Elastically-mediated collective organisation of magnetic microparticles.

Gels are soft elastic materials made of a three-dimensional cross-linked polymer network and featuring both elastic and dissipative responses under external mechanical stimuli. Here we investigate how such gels mediate the organization of embedded magnetic microparticles when driven by an external field. By constructing a continuum theory, we demonstrate that the collective dynamics of the embedded particles result from the delicate balance between magnetic dipole-dipole interactions, thermal fluctuations and elasticity of the polymer network, verified by our experiments. The proposed model could be extended to other soft magnetic composites in order to predict how the elastic interactions mediate the aggregation of the embedded elements, fostering technological implications for multifunctional hydrogel materials.

Stokes layers in oscillatory flows of viscoelastic fluids.

Oscillatory flows of viscoelastic fluids are studied from the perspective of Stokes viscoelastic layers. We identify the governing dimensionless variables, and study the flows in a general way for fluids with linear rheology. Nonlinearities can be treated perturbatively to account for reported flow instabilities. This article is part of the theme issue 'Stokes at 200 (Part 1)'.

Spatiotemporal Organization of Correlated Local Activity within Global Avalanches in Slowly Driven Interfaces.

We study the jerky response of slowly driven fronts in disordered media, just above the depinning transition. We focus on how spatially disconnected clusters of internally correlated activity lead to large-scale velocity fluctuations in the form of global avalanches and identify three different ways in which local activity clusters may organize within a global avalanche, depending on the distance to criticality. Our analysis provides new scaling relations between the power-law exponents of the statistical distributions of sizes and durations of local bursts and global avalanches. Fluid fronts of imbibition in heterogeneous media are taken as a case study to validate these scaling relations.

Laning, thinning and thickening of sheared colloids in a two-dimensional Taylor-Couette geometry.

We investigate the dynamics and rheological properties of a circular colloidal cluster that is continuously sheared by magnetic and optical torques in a two-dimensional (2D) Taylor-Couette geometry. By varying the two driving fields, we obtain the system flow diagram and report the velocity profiles along the colloidal structure. We then use the inner magnetic trimer as a microrheometer, and observe continuous thinning of all particle layers followed by thickening of the third one above a threshold field. Experimental data are supported by Brownian dynamics simulations. Our approach gives a unique microscopic view on how the structure of strongly confined colloidal matter weakens or strengthens upon shear, envisioning the engineering of rheological devices at the microscales.

Experimental study of stable imbibition displacements in a model open fracture. I. Local avalanche dynamics.

We report the results of an experimental investigation of the spatiotemporal dynamics of stable imbibition fronts in a disordered medium, in the regime of capillary disorder, for a wide range of experimental conditions. We have used silicone oils of various viscosities µ and nearly identical oil-air surface tension and forced them to slowly invade a model open fracture at different constant flow rates v. In this first part of the study we have focused on the local dynamics at a scale below the size of the quenched disorder. Changing µ and v independently, we have found that the dynamics is not simply controlled by the capillary number Ca∼µv. Specifically, we have found that the wide statistical distributions of local front velocities, and their large spatial correlations along the front, are indeed controlled by the capillary number Ca. However, local velocities exhibit also very large temporal correlations, and these correlations depend more strongly on the mean imposed velocity v than on the viscosity µ of the invading fluid. Correlations between local velocities lead to a burstlike dynamics. Avalanches, defined as clusters of large local velocities, follow power-law distributions-both in size and duration-with exponential cutoffs that diverge as Ca→0, the pinning-depinning transition of stable imbibition displacements. Large data sets have led to reliable statistics, from which we have derived accurate values of critical exponents of the relevant power-law distributions. We have investigated also the dependence of their cutoffs on µ and v and related them to the autocorrelations of local velocities in space and time.

Experimental study of stable imbibition displacements in a model open fracture. II. Scale-dependent avalanche dynamics.

We report the results of an experimental investigation of the spatiotemporal dynamics of stable imbibition fronts in a disordered medium, in the regime of capillary disorder, for a wide range of experimental conditions. We have used silicone oils of various viscosities µ and nearly identical oil-air surface tension, and forced them to slowly invade a model open fracture at very different flow rates v. In this second part of the study we have carried out a scale-dependent statistical analysis of the front dynamics. We have specifically analyzed the influence of µ and v on the statistical properties of the velocity V_{ℓ}, the spatial average of the local front velocities over a window of lateral size ℓ. We have varied ℓ from the local scale defined by our spatial resolution up to the lateral system size L. Even though the imposed flow rate is constant, the signals V_{ℓ}(t) present very strong fluctuations which evolve systematically with the parameters µ, v, and ℓ. We have verified that the non-Gaussian fluctuations of the global velocity V_{ℓ}(t) are very well described by a generalized Gumbel statistics. The asymmetric shape and the exponential tail of those distributions are controlled by the number of effective degrees of freedom of the imbibition fronts, given by N_{eff}=ℓ/ℓ_{c} (the ratio of the lateral size of the measuring window ℓ to the correlation length ℓ_{c}∼1/sqrt[µv]). The large correlated excursions of V_{ℓ}(t) correspond to global avalanches, which reflect extra displacements of the imbibition fronts. We show that global avalanches are power-law distributed, both in sizes and durations, with robustly defined exponents-independent of µ, v, and ℓ. Nevertheless, the exponential upper cutoffs of the distributions evolve systematically with those parameters. We have found, moreover, that maximum sizes ξ_{S} and maximum durations ξ_{T} of global avalanches are not controlled by the same mechanism. While ξ_{S} are also determined by ℓ/ℓ_{c}, like the amplitude fluctuations of V_{ℓ}(t), ξ_{T} and the temporal correlations of V_{ℓ}(t) evolve much more strongly with imposed flow rate v than with fluid viscosity µ.

Disorder-induced capillary bursts control intermittency in slow imbibition.

A multiscale analysis of the spatially averaged velocity of an imbibition front V_{ℓ}(t) measured at scale ℓ reveals that the slow front dynamics is intermittent: the distributions of ΔV_{ℓ}(τ)=V_{ℓ}(t+τ)-V_{ℓ}(t) evolve continuously through time scales τ, from heavy-tailed to Gaussian-reached at a time lag τ_{c} set by the extent of the medium heterogeneities. Intermittency results from capillary bursts triggered from the smallest scale of the disorder up to the scale ℓ_{c} at which viscous dissipation becomes dominant. The effective number of degrees of freedom of the front ℓ/ℓ_{c} controls its intensity.

Capillary rise in Hele-Shaw models of disordered media.

We study the capillary rise of a viscous liquid in large Hele-Shaw models of disordered media, both analytically and experimentally. Compared to the Fries-Dreyer and Lucas-Washburn solutions for capillary rise with and without gravity, our experimental data reveal a systematic deviation at short and intermediate times. The original pressure balance equation leading to Washburn's results is reformulated in order to include an additional resisting term, proportional to the mean velocity of the front h˙, which appears naturally as a result of the geometry of the cell. Analytical solutions h(t) are found for displacements with and without gravity. These new solutions reproduce the experimental results very accurately in Hele-Shaw cells of constant gap thickness, where the capillary pressure can be approximated by a constant. In cells of fluctuating gap thickness, where the capillary pressure fluctuates in space, a small additional pressure contribution is required. This correction that depends on h˙ is also studied.

Roughness and intermittent dynamics of imbibition fronts due to capillary and permeability disorder.

We follow the propagation of an air-liquid interface during forced-flow imbibition of a viscous wetting liquid by a random medium, using a high resolution fast camera. Our model disordered medium mimics an open fracture by a Hele-Shaw cell with a two-valued gap spacing randomly distributed in the fracture (or Hele-Shaw) plane. By systematically varying the imposed flow rate we achieve average imbibition front velocities in the range 0.057

Avalanches and non-Gaussian fluctuations of the global velocity of imbibition fronts.

We present an experimental study of the global velocity V(t) of a viscous fluid interface during forced-flow imbibition in a disordered medium. Our high resolution setup shows that the fronts display an intermittent behavior signature of a burstlike dynamics, with power-law distributed avalanches. When measured at scales comparable to the correlation length, velocity fluctuations follow an asymmetric non-Gaussian distribution, whose skewness increases with decreasing measuring window and/or injection flow rate, offering the effective number of degrees of freedom probed in our experiment.

Anomalous roughening in experiments of interfaces in Hele-Shaw flows with strong quenched disorder.

We report experimental evidence of anomalous kinetic roughening in the stable displacement of an oil-air interface in a Hele-Shaw cell with strong quenched disorder. The disorder consists of a random modulation of the gap spacing that is transverse to the growth direction (tracks). Experiments were performed by varying the average interface velocity and the gap spacing, and measuring the scaling exponents. The following values of the scaling exponents were obtained; beta approximately 0.50, beta* approximately 0.25, alpha approximately 1.0, alpha(loc) approximately 0.5, and z approximately 2. When there is no fluid injection, the interface is driven solely by capillary forces, and a higher value of beta of approximately beta=0.65 is measured. The presence of multiscaling and the particular morphology of the interfaces, characterized by large height differences that follow a Lévy distribution, confirms the existence of anomalous scaling. From a detailed study of the motion of the oil-air interface, we show that the anomaly is a consequence of different local velocities on the tracks plus the coupling in the motion between neighboring tracks. The anomaly disappears at high interface velocities, weak capillary forces, or when the disorder is not sufficiently persistent in the growth direction. We have also observed the absence of scaling when the disorder is very strong or when a regular modulation of the gap spacing is introduced.

Experiments of interfacial roughening in Hele-Shaw flows with weak quenched disorder.

We have studied the kinetic roughening of an oil-air interface in a forced imbibition experiment in a horizontal Hele-Shaw cell with quenched disorder. Different disorder configurations, characterized by their persistence length in the direction of growth, have been explored by varying the average interface velocity v and the gap spacing b. Through the analysis of the rms width as a function of time, we have measured a growth exponent beta approximately 0.5 that is almost independent of the experimental parameters. The analysis of the roughness exponent alpha through the power spectrum has shown different behaviors at short (alpha(1)) and long (alpha(2)) length scales, separated by a crossover wave number q(c). The values of the measured roughness exponents depend on experimental parameters, but at large velocities we obtain alpha(1) approximately 1.3 independently of the disorder configuration. The dependence of the crossover wave number with the experimental parameters has also been investigated, measuring q(c) approximately v(0.47) for the shortest persistence length, in agreement with theoretical predictions.