Color-gradient-based phase-field equation for multiphase flow.

In this paper, the underlying problem with the color-gradient (CG) method in handling density-contrast fluids is explored. It is shown that the CG method is not fluid invariant. Based on nondimensionalizing the CG method, a phase-field interface-capturing model is proposed which tackles the difficulty of handling density-contrast fluids. The proposed formulation is developed for incompressible, immiscible two-fluid flows without phase-change phenomena, and a solver based on the lattice Boltzmann method is proposed. Coupled with an available robust hydrodynamic solver, a binary fluid flow package that handles fluid flows with high density and viscosity contrasts is presented. The macroscopic and lattice Boltzmann equivalents of the formulation, which make the physical interpretation of it easier, are presented. In contrast to existing color-gradient models where the interface-capturing equations are coupled with the hydrodynamic ones and include the surface tension forces, the proposed formulation is in the same spirit as the other phase-field models such as the Cahn-Hilliard and the Allen-Cahn equations and is solely employed to capture the interface advected due to a flow velocity. As such, similarly to other phase-field models, a so-called mobility parameter comes into play. In contrast, the mobility is not related to the density field but a constant coefficient. This leads to a formulation that avoids individual speed of sound for the different fluids. On the lattice Boltzmann solver side, two separate distribution functions are adopted to solve the formulation, and another one is employed to solve the Navier-Stokes equations, yielding a total of three equations. Two series of numerical tests are conducted to validate the accuracy and stability of the model, where we compare simulated results with available analytical and numerical solutions, and good agreement is observed. In the first set the interfacial evolution equations are assessed, while in the second set the hydrodynamic effects are taken into account.

Hyper-Ballistic Superdiffusion of Competing Microswimmers.

Hyper-ballistic diffusion is shown to arise from a simple model of microswimmers moving through a porous media while competing for resources. By using a mean-field model where swimmers interact through the local concentration, we show that a non-linear Fokker-Planck equation arises. The solution exhibits hyper-ballistic superdiffusive motion, with a diffusion exponent of four. A microscopic simulation strategy is proposed, which shows excellent agreement with theoretical analysis.

Structure-function relationships in the nasal cavity of Arctic and subtropical seals.

The heating and moistening of inhaled air, and the cooling and moisture removal from exhaled air, are crucial for the survival of animals under severe environmental conditions. Arctic mammals have evolved specific adaptive mechanisms to retain warmth and water and restrict heat loss during breathing. Here, the role of the porous turbinates of the nasal cavities of Arctic and subtropical seals is studied with this in mind. Mass and energy balance equations are used to compute the time-dependent temperature and water vapor profiles along the nasal passage. A quasi-1D model based on computed tomography images of seal nasal cavities is used in numerical simulations. Measured cross-sectional areas of the air channel and the perimeters of the computed tomography slices along the nasal cavities of the two seal species are used. The model includes coupled heat and vapor transfer at the air-mucus interface and heat transfer at the interfaces between the tissues and blood vessels. The model, which assumes constant blood flow to the nose, can be used to predict the temperature of the exhaled air as a function of ambient temperature. The energy dissipation (entropy production) in the nasal passages was used to measure the relative importance of structural parameters for heat and water recovery. We found that an increase in perimeter led to significant decreases in the total energy dissipation. This is explained by improved conditions for heat and water transfer with a larger complexity of turbinates. Owing to differences in their nasal cavity morphology, the Arctic seal is expected to be advantaged in these respects relative to the subtropical seal.

Capillary washboarding during slow drainage of a frictional fluid.

Numerous natural and industrial processes involve the mixed displacement of liquids, gases and granular materials through confining structures. However, understanding such three-phase flows remains a formidable challenge, despite their tremendous economic and environmental impact. To unveil the complex interplay of capillary and granular stresses in such flows, we consider here a model configuration where a frictional fluid (an immersed sedimented granular layer) is slowly drained out of a horizontal capillary. Analyzing how liquid/air menisci displace particles from such granular beds, we reveal various drainage patterns, notably the periodic formation of dunes, analogous to road washboard instability. Considering the competitive role of friction and capillarity, a 2D theoretical approach supported by numerical simulations of a meniscus bulldozing a front of particles provides quantitative criteria for the emergence of those dunes. A key element is the strong increase of the frictional forces, as the bulldozed particles accumulate and bend the meniscus horizontally. Interestingly, this frictional enhancement with the attack angle is also crucial in small-legged animals' locomotion over granular media.

Frictional fluid instabilities shaped by viscous forces.

Multiphase flows involving granular materials are complex and prone to pattern formation caused by competing mechanical and hydrodynamic interactions. Here we study the interplay between granular bulldozing and the stabilising effect of viscous pressure gradients in the invading fluid. Injection of aqueous solutions into layers of dry, hydrophobic grains represent a viscously stable scenario where we observe a transition from growth of a single frictional finger to simultaneous growth of multiple fingers as viscous forces are increased. The pattern is made more compact by the internal viscous pressure gradient, ultimately resulting in a fully stabilised front of frictional fingers advancing as a radial spoke pattern.

Thermal modeling of the respiratory turbinates in arctic and subtropical seals.

Mammals possess complex structures in their nasal cavities known as respiratory turbinate bones, which help the animal to conserve body heat and water during respiratory gas exchange. We considered the function of the maxilloturbinates of two species of seals, one arctic (Erignathus barbatus), one subtropical (Monachus monachus). By means of a thermo-hydrodynamic model that describes the heat and water exchange in the turbinate region we are able to reproduce the measured values of expired air temperatures in grey seals (Halichoerus grypus), a species for which experimental data are available. At the lowest environmental temperatures, however, this is only possible in the arctic seal, and only if we allow for the possibility of ice forming on the outermost turbinate region. At the same time the model predicts that for the arctic seals, the inhaled air is brought to deep body temperature and humidity conditions in passing the maxilloturbinates. The modeling shows that heat and water conservation go together in the sense that one effect implies the other, and that the conservation is most efficient and most flexible in the typical environment of both species. By controlling the blood flow through the turbinates the arctic seal is able to vary the heat and water conservation substantially at its average habitat temperatures, but not at temperatures around -40 °C. The subtropical species has simpler maxilloturbinates, and our model predicts that it is unable to bring inhaled air to deep body conditions, even in its natural environment, without some congestion of the vascular mucosa covering the maxilloturbinates. Physiological control of both blood flow rate and mucosal congestion is expected to have profound effects on the heat exchange function of the maxilloturbinates in seals.

Dynamics of Dendritic Ice Freezing in Confinement.

We use high-speed photography to observe the dendritic freezing of ice between two closely spaced parallel plates. Measuring the propagation speeds of dendrites, we investigate whether there is a confinement-induced thermal influence upon the speed beyond that provided by a single surface. Plates of thermally insulating plastic and moderately thermally conductive glass are used alone and in combination, at temperatures between -10.6 and -4.8 °C, with separations between 17 and 135 µm wide. No effect of confinement was detected for propagation on glass surfaces, but a possible slowing of propagation speed was seen between insulating plates. The pattern of dendritic growth was also studied, with a change from curving to straight dendrites being strongly associated with a switch from a glass to a plastic substrate.

Thermal dissipation as both the strength and weakness of matter. A material failure prediction by monitoring creep.

In any domain involving some stressed solids, that is, from seismology to general engineering, the strength of matter is a paramount feature to understand. We here discuss the ability of a simple thermally activated sub-critical model, which includes the auto-induced thermal evolution of cracks tips, to predict the catastrophic failure of a vast range of materials. It is in particular shown that the intrinsic surface energy barrier, for breaking the atomic bonds of many solids, can be easily deduced from the slow creeping dynamics of a crack. This intrinsic barrier is however higher than the macroscopic load threshold at which brittle matter brutally fails, possibly as a result of thermal activation and of a thermal weakening mechanism. We propose a novel method to compute this macroscopic energy release rate of rupture, Ga, solely from monitoring slow creep, and we show that this reproduces the experimental values within 50% accuracy over twenty different materials, and over more than four decades of fracture energy.

Active Brownian particles moving through disordered landscapes.

Disordered media are ubiquitous in systems where self-propelled particles are present, ranging from biological settings to synthetic systems, like in active microfluidic devices. Here we investigate the behavior of active Brownian particles that have an internal energy depot and move through a landscape with a quenched frictional disorder. We consider the cases of very fast internal relaxation processes and the limit of strong disorder. Analytical calculations of the mean-square displacement in the fast-relaxation approximation is shown to agree well with numerically integrated energy depot dynamics and predict normal dispersion for a bounded drag coefficient and anomalous dispersion for power-law dependence of the drag on spatial coordinates. Furthermore, we show that in the strongly disordered limit the self-propulsion speed can, for practical purposes, be considered a fluctuating quantity. Distributions of self-propulsion speeds are investigated numerically for different parameter choices.

How heat controls fracture: the thermodynamics of creeping and avalanching cracks.

While of paramount importance in material science, the dynamics of cracks still lacks a complete physical explanation. The transition from their slow creep behavior to a fast propagation regime is a notable key, as it leads to full material failure if the size of a fast avalanche reaches that of the system. We here show that a simple thermodynamics approach can actually account for such complex crack dynamics, and in particular for the non-monotonic force-velocity curves commonly observed in mechanical tests on various materials. We consider a thermally activated failure process that is coupled with the production and the diffusion of heat at the fracture tip. In this framework, the rise in temperature only affects the sub-critical crack dynamics and not the mechanical properties of the material. We show that this description can quantitatively reproduce the rupture of two different polymeric materials (namely, the mode I opening of polymethylmethacrylate (PMMA) plates, and the peeling of pressure sensitive adhesive (PSA) tapes), from the very slow to the very fast fracturing regimes, over seven to nine decades of crack propagation velocities. In particular, the fastest regime is obtained with an increase of temperature of thousands of Kelvins, on the molecular scale around the crack tip. Although surprising, such an extreme temperature is actually consistent with different experimental observations that accompany the fast propagation of cracks, namely, fractoluminescence (i.e., the emission of visible light during rupture) and a complex morphology of post-mortem fracture surfaces, which could be due to the sublimation of bubbles.

Seeking minimum entropy production for a tree-like flow-field in a fuel cell.

Common for tree-shaped, space-filling flow-field plates in polymer electrolyte fuel cells is their ability to distribute reactants uniformly across the membrane area, thereby avoiding excess concentration polarization or entropy production at the electrodes. Such a flow field, as predicted by Murray's law for circular tubes, was recently shown experimentally to give a better polarization curve than serpentine or parallel flow fields. In this theoretical work, we document that a tree-shaped flow-field, composed of rectangular channels with T-shaped junctions, has a smaller entropy production than the one based on Murray's law. The width w0 of the inlet channel and the width scaling parameter, a, of the tree-shaped flow-field channels were varied, and the resulting Peclet number at the channel outlets was computed. We show, using 3D hydrodynamic calculations as a reference, that pressure drops and channel flows can be accounted for within a few percents by a quasi-1D model, for most of the investigated geometries. Overall, the model gives lower energy dissipation than Murray's law. The results provide new tools and open up new possibilities for flow-field designs characterized by uniform fuel delivery in fuel cells and other catalytic systems.

Pressure evolution and deformation of confined granular media during pneumatic fracturing.

By means of digital image correlation, we experimentally characterize the deformation of a dry granular medium confined inside a Hele-Shaw cell due to air injection at a constant overpressure high enough to deform it (from 50 to 250 kPa). Air injection at these overpressures leads to the formation of so-called pneumatic fractures, i.e., channels empty of beads, and we discuss the typical deformations of the medium surrounding these structures. In addition we simulate the diffusion of the fluid overpressure into the medium, comparing it with the Laplacian solution over time and relating pressure gradients with corresponding granular displacements. In the compacting medium we show that the diffusing pressure field becomes similar to the Laplace solution on the order of a characteristic time given by the properties of the pore fluid, the granular medium, and the system size. However, before the diffusing pressure approaches the Laplace solution on the system scale, we find that it resembles the Laplacian field near the channels, with the highest pressure gradients on the most advanced channel tips and a screened pressure gradient behind them. We show that the granular displacements more or less always move in the direction against the local pressure gradients, and when comparing granular velocities with pressure gradients in the zone ahead of channels, we observe a Bingham type of rheology for the granular paste (the mix of air and beads), with an effective viscosity µ_{B} and displacement thresholds ∇[over ⃗]P_{c} evolving during mobilization and compaction of the medium. Such a rheology, with disorder in the displacement thresholds, could be responsible for placing the pattern growth at moderate injection pressures in a universality class like the dielectric breakdown model with η=2, where fractal dimensions are found between 1.5 and 1.6 for the patterns.

Verification of a Dynamic Scaling for the Pair Correlation Function during the Slow Drainage of a Porous Medium.

In this Letter we give experimental grounding for the remarkable observation made by Furuberg et al. [Phys. Rev. Lett. 61, 2117 (1988)PRLTAO0031-900710.1103/PhysRevLett.61.2117] of an unusual dynamic scaling for the pair correlation function N(r,t) during the slow drainage of a porous medium. Those authors use an invasion percolation algorithm to show numerically that the probability of invasion of a pore at a distance r away and after a time t from the invasion of another pore scales as N(r,t)∝r^{-1}f(r^{D}/t), where D is the fractal dimension of the invading cluster and the function f(u)∝u^{1.4}, for u≪1 and f(u)∝u^{-0.6}, for u≫1. Our experimental setup allows us to have full access to the spatiotemporal evolution of the invasion, which is used to directly verify this scaling. Additionally, we connect two important theoretical contributions from the literature to explain the functional dependency of N(r,t) and the scaling exponent for the short-time regime (t≪r^{D}). A new theoretical argument is developed to explain the long-time regime exponent (t≫r^{D}).

Pneumatic fractures in confined granular media.

We perform experiments where air is injected at a constant overpressure P_{in}, ranging from 5 to 250 kPa, into a dry granular medium confined within a horizontal linear Hele-Shaw cell. The setup allows us to explore compacted configurations by preventing decompaction at the outer boundary, i.e., the cell outlet has a semipermeable filter such that beads are stopped while air can pass. We study the emerging patterns and dynamic growth of channels in the granular media due to fluid flow, by analyzing images captured with a high speed camera (1000 images/s). We identify four qualitatively different flow regimes, depending on the imposed overpressure, ranging from no channel formation for P_{in} below 10 kPa, to large thick channels formed by erosion and fingers merging for high P_{in} around 200 kPa. The flow regimes where channels form are characterized by typical finger thickness, final depth into the medium, and growth dynamics. The shape of the finger tips during growth is studied by looking at the finger width w as function of distance d from the tip. The tip profile is found to follow w(d)∝d^{ß}, where ß=0.68 is a typical value for all experiments, also over time. This indicates a singularity in the curvature d^{2}d/dw^{2}∼κ∼d^{1-2ß}, but not of the slope dw/dd∼d^{ß-1}, i.e., more rounded tips rather than pointy cusps, as they would be for the case ß>1. For increasing P_{in}, the channels generally grow faster and deeper into the medium. We show that the channel length along the flow direction has a linear growth with time initially, followed by a power-law decay of growth velocity with time as the channel approaches its final length. A closer look reveals that the initial growth velocity v_{0} is found to scale with injection pressure as v_{0}∝P_{in}^{3/2}, while at a critical time t_{c} there is a cross-over to the behavior v(t)∝t^{-α}, where α is close to 2.5 for all experiments. Finally, we explore the fractal dimension of the fully developed patterns. For example, for patterns resulting from intermediate P_{in} around 100-150 kPa, we find that the box-counting dimensions lie within the range D_{B}∈[1.53,1.62], similar to viscous fingering fractals in porous media.

Dispersive transport and symmetry of the dispersion tensor in porous media.

The macroscopic laws controlling the advection and diffusion of solute at the scale of the porous continuum are derived in a general manner that does not place limitations on the geometry and time evolution of the pore space. Special focus is given to the definition and symmetry of the dispersion tensor that is controlling how a solute plume spreads out. We show that the dispersion tensor is not symmetric and that the asymmetry derives from the advective derivative in the pore-scale advection-diffusion equation. When flow is spatially variable across a voxel, such as in the presence of a permeability gradient, the amount of asymmetry can be large. As first shown by Auriault [J.-L. Auriault et al. Transp. Porous Med. 85, 771 (2010)TPMEEI0169-391310.1007/s11242-010-9591-y] in the limit of low Péclet number, we show that at any Péclet number, the dispersion tensor D_{ij} satisfies the flow-reversal symmetry D_{ij}(+q)=D_{ji}(-q) where q is the mean flow in the voxel under analysis; however, Reynold's number must be sufficiently small that the flow is reversible when the force driving the flow changes sign. We also demonstrate these symmetries using lattice-Boltzmann simulations and discuss some subtle aspects of how to measure the dispersion tensor numerically. In particular, the numerical experiments demonstrate that the off-diagonal components of the dispersion tensor are antisymmetric which is consistent with the analytical dependence on the average flow gradients that we propose for these off-diagonal components.

Onsager symmetry from mesoscopic time reversibility and the hydrodynamic dispersion tensor for coarse-grained systems.

Onsager reciprocity relations derive from the fundamental time reversibility of the underlying microscopic equations of motion. This gives rise to a large set of symmetric cross-coupling phenomena. We here demonstrate that different reciprocity relations may arise from the notion of mesoscopic time reversibility, i.e., reversibility of intrinsically coarse-grained equations of motion. We use Brownian dynamics as an example of such a dynamical description and show how it gives rise to reciprocity in the hydrodynamic dispersion tensor as long as the background flow velocity is reversed as well.

Minimal model for anomalous diffusion.

A random walk model with a local probability of removal is solved exactly and shown to exhibit subdiffusive behavior with a mean square displacement the evolves as 〈x^{2}(t)〉∼t^{1/2} at late times. This model is shown to be well described by a diffusion equation with a sink term, which also describes the evolution of a pressure or temperature field in a leaky environment. For this reason a number of physical processes are shown to exhibit anomalous diffusion. The presence of the sink term is shown to change the late time behavior of the field from 1/t^{1/2} to 1/t^{3/2}.

Transient anomalous diffusion regimes in reversible adsorbing systems.

A solvable, minimal model of diffusion in the presence of a reversible adsorption site is investigated. We show that the diffusive particles are influenced by the adsorbing site on transient times when they have anomalous subdiffusive behavior. However, the particle dispersion law crosses over to the normal diffusive regime on asymptotically long times. The subdiffusive regime is characterized by a t^{1/4} transient scaling with the same exponent as for the irreversible adsorption. On this transient time scale dominated by particle adsorption, there is a depletion of particles near the adsorbing site, and the typical width of the depletion zone grows in time as t^{1/4} with the same exponent as the subdiffusive dispersion. We show that having a nonzero desorption probability for the adsorbed particles produces a crossover towards normal diffusion on time scales larger than a characteristic reactive time, which we show scales with diffusivity and the adsorption site reactivity.

Note: Localization based on estimated source energy homogeneity.

Acoustic signal localization is a complex problem with a wide range of industrial and academic applications. Herein, we propose a localization method based on energy attenuation and inverted source amplitude comparison (termed estimated source energy homogeneity, or ESEH). This inversion is tested on both synthetic (numerical) data using a Lamb wave propagation model and experimental 2D plate data (recorded with 4 accelerometers sensitive up to 26 kHz). We compare the performance of this technique with classic source localization algorithms: arrival time localization, time reversal localization, and localization based on energy amplitude. Our technique is highly versatile and out-performs the conventional techniques in terms of error minimization and cost (both computational and financial).

Frictional Fluid Dynamics and Plug Formation in Multiphase Millifluidic Flow.

We study experimentally the flow and patterning of a granular suspension displaced by air inside a narrow tube. The invading air-liquid interface accumulates a plug of granular material that clogs the tube due to friction with the confining walls. The gas percolates through the static plug once the gas pressure exceeds the pore capillary entry pressure of the packed grains, and a moving accumulation front is reestablished at the far side of the plug. The process repeats, such that the advancing interface leaves a trail of plugs in its wake. Further, we show that the system undergoes a fluidization transition-and complete evacuation of the granular suspension-when the liquid withdrawal rate increases beyond a critical value. An analytical model of the stability condition for the granular accumulation predicts the flow regime.