iii) the development of a uniformly rigid elastic film. Varying solution pH between pH = 5.2, the isoelectric point of beta-lactoglobulin, and pH = 7.0 has no qualitative effect on this mechanical evolution. The active microrheology, which employs ferromagnetic nanowires rotating in response to magnetic torques, similarly shows an increasing interfacial viscosity at early times and evidence of mechanical heterogeneity at intermediate times. However, at late times, the nanowire mobility becomes strongly pH dependent. For pH = 5.2, the layer responds as a rigid elastic film to the stress imposed by the wire. For pH = 7.0, it displays a viscous response that contrasts with the passive measurements. We associate this contrast with a nonlinear response to the wire at late times that reflects a low yield stress of the film at higher pH. This ability to compare passive and active measurements demonstrates the advantage of applying multiple microrheological methods to resolve ambiguity in any single approach.

Evaporation of an emulsion trapped in a yield stress fluid

The present work deals with emulsions of volatile alkanes in an aqueous clay suspension, Laponite, which forms a yield stress fluid. For a large enough yield stress (i.e. Laponite concentration), the oil droplets are prevented from creaming and the emulsions are thus mechanically stabilized. We have studied the evaporation kinetics of the oil phase of those emulsions in contact with the atmosphere. We show that the evaporation process is characterized by the formation of a sharp front separating the emulsion from a droplet-free Laponite phase, and that the displacement of the front vs. time follows a diffusion law. Experimental data are confronted to a diffusion-controlled model, in the case where the limiting step is the diffusion of the dissolved oil through the aqueous phase. The nature of the alkane, as well as its volume fraction in the emulsion, has been varied. Quantitative agreement with the model is achieved without any adjustable parameter and we describe the mechanism leading to the formation of a front.

Gelation on the microscopic scale

Particle-tracking methods are used to study gelation in a colloidal suspension of Laponite clay particles. We track the motion of small fluorescent polystyrene spheres added to the suspension, and obtain the micron-scale viscous and elastic moduli of the material from their mean-squared displacement. The fluorescent spheres move subdiffusively due to the microstructure of the suspension, with the diffusive exponent decreasing from close to one at early times to near zero as the material gels. The particle-tracking data show that the system becomes more heterogeneous on the microscopic scale as gelation proceeds. We also determine the bulk-scale moduli using small-amplitude oscillatory shear rheometry. Both the macroscopic and microscopic moduli increase with time, and on both scales we observe a transition from a primarily viscous fluid to an elastic gel. We find that the gel point, determined as the time at which the viscous and elastic moduli are equal, is length-scale dependent--gelation occurs earlier on the bulk scale than on the microscopic scale.

Particle tracking to reveal gelation of hectorite dispersions

Passive microrheological techniques using particle tracking have been developed for the study of the gelation of hectorite suspensions. By following the Brownian motion of the particles, it is possible to determine the increasing caging of the particles with time, as the system gels. Since only the Brownian motion is followed, the gelation process itself should not be affected by the measurement. As gelation proceeds the increasing heterogeneity of the particle environments can be monitored by a variety of measures, including kurtosis. An effective viscosity can be extracted from the measurements and used to indicate the gelation process.

Aggregation behavior of two spheres falling through an aging fluid

We study the behavior of two spheres that settle along their line of center in a yield stress fluid that "ages:" a Laponite suspension. In such a fluid, the fluid flow behind a falling single particle can either exhibit a negative wake, i.e., an upward motion, or not, according to the stress exerted by the particle on the fluid. We show that, if their initial separation distance is smaller than 15 radii, two identical particles cluster whatever the wake's structure. In addition, in the conditions within which a negative wake is observed, we evidence an unexpected lateral motion of the spheres.

Use of Rigid Spherical Inclusions in Young’s Moduli Determination: Application to DNA-Crosslinked Gels

Current techniques for measuring the bulk shear or elastic (E) modulus of small samples of soft materials are usually limited by materials handling issues. This paper describes a nondestructive testing method based on embedded spherical inclusions. The technique simplifies materials preparation and handling requirements and is capable of continuously monitoring changes in stiffness. Exact closed form derivations of E as functions of the inclusion force-displacement relationship are presented. Analytical and numerical analyses showed that size effects are significant for medium dimensions up to several times those of the inclusion. Application of the method to DNA-crosslinked gels showed good agreement with direct compression tests.

Kinetics of ergodic-to-nonergodic transitions in charged colloidal suspensions: aging and gelation

There are two types of isotropic disordered nonergodic states in colloidal suspensions: colloidal glasses and gels. In a recent paper [H. Tanaka, J. Meunier, and D. Bonn, Phys. Rev. E 69, 031404 (2004)], we discussed the static aspect of the differences and the similarities between the two. In this paper, we focus on the dynamic aspect. The kinetics of the liquid-glass transition is called "aging," while that of the sol-gel transition is called "gelation." The former is primarily governed by repulsive interactions between particles, while the latter is dominated by attractive interactions. Slowing down of the dynamics during aging reflects the increasing cooperativity required for the escape of a particle from the cage formed by the surrounding particles, while that during gelation reflects the increase in the size of particle clusters towards the percolation transition. Despite these clear differences in the origin of the slowing down of the kinetics between the two, it is not straightforward experimentally to distinguish them in a clear manner. For an understanding of the universal nature of ergodic-to-nonergodic transitions, it is of fundamental importance to elucidate the differences and the similarities in the kinetics between aging and gelation. We consider this problem, taking Laponite suspension as an explicit example. In particular, we focus on the two types of nonergodic states: (i) an attractive gel formed by van der Waals attractions for high ionic strengths and (ii) a repulsive Wigner glass stabilized by long-range Coulomb repulsions for low ionic strengths. We demonstrate that the aging of colloidal Wigner glass crucially differs not only from gelation, but also from the aging of structural and spin glasses. The aging of the colloidal Wigner glass is characterized by the unique cage-forming regime that does not exist in the aging of spin and structural glasses.

Phase diagrams of Wyoming Na-montmorillonite clay. Influence of particle anisotropy

Natural Na-Wyoming montmorillonite was size fractionated by successive centrifugation. Polydisperse particles with average sizes of 400, 290, and 75 nm were then obtained. As the structural charge of the particles belonging to three fractions (determined by cationic exchange capacity measurements) is the same, such a procedure allows studying the effect of particle anisotropy on the colloidal phase behavior of swelling clay particles. Osmotic stress experiments were carried out at different ionic strengths. The osmotic pressure curves display a plateau whose beginning systematically coincides with the sol/gel transition determined by oscillatory stress measurements. The concentration corresponding to the sol/gel transition increases linearly with particle anisotropy, which shows that the sol/gel transition is not directly related to an isotropic/nematic transition of individual clay particles. Indeed, a reverse evolution should be observed for an I/N transition involving the individual clay particles. Still, when observed between crossed polarizer and analyzer, the gel samples exhibit permanent birefringent textures, whereas in the "sol" region, transient birefringence is observed when the samples are sheared. This suggests that interacting clay particles are amenable to generate, at rest and/or under shear, large anisotropic particle associations.

Rotational magnetic particles microrheology: the Maxwellian case

An experimental method based on the rotational dynamics of a magnetic probe is reported to measure the local viscoelasticity of soft materials on microscopic scales. The technique is based on the alignment of dipolar chains of submicrometer magnetic particles in the direction of an applied magnetic field. On one hand, light scattering is used to detect the chains' oscillations over a 0.001-100 Hz frequency range when submitted to an oscillating magnetic field and leads to global microrheological measurements. On the other hand, the chains' rotation toward a permanent magnetic field is observed with a microscope, allowing a local determination of viscoelastic properties on the scale of the chains of particles. We demonstrate the accuracy of both assays with a micellar Maxwellian solution and validate theoretical predictions.