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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.

Emerging evidence points to coordinated action of chemical and mechanical cues during brain development. At early stages of neocortical development, angiogenic factors and chemokines such as CXCL12, ephrins, and semaphorins assume crucial roles in orchestrating neuronal migration and axon elongation of postmitotic neurons. Here we explore the intrinsic mechanical properties of the developing marginal zone of the pallium in the migratory pathways and brain distribution of the pioneer Cajal-Retzius cells. These pioneer neurons are generated in several proliferative regions in the developing brain (e.g., the cortical hem and the pallial subpallial boundary) and migrate tangentially in the preplate/marginal zone covering the upper portion of the neocortex. These cells play crucial roles in correct neocortical layer formation by secreting several molecules such as Reelin. Our results indicate that the motogenic properties of Cajal-Retzius cells and their perinatal distribution in the marginal zone are also modulated by both chemical and mechanical factors, by the specific mechanical properties of Cajal-Retzius cells, and by the differential stiffness of the migratory routes. Indeed, cells originating in the cortical hem display higher migratory capacities than those generated in the pallial subpallial boundary which may be involved in the differential distribution of these cells in the dorsal-lateral axis in the developing marginal zone.

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)’.

Correction to: Communications Physics https://doi.org/10.1038/s42005-020-00492-1, published online 4 December 2020.

We study a liquid-gas front propagation in a modulated Hele-Shaw cell by means of multiphase computational fluid mechanics based on the three-dimensional Navier-Stokes equations. In the simulations an obstacle that partially fills the gap is placed at the center of the cell, and the liquid-gas interface is driven at a constant velocity. We study the morphological differences between imbibition and drainage for a wide range of capillary numbers, and explore how the wetting properties of the constriction affect the amount of liquid that remains trapped in the draining process. We observe increasing remaining volumes with increasing capillary number and decreasing contact angle. The present CFD implementation for a single mesa defect provides insight into a wide number of practical applications.

Cyclic fluid-fluid displacements in disordered media feature hysteresis, multivaluedness, and memory properties in the pressure-saturation relationship. Quantitative understanding of the underlying pore-scale mechanisms and their extrapolation across scales constitutes a major challenge. Here we find that the capillary action of a single constriction in the fluid passage contains the key features of hysteresis. This insight forms the building block for an ab initio model that provides the quantitative link between the microscopic capillary physics, spatially-extended collective events (Haines jumps) and large-scale hysteresis. The mechanisms identified here apply to a broad range of problems in hydrology, geophysics and engineering., R.H. acknowledges partial support from the Israeli Science Foundation (#ISF-867/13); M.D. and J.O. received support from the Spanish Ministry of Science and Innovation through the project HydroPore (PID2019-106887GB-C31 and C32). R.P. and J.O. received support from AGAUR (Generalitat de Catalunya) through grant 2017-SGR-1061.

We experimentally analyze the intermittent nature of granular silo flow when the discharge is controlled by an extracting belt at the bottom. We discover the existence of four different scenarios. For low extraction rates, the system is characterized by an on-off intermittency. When the extraction rate is increased the structure functions of the grains velocity increments, calculated for different lag times, reveal the emergence of multifractal intermittency. Finally, for very high extraction rates that approach the purely gravitational discharge, we observe that the dynamics become dependent on the outlet size. For large orifices the behavior is monofractal, whereas for small ones, the fluctuations of the velocity increments deviate from Gaussianity even for very large time lags.

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.

We consider the displacement of an inviscid fluid (air) by a viscous fluid (oil) in a narrow channel with gap-thickness modulations. The interfacial dynamics of this problem is strongly nonlocal and exhibits competing effects from capillarity and permeability. We derive analytical predictions of steady-state front morphologies, which are exact at linear level in the case of a persistent modulation in the direction of front advancement. The theoretical predictions are in good agreement with experimental measurements of steady-state front morphologies obtained in a Hele-Shaw cell with modulations of the channel depth, consisting on three parallel tracks of reduced depth, for small gap modulations. The relative average distance between theoretical and experimental fronts in the region around the central track is smaller than about 4%, provided that the height of the tracks is less than 13% of the total channel depth and the local distortion of the front height h is small enough (|∇h

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.

We review our work on the invasion of a model open fracture by a viscous wetting fluid , in the context of research on the spatiotemporal dynamics of fronts in disordered media . The model consists on a Hele-Shaw cell with randomly-distributed dichotomic variations of gap thickness. Distortions of the advancing front produced by fluctuations in capillary pressure and permeability are damped by interfacial tension and fluid viscosity . Competition of forces at different length scales makes that an initially flat front undergoes a kinetic roughening process , leading to a statistically-stationary state characterized by critical interfacial fluctuations and a collective avalanche dynamics . Using fast and high-resolution imaging we are able to track the evolution of the advancing front in space and time with high accuracy. The motion of the front takes place by localized bursts whose lateral sizes, areas and durations are found to be power-law distributed–up to a cutoff scale which diverges as the capillary number of the displacement \(\text {Ca} \rightarrow 0\), a limit corresponding to a critical depinning transition . A scale-dependent statistical analysis of the temporal behavior of the spatially-averaged velocity of the front reveals the presence of non-Gaussian fluctuations , strongly intermittent dynamics and global avalanches.

The dynamics of a fluid in a vertical tube, subjected to an oscillatory pressure gradient, is studied experimentally for both a Newtonian and a viscoelastic shear-thinning fluid. Particle image velocimetry is used to determine the two-dimensional velocity fields in the vertical plane of the tube axis, in a range of driving amplitudes from 0.8 to 2.5 mm and of driving frequencies from 2.0 to 11.5 Hz. The Newtonian fluid exhibits a laminar flow regime, independent of the axial position, in the whole range of drivings. For the complex fluid, instead, the parallel shear flow regime exhibited at low amplitudes [Torralba, Phys. Rev. E 72, 016308 (2005)] becomes unstable at higher drivings against the formation of symmetric vortices, equally spaced along the tube. At even higher drivings the vortex structure itself becomes unstable, and complex nonsymmetric structures develop. Given that inertial effects remain negligible even at the hardest drivings (Re < 10(-1)), it is the complex rheology of the fluid that is responsible for the instabilities observed. The system studied represents an interesting example of the development of shear-induced instabilities in nonlinear complex fluids in purely parallel shear flow.

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.

We report new experimental results of the oscillatory flow of a solution of giant micelles in a narrow vertical tube. We explore small driving amplitudes (laminar flow) and a large range of driving frequencies. High-resolution particle image velocimetry measurements of the flow field in a meridional plane of the tube show that the velocity magnitude at the tube axis peaks at well-defined resonance frequencies, where the phase lag with the forcing changes abruptly. The velocity field is highly inflectional and eventually exhibits some hints of shear banding. The results are compared with theoretical predictions based on the upper-convected Maxwell and Oldroyd-B models of the linear shear rheology of the solution, and observed coincidences and discrepancies are discussed in detail.

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

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.

In recent years, large amplitude oscillatory shear (LAOS) has become a prime tool to investigate the nonlinear rheology of complex fluids. More specifically, most studies use LAOS data as a macroscopic probe for hypothetical microscopic changes, sometimes successfully. Nevertheless, we would like to raise awareness on the potential impact of secondary flows triggered by instabilities in LAOS performed in curved shear flows exemplified by the Taylor–Couette geometry. First, we show that even for Newtonian fluids, where no micro-structural changes are expected, complex flow patterns can emerge in the LAOS data. Second, we stress the potential impact of similar effects in complex fluids by studying LAOS flows of a well-known shear-banding surfactant solution. Our hope is that our thorough study of the Newtonian case together with preliminary experiments on a complex fluid will reinforce the already successful analogy existing between inertial and elastic instabilities, suggest caution for future LAOS studies focused solely on a structural perspective, and open new research avenues combining flow instabilities and unsteady flows in complex fluids.

We present an overview of hysteresis phenomena in the martensitic transformation, and their relevance in the thermomechanical behaviour of shape-memory alloys. The first part of the paper introduces the concept of hysteresis, and the related phenomena of branching, dissipation and memory. The second part deals with revising some aspects of the thermomechanical behaviour of shape-memory alloys, emphasizing the hysteretic behaviour of single crystals and polycrystals under different driving conditions. The last part of the work is dedicated to the problem of modelling hysteresis phenomena in shape-memory alloys. Our focus is on phenomenological approaches which, as shown in the paper, account for the memory properties observed in hysteretic trajectories and open the possibility of deriving a generic energy balance for systems with hysteresis.

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.

The destabilization of rectilinear oscillatory pipe flow and the formation of vortex rings in a wormlike micellar solution, CPyCl/NaSal [100:60] mM, oscillated in a vertical cylinder of large aspect ratio, has been studied by means of time-resolved-particle image velocimetry measurements in a meridional plane of the cylinder. The flow was inertialess (Re

We present an efficient algorithm that, combined with a max-flow, min-cut minimization algorithm, makes it possible to find the ground states of the Gaussian Random Field Ising model when the external applied field B is continuously varied from ?∞ to +∞. The algorithm exactly finds all the possible ground states and their limiting range (Bmin, Bmax). Examples of the dependence of the magnetization and energy with B are shown for the 2d-RFIM.

This work focuses on the macroscopic behaviour of a large family of first-order phase transitions, including thermoelastic martensitic transformations, which are practically insensitive to thermal fluctuations and need to be driven by an external field. The Random Field Ising Model at T = 0 is used to carry out a detailed study of the dynamics and thermodynamics of this family of fluctuationless transitions. The main difficulties expected for performing the same kind of analysis on martensitic transformations are outlined.

We introduce a modification to Hele-Shaw flows consisting of a rotating cell. A viscous fluid (oil) is injected at the rotation axis of the cell, which is open to air. The morphological instability of the oil-air interface is thus driven by centrifugal force and is controlled by the density (not viscosity) difference. We derive the linear dispersion relation and verify the maximum growth rate selection of initial patterns within experimental uncertainty. The nonlinear growth regime is studied in the case of vanishing injection rate. Several characteristic lengths are studied to quantify the patterns obtained. Experimental data exhibit good collapse for two characteristic lengths, namely, the radius of gyration and the radial finger length, which in the nonlinear regime appear to grow linearly in time.

We have systematically analyzed six different reticular models with quenched disorder and no thermal fluctuations exhibiting a field-driven first-order phase transition. We have studied the nonequilibrium transition, appearing when varying the amount of disorder, characterized by the change from a discontinuous hysteresis cycle (with one or more large avalanches) to a smooth one (with only tiny avalanches). We have computed critical exponents using finite size scaling techniques and shown that they are consistent with universal values depending only on the space dimensionality d.

An experimental study of the acoustic emission generated during a martensitic transformation is presented. A statistical analysis of the amplitude and lifetime of a large number of signals has revealed power-law behavior for both magnitudes. The exponents of these distributions have been evaluated and, through independent measurements of the statistical lifetime to amplitude dependence, we have checked the scaling relation between the exponents. Our results are discussed in terms of current ideas on avalanche dynamics.

An experimental realization is presented of the problem of heat conduction along a one‐dimensional rod subjected to an externally imposed constant temperature difference and allowing for heat losses to the environment. One end of the rod is at a fixed elevated temperature, while, untypically, both the lateral surface and far end of the rod are considered to be at the same fixed lower temperature. Newton’s Law of Cooling has been invoked as a boundary condition. The experimental results are used to illustrate some fundamental concepts of nonequilibrium thermodynamics such as the meaning and temporal evolution of the different contributions to the entropy balance equation, including entropy production, and the influence of initial and boundary conditions on the steady state.

The authors report a systematic calorimetric study of the formation of the R-phase in a polycrystalline TiNi:Fe alloy, conducted using a high-sensitivity scanning device. Thermograms performed at very slow heating/cooling rates always appear as an overlap of two peaks. The high-temperature peak does not present any hysteresis and is associated with a continuous transition to the intermediate incommensurate phase. Extrapolation at zero heating/cooling rates gives a value of 1.8 K for the intrinsic thermal hysteresis of the second peak at lower temperatures, ascribed to the first-order transition from the incommensurate to the R-phase. The paper also reports ultrasonic measurements on this alloy. Elastic anomalies in both longitudinal and shear elastic constants and in the ultrasonic attenuation have been detected in the same temperature region as the overall thermal effect.

This paper describes a high-sensitivity calorimeter which is capable of carrying out measurements on samples whilst they are subjected to uniaxial tensile stress. It is shown how this device can be...

Viscous fingering dynamics driven by centrifugal forcing is studied for arbitrary viscosity contrast. Theoretical methods, including exact solutions, and numerics based on a phase-field approach are used. Both confirm that pinch-off singularities in patterns originated from the centrifugally driven instability may occur spontaneously and be inherent to the two-dimensional Hele-Shaw dynamics. They are systematically more frequent for lower viscosity contrasts consistently with experimental evidence. The analytical insights provide an interpretation of this fact in terms of the asymptotic matching of the different regions of the fingering patterns. The phase-field numerical scheme is shown to be particularly adequate to elucidate the existence of finite-time singularities through the dependence of the singularity time on the interface thickness, in particular for varying viscosity contrast.

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.

Measurements of the enthalpy ([MATH]H) and entropy ([MATH]S) changes associated with the martensitic transformation of Cu-Al-Be single crystals of different compositions, were performed by differential scanning calorimetry. In addition, the elastic constants of the body-centered-cubic parent phase single crystals were measured as a function of temperature, using the ultrasonic pulse-echo frequency varying - phase detection method, and the value of the elastic anisotropy (A = C44/C') was computed at the martensitic transformation temperature. The results are in good agreement with a theoretical expression obtained according to models previously proposed, which relates [MATH]S to the elastic anisotropy of the parent phase at the martensitic transformation temperature.

This work reviews different approaches to the thermodynamics of the martensitic transformation in shape-memory alloys developed in the last years, and attempts to give a general unified version in terms of an energy balance which not only considers equilibrium situations but includes as well the possibility of dissipative effects. The thermoelastic transformation is studied in a quasistatic continuous formalism which results from the assumption that the characteristic relaxation times between thermoelastic equilibrium states are comparatively negligible. The analysis reveals the role of different energy contributions (chemical, elastic and dissipative) in the transformation, and the possibility of their evaluation from calorimetric measurements. Concerning hysteresis, we review the memory properties of partial cycles common to this whole class of systems, and present a number of recent approaches developed to model these properties.

We report on an experimental study of long normal Saffman-Taylor fingers subject to periodic forcing. The sides of the finger develop a low amplitude, long wavelength instability. We discuss the finger response in stationary and nonstationary situations, as well as the dynamics towards the stationary states. The response frequency of the instability increases with forcing frequency at low forcing frequencies, while, remarkably, it becomes independent of forcing frequency at large forcing frequencies. This implies a process of wavelength selection. These observations are in good agreement with previous numerical results reported in [Ledesma-Aguilar et al., Phys. Rev. E 71, 016312 (2005)]. We also study the average value of the finger width, and its fluctuations, as a function of forcing frequency. The average finger width is always smaller than the width of the steady-state finger. Fluctuations have a nonmonotonic behavior with a maximum at a particular frequency.

The scaling properties of the rough liquid-air interface formed in the spontaneous imbibition of a viscous liquid by a model porous medium are found to be very sensitive to the magnitude of the pressure difference applied at the liquid inlet. Interface fluctuations change from obeying intrinsic anomalous scaling at large negative pressure differences, to being super-rough with the same dynamic exponent z approximately =3 at less negative pressure differences, to finally obeying ordinary Family-Vicsek scaling with z approximately =2 at large positive pressure differences. This rich scenario reflects the relative importance on different length scales of capillary and permeability disorder, and the role of surface tension and viscous pressure in damping interface fluctuations.

We make an experimental characterization of the effect that static disorder has on the shape of a normal Saffman-Taylor finger. We find that static noise induces a small amplitude and long wavelength instability on the sides of the finger. Fluctuations on the finger sides have a dominant wavelength, indicating that the system acts as a selective amplifier of static noise. The dominant wavelength does not seem to be very sensitive to the intensity of static noise present in the system. On the other hand, at a given flow rate, rms fluctuations of the finger width, decrease with decreasing intensity of static noise. This might explain why the sides of the fingers are flat for typical Saffman-Taylor experiments. Comparison with previous numerical studies of the effect that temporal noise has on the Saffman-Taylor finger, leads to conclude that the effect of temporal noise and static noise are similar. The behavior of fluctuations of the finger width found in our experiments, is qualitatively similar to one recently reported, in the sense that, the magnitude of the width fluctuations decays as a power law of the capillary number, at low flow rates, and increases with capillary number for larger flow rates.

We analyze the energy terms corresponding to the spin-spin exchange and spin-random field coupling of the zero temperature random-field Ising model on the Bethe lattice driven by an external field with metastable dynamics. Exact results are calculated as a function of the standard deviation of the disorder and the coordination number z, and compared with numerical simulations on random graphs for z=4, for which a disorder-induced transition takes place.

We present the dynamic velocity profiles of a Newtonian fluid (glycerol) and a viscoelastic Maxwell fluid (CPyCl/NaSal in water) driven by an oscillating pressure gradient in a vertical cylindrical pipe. The frequency range explored has been chosen to include the first three resonance peaks of the dynamic permeability of the viscoelastic fluid / pipe system. Three different optical measurement techniques have been employed. Laser Doppler Anemometry has been used to measure the magnitude of the velocity at the centre of the liquid column. Particle Image Velocimetry and Optical Deflectometry are used to determine the velocity profiles at the bulk of the liquid column and at the liquid--air interface respectively. The velocity measurements in the bulk are in good agreement with the theoretical predictions of a linear theory. The results, however, show dramatic differences in the dynamic behaviour of Newtonian and viscoelastic fluids, and demonstrate the importance of resonance phenomena in viscoelastic fluid flows, biofluids in particular, in confined geometries., Paper to be published in Physical Review E, other related papers in http://www.cie.unam.mx/~arp

We study the fingering instability of a circular interface between two immiscible liquids in a radial Hele-Shaw cell. The cell rotates around its vertical symmetry axis, and the instability is driven by the density difference between the two fluids. This kind of driving allows studying the interfacial dynamics in the particularly interesting case of an interface separating two liquids of comparable viscosity. An accurate experimental study of the number of fingers emerging from the instability reveals a slight but systematic dependence of the linear dispersion relation on the gap spacing. We show that this result is related to a modification of the interface boundary condition which incorporates stresses originated from normal velocity gradients. The early nonlinear regime shows nearly no competition between the outgrowing fingers, characteristic of low viscosity contrast flows. We perform experiments in a wide range of experimental parameters, under conditions of mass conservation (no injection), and characterize the resulting patterns by data collapses of two characteristic lengths: the radius of gyration of the pattern and the interface stretching. Deep in the nonlinear regime, the fingers which grow radially outwards stretch and become gradually thinner, to a point that the fingers pinch and emit drops. We show that the amount of liquid emitted in the first generation of drops is a constant independent of the experimental parameters. Further on there is a sharp reduction of the amount of liquid centrifugated, punctuated by periods of no observable centrifugation.

We show, both theoretically and experimentally, that the interface between two viscous fluids in a Hele-Shaw cell can be nonlinearly unstable before the Saffman-Taylor linear instability point is reached. We identify the family of exact elastica solutions [Nye et al., Eur. J. Phys. 5, 73 (1984)]] as the unstable branch of the corresponding subcritical bifurcation which ends up at a topological singularity defined by interface pinchoff. We devise an experimental procedure to prepare arbitrary initial conditions in a Hele-Shaw cell. This is used to test the proposed bifurcation scenario and quantitatively asses its practical relevance.

We report experiments on spontaneous imbibition of a viscous fluid by a model porous medium in the absence of gravity. The average position of the interface satisfies Washburn's law. Scaling of the interface fluctuations provides a dynamic exponent z \simeq 3, indicative of global dynamics driven by capillary forces. The complete set of exponents clearly shows that interfaces are not self-affine, exhibiting distinct local and global scaling, both for time (b=0.64\pm 0.02, b* =0.33 \pm 0.03) and space (a=1.94 \pm 0.20, a_loc=0.94 \pm 0.10). These values are compatible with an intrinsic anomalous scaling scenario., Comment: 4 pages, 5 figures

We present a weakly nonlinear analysis of the interface dynamics in a radial Hele-Shaw cell driven by both injection and rotation. We extend the systematic expansion introduced in [E. Alvarez-Lacalle et al., Phys. Rev. E 64, 016302 (2001)] to the radial geometry, and compute explicitly the first nonlinear contributions. We also find the necessary and sufficient condition for the uniform convergence of the nonlinear expansion. Within this region of convergence, the analytical predictions at low orders are compared satisfactorily to exact solutions and numerical integration of the problem. This is particularly remarkable in configurations (with no counterpart in the channel geometry) for which the interplay between injection and rotation allows that condition to be satisfied at all times. In the case of the purely centrifugal forcing we demonstrate that nonlinear couplings make the interface more unstable for lower viscosity contrast between the fluids.

The kinetic roughening of a stable oil--air interface, moving in a Hele--Shaw cell which contains a quenched columnar disorder (tracks) has been studied. A capillary effect is responsible for the dynamic evolution of the resulting rough interface, which exhibits anomalous scaling. The three independent exponents needed to characterize the anomalous scaling are determined experimentally. The anomalous scaling is explained in terms of the initial acceleration and subsequent deceleration of the interface tips in the tracks coupled by mass conservation. A phenomenological model that reproduces the measured global and local exponents has been introduced., Comment: 4 pages, 5 figures, uses epsf. To appear in PRL

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 ~= 0.5 that is almost independent of the experimental parameters. The analysis of the roughness exponent alpha through the power spectrum have shown different behaviors at short (alpha_1) and long (alpha_2) length scales, separated by a crossover wavenumber q_c. The values of the measured roughness exponents depend on experimental parameters, but at large velocities we obtain alpha_1 ~= 1.3 independently of the disorder configuration. The dependence of the crossover wavenumber with the experimental parameters has also been investigated, measuring q_c ~ v^{0.47} for the shortest persistence length, in agreement with theoretical predictions., 20 pages, 22 figures

We study the forced fluid invasion of an air-filled model porous medium at constant flow rate, in 1+1 dimensions, both experimentally and theoretically. We focus on the non-local character of the interface dynamics, due to liquid conservation, and its effect on the scaling properties of the interface upon roughening. Specifically, we study the limit of large flow rates and weak capillary forces. Our theory predicts a roughening behaviour characterized at short times by a growth exponent $\beta_1 = 5/6$, a roughness exponent $\alpha_1=5/2$, and a dynamic exponent $z_1=3$, and by $\beta_2=1/2$, $\alpha_2=1/2$, and $z_2=1$ at long times, before saturation. This theoretical prediction is in good agreement with the experiments at long times.The ensemble of experiments, theory, and simulations provides evidence for a new universality class of interface roughening in 1+1 dimensions., Comment: 7 pages, 3 figures, EuroTeX (style included), accepted in Europhysics Letters

The radial displacement of a fluid annulus in a rotating circular HeleShaw cell has been investigated experimentally. It has been found that the flow depends sensitively on the wetting conditions at the outer interface. Displacements in a prewet cell are well described by Darcy"s law in a wide range of experimental parameters, with little influence of capillary effects. In a dry cell, however, a more careful analysis of the interfacemotion is required; the interplay between a gradual loss of fluid at the inner interface, and the dependence of capillary forces at the outer interface on interfacial velocity and dynamic contact angle, result in a constant velocity for the interfaces. The experimental results in this case correlate in the form of an empirical scaling relation between the capillary number Ca and a dimensionless group, related to the ratio of centrifugal to capillary forces, which spans about three orders of magnitude in both quantities. Finally, the relative thickness of the coating film left by the inner interface is obtained as a function of Ca.

Acoustic emission avalanche distributions are studied in different alloy systems that exhibit a phase transition from a bcc to a close-packed structure. After a small number of thermal cycles through the transition, the distributions become critically stable (exhibit power-law behavior) and can be characterized by an exponent $\ensuremath{\alpha}$. The values of $\ensuremath{\alpha}$ can be classified into universality classes, which depend exclusively on the symmetry of the resulting close-packed structure.