In the technique of microrheology, macroscopic rheological parameters as well as information about local structure are deduced from the behavior of microscopic probe particles under thermal or active forcing. Microrheology requires knowledge of the relation between macroscopic parameters and the force felt by a particle in response to displacements. We investigate this response function for a spherical particle using the two-fluid model, in which the gel is represented by a polymer network coupled to a surrounding solvent via a drag force. We obtain an analytic solution for the response function in the limit of small volume fraction of the polymer network, and neglecting inertial effects. We use no-slip boundary conditions for the solvent at the surface of the sphere. The boundary condition for the network at the surface of the sphere is a kinetic friction law, for which the tangential stress of the network is proportional to relative velocity of the network and the sphere. This boundary condition encompasses both no-slip and frictionless boundary conditions as limits. Far from the sphere there is no relative motion between the solvent and network due to the coupling between them. However, the different boundary conditions on the solvent and network tend to produce different far-field motions. We show that the far field motion and the force on the sphere are controlled by the solvent boundary conditions at high frequency and by the network boundary conditions at low frequency. At low frequencies compression of the network can also affect the force on the sphere. We find the crossover frequencies at which the effects of sliding of the sphere past the polymer network and compression of the gel become important.
Optical tweezers have been successfully adopted as exceptionally sensitive transducers for microrheology studies of complex 'fluids'. Despite the general trend, a similar approach cannot be adopted for microrheology studies of 'gel-like' materials, e.g. living cells.
Optical tweezers (OTs) can detect pico-Newton range forces operating on a colloidal particle trapped in a medium and have been successfully utilized to investigate complex systems with internal structures. Laponite clay particles in an aqueous medium self-assemble to form microscopic networks over time as electrostatic interactions between the particles gradually evolve in a physical aging process. We investigate the forced movements of an optically trapped micron-sized colloidal probe particle, suspended in an aging Laponite suspension, as the underlying Laponite microstructures gradually dev…
We present an extension of the two-point optical microrheology technique introduced by Crocker \textit{et al.} [Phys. Rev. Lett. \textbf{85}, 888 (2000)] to high frequencies. The correlated fluctuations of two probe spheres held by a pair of optical tweezers within a viscoelastic medium are determined using optical interferometry. A theoretical model is developed to yield the frequency-dependent one- and two-particle response functions from the correlated motion. We demonstrate the validity of this method by determining the one- and two-particle correlations in a semi-dilute solution of polyst…
We present an extensive experimental study and scaling analysis of friction of gelatin gels on glass. At low driving velocities, sliding occurs via propagation of periodic self-healing slip pulses whose velocity is limited by collective diffusion of the gel network. Healing can be attributed to a frictional instability occurring at the slip velocity $v = V_c$. For $v > V_c$, sliding is homogeneous and friction is ruled by the shear-thinning rheology of an interfacial layer of thickness of order the (nanometric) mesh size, containing a semi-dilute solution of polymer chain ends hanging from the…
We present an experimental evidence of self-healing shear cracks at a gel/glass interface. This system exhibits two dynamical regimes depending on the driving velocity : steady sliding at high velocity (> Vc = 100-125 μm/s), caracterized by a shear-thinning rheology, and periodic stick-slip dynamics at low velocity. In this last regime, slip occurs by propagation of pulses that restick via a ``healing instability'' occuring when the local sliding velocity reaches the macroscopic transition velocity Vc. At driving velocities close below Vc, the system exhibits complex spatio-temporal behavior.
The growth dynamics of an air finger injected in a visco-elastic gel (a PVA/borax aqueous solution) is studied in a linear Hele-Shaw cell. Besides the standard Saffmann-Taylor instability, we observe - with increasing finger velocities - the existence of two new regimes: (a) a stick-slip regime for which the finger tip velocity oscillates between 2 different values, producing local pinching of the finger at regular intervals, (b) a ``tadpole'' regime where a fracture-type propagation is observed. A scaling argument is proposed to interpret the dependence of the stick-slip frequency with the me…
The mechanical properties of polymer gels based on cytoskeleton proteins (e.g. actin) have been studied extensively due to their significant role in biological cell motility and in maintaining the cell's structural integrity. Microrheology is the natural method of choice for such studies due to its economy in sample volume, its wide frequency range, and its spatial sensitivity. In microrheology, the thermal motion of tracer particles embedded in a complex fluid is used to extract the fluid's viscoelastic properties. Comparing the motion of a single particle to the correlated motion of particle…
The motility of motile Amoeba proteus was examined using the technique of passive particle tracking microrheology, with the aid of newly-developed particle tracking software, a fast digital camera and an optical microscope. We tracked large numbers of endogeneous particles in the amoebae, which displayed subdiffusive motion at short time scales, corresponding to thermal motion in a viscoelastic medium, and superdiffusive motion at long time scales due to the convection of the cytoplasm. Subdiffusive motion was characterised by a rheological scaling exponent of 3/4 in the cortex, indicative of …
The ability to predict and/or control wall slip is a fundamental problem in the hydrodynamics of yield stress fluids, which is poorly understood to date and has important applications in bio- and micro-fluidic systems. Systematic measurements of steady flows of a simple yield stress fluid (Carbopol Ultrez 10) in a plane acrylic micro-channel are used to establish rigorous scaling laws for the wall velocity gradient and the slip velocity. By means of epi-fluorescent microscopy combined with a custom developed Digital Particle Image Velocimetry (DPIV) technique, times series of velocity fields w…
A experimental study of low Reynolds numbers unsteady pipe flows of a yield stress shear thinning fluid (Carbopol- 980) is presented. The investigation of the solid-fluid transition in a rheometric flow in the presence and in the ab- sence of the wall slip reveals a coupling between the irreversible deformation states and the wall slip phenomenon. Particularly, the presence of wall slip nearly suppresses the scaling of the deformation power deficit associated to the rheological hysteresis with the rate at which the material is forced. The irreversible solid-fluid transition and the wall slip b…
We present a simple and \emph{non-invasive} experimental procedure to measure the linear viscoelastic properties of cells by passive video particle tracking microrheology. In order to do this, a generalised Langevin equation is adopted to relate the time-dependent thermal fluctuations of a bead, chemically bound to the cell's \emph{exterior}, to the frequency-dependent viscoelastic moduli of the cell. It is shown that these moduli are related to the cell's cytoskeletal structure, which in this work is changed by varying the solution osmolarity from iso- to hypo-osmotic conditions. At high freq…
We study a model for the motion of a tracer particle inside an active gel, exposing the properties of the van Hove distribution of the particle displacements. Active events of a typical force magnitude give rise to non-Gaussian distributions, having exponential tails or side-peaks. The side-peaks appear when the local bulk elasticity of the gel is large enough and few active sources are dominant. We explain the regimes of the different distributions, and study the structure of the peaks for active sources that are susceptible to the elastic stress that they cause inside the gel. We show how th…
We characterize the scale-dependent rheological properties of mucus from the Chaetopterus marine worm and determine the intrinsic lengthscales controlling distinct rheological and structural regimes. Mucus produced by this ubiquitous filter feeder serves a host of roles including filtration, protection and trapping nutrients. The ease of clean mucus extraction coupled with similarities to human mucus rheology also make Chaetopterus mucus a potential model system for elucidating human mucus mechanics. We use optically trapped microsphere probes of 2-10 microns, to induce oscillatory strains and…
We report on the fluidization dynamics of an attractive gel composed of non-Brownian particles made of fused silica colloids. Extensive rheology coupled to ultrasonic velocimetry allows us to characterize the global stress response together with the local dynamics of the gel during shear startup experiments. In practice, after being rejuvenated by a preshear, the gel is left to age during a time $t_w$ before being submitted to a constant shear rate $\dot γ$. We investigate in detail the effects of both $t_w$ and $\dot γ$ on the fluidization dynamics and build a detailed state diagram of the ge…
The stress-induced yielding scenario of colloidal gels is investigated under rough boundary conditions by means of rheometry coupled to local velocity measurements. Under an applied shear stress, the fluidization of gels made of attractive carbon black particles suspended in a mineral oil is shown to involve a previously unreported shear rate response $\dot γ(t)$ characterized by two well-defined and separated timescales $τ_c$ and $τ_f$. First $\dot γ(t)$ decreases as a weak power law strongly reminiscent of the primary creep observed in numerous crystalline and amorphous solids, coined the "A…
In a diversity of physiological contexts, eukaryotic cells adhere to an extracellular matrix (ECM), a disordered network with complex nonlinear mechanics. Such cells can perform mechanosensation: using local force probing they can measure and respond to their substrate's mechanical properties. It remains unclear, however, how the mechanical complexity of the ECM at the cellular scale impacts mechanosensation. Here, we investigate the physical limits of mechanosensation imposed by the inherent structural disorder and nonlinear elastic response of the ECM. Using a theoretical framework for disor…
