Fluid flow drives phenotypic heterogeneity in bacterial growth and adhesion on surfaces.

Bacteria often thrive in surface-attached communities, where they can form biofilms affording them multiple advantages. In this sessile form, fluid flow is a key component of their environments, renewing nutrients and transporting metabolic products and signaling molecules. It also controls colonization patterns and growth rates on surfaces, through bacteria transport, attachment and detachment. However, the current understanding of bacterial growth on surfaces neglects the possibility that bacteria may modulate their division behavior as a response to flow. Here, we employed single-cell imaging in microfluidic experiments to demonstrate that attached Escherichia coli cells can enter a growth arrest state while simultaneously enhancing their adhesion underflow. Despite utilizing clonal populations, we observed a non-uniform response characterized by bistable dynamics, with co-existing subpopulations of non-dividing and actively dividing bacteria. As the proportion of non-dividing bacteria increased with the applied flow rate, it resulted in a reduction in the average growth rate of bacterial populations on flow-exposed surfaces. Dividing bacteria exhibited asymmetric attachment, whereas non-dividing counterparts adhered to the surface via both cell poles. Hence, this phenotypic diversity allows bacterial colonies to combine enhanced attachment with sustained growth, although at a reduced rate, which may be a significant advantage in fluctuating flow conditions.

Electrical Signatures of Diffusion-Limited Mixing: Insights from a Milli-fluidic Tracer Experiment.

We investigate how diffusion-limited mixing of a layered solute concentration distribution within a porous medium impacts bulk electrical conductivity. To do so, we perform a milli-fluidic tracer test by injecting a fluorescent and electrically conductive tracer in a quasi two-dimensional (2D) water-saturated porous medium. High resolution optical- and geoelectrical monitoring of the tracer is achieved by using a fluorimetry technique and equipping the flow cell with a resistivity meter, respectively. We find that optical and geoelectrical outputs can be related by a temporal re-scaling that accounts for the different diffusion rates of the optical and electrical tracers. Mixing-driven perturbations of the electrical equipotential field lines cause apparent electrical conductivity time-series, measured perpendicularly to the layering, to peak at times that are in agreement with the diffusion transport time-scale associated with the layer width. Numerical simulations highlight high sensitivity of such electrical data to the layers' degree of mixing and their distance to the injection electrodes. Furthermore, the electrical data correlate well with time-series of two commonly used solute mixing descriptors: the concentration variance and the scalar dissipation rate.

Two-dimensional micromodels for studying the convective dissolution of carbon dioxide in 2D water-saturated porous media.

Convective dissolution is a perennial trapping mechanism of carbon dioxide in geological formations saturated with an aqueous phase. This process, which couples dissolution of supercritical CO2, convection of the liquid containing the dissolved CO2, and mixing of the latter within the liquid, has so far not been studied in two-dimensional porous media. In order to do so, two-dimensional (2D) porous micromodels (patterned Hele-Shaw cells) have been fabricated from UV-curable NOA63 glue. NOA63 is used instead of PDMS, which is permeable to CO2 and does not allow for a controlled no flux boundary condition at the walls. The novel fabrication protocol proposed here, based on the bonding of a patterned photo-lithographed NOA63 layer on a flat NOA63 base, shows good reproducibility regardless of the patterns' typical size, and allows for easy filling of the cell despite the small value of the gap. A pressure chamber allows pressurizing the CO2 and outside of the flow cell up to 10 bars. Experiments were performed in 11 different porous media geometries. As expected, a gravitational fingering instability is observed upon injection of gaseous carbon dioxide in the cell, resulting in the downwards migration of dissolved CO2 plumes through the 2D porous structure. The initial wavelength of the fingers is larger in the presence of a hexagonal lattice of pillars. This effect can be correctly predicted from the theory for the gravitational instability in a Hele-Shaw cell devoid of pillars, provided that the permeability of the hexagonal porous medium is considered in the theory instead of that of the Hele-Shaw cell. Fluctuations around the theoretical prediction observed in the data are mostly attributed to a hitherto unknown weak locking of the wavelength on the distance between closest pillars.

Pore-Scale Mechanisms for Spectral Induced Polarization of Calcite Precipitation Inferred from Geo-Electrical Millifluidics.

Spectral induced polarization (SIP) has the potential for monitoring reactive processes in the subsurface. While strong SIP responses have been measured in response to calcite precipitation, their origin and mechanism remain debated. Here we present a novel geo-electrical millifluidic setup designed to observe microscale reactive transport processes while performing SIP measurements. We induced calcite precipitation by injecting two reactive solutions into a porous medium, which led to highly localized precipitates at the mixing interface. Strikingly, the amplitude of the SIP response increased by 340% during the last 7% increase in precipitate volume. Furthermore, while the peak frequency in SIP response varied spatially over 1 order of magnitude, the crystal size range was similar along the front, contradicting assumptions in the classical grain polarization model. We argue that the SIP response of calcite precipitation in such mixing fronts is governed by Maxwell-Wagner polarization due to the establishment of a precipitate wall. Numerical simulations of the electric field suggested that spatial variation in peak frequency was related to the macroscopic shape of the front. These findings provide new insights into the SIP response of calcite precipitation and highlight the potential of geoelectrical millifluidics for understanding and modeling electrical signatures of reactive transport processes.

Stretching and folding sustain microscale chemical gradients in porous media.

Fluid flow in porous media drives the transport, mixing, and reaction of molecules, particles, and microorganisms across a wide spectrum of natural and industrial processes. Current macroscopic models that average pore-scale fluctuations into an effective dispersion coefficient have shown significant limitations in the prediction of many important chemical and biological processes. Yet, it is unclear how three-dimensional flow in porous structures govern the microscale chemical gradients controlling these processes. Here, we obtain high-resolution experimental images of microscale mixing patterns in three-dimensional porous media and uncover an unexpected and general mixing mechanism that strongly enhances concentration gradients at pore-scale. Our experiments reveal that systematic stretching and folding of fluid elements are produced in the pore space by grain contacts, through a mechanism that leads to efficient microscale chaotic mixing. These insights form the basis for a general kinematic model linking chaotic-mixing rates in the fluid phase to the generic structural properties of granular matter. The model successfully predicts the resulting enhancement of pore-scale chemical gradients, which appear to be orders of magnitude larger than predicted by dispersive approaches. These findings offer perspectives for predicting and controlling the vast diversity of reactive transport processes in natural and synthetic porous materials, beyond the current dispersion paradigm.

Dynamics of foam flow in a rock fracture: Effects of aperture variation on apparent shear viscosity and bubble morphology.

There has recently been renewed interest in understanding the physics of foam flow in permeable media. As for Newtonian flows in fractures, the heterogeneity of local apertures in natural fractures is expected to strongly impact the spatial distribution of foam flow. Although several experimental studies have been previously performed to study foam flow in fractured media, none of them has specifically addressed that impact for parallel flow in a realistic fracture geometry and its consequences for the foam's in situ shear viscosity and bubble morphologies. To do so, a comprehensive series of single-phase experiments have been performed by injecting pre-generated foams with six different qualities at a constant flow rate through a replica of a Vosges sandstone fracture of well-characterized aperture map. These measurements were compared to measurements obtained in a Hele-Shaw (i.e., smooth) fracture of identical hydraulic aperture. The results show that fracture wall roughness strongly increases the foam's apparent viscosity and shear rate. Moreover, foam bubbles traveling in regions of larger aperture exhibit larger velocity, size, a higher coarsening rate, and are subjected to a higher shear rate. This study also presents the first in situ measurement of foam bubbles velocities in fracture geometry, and provides hints towards measuring the in situ rheology of foam in a rough fracture from the velocity maps, for various imposed mean flow rates. These findings echo the necessity of considering fracture wall when predicting the pressure drop through the fracture and the effective viscosity, as well as in situ rheology, of the foam.

Water vapor diffusive transport in a smectite clay: Cationic control of normal versus anomalous diffusion.

The transport of chemical species in porous media is ubiquitous in subsurface processes, including contaminant transport, soil drying, and soil remediation. We study vapor transport in a multiscale porosity material, a smectite clay, in which water molecules travel in mesopores and macropores between the clay grains but can also intercalate inside the nanoporous grains, making them swell. The intercalation dynamics is known to be controlled by the type of cation that is present in the nanopores; in this case exchanging the cations from Na^{+} to Li^{+} accelerates the dynamics. By inferring spatial profiles of mesoporous humidity from a space-resolved measurement of grain swelling, and analyzing them with a fractional diffusion equation, we show that exchanging the cations changes mesoporous transport from Fickian to markedly subdiffusive. This results both from modifying the exchange dynamics between the mesoporous and nanoporous phases, and from the feedback of transport on the medium's permeability due to grain swelling. An important practical implication is a large difference in the time needed for vapor to permeate a given length of the clay depending on the type of intercalated cation.

Lamella Division in a Foam Flowing through a Two-Dimensional Porous Medium: A Model Fragmentation Process.

We flow a 2D foam through a model 2D porous medium and study experimentally and numerically how the bubble size distribution evolves along the medium. The dominant mechanism of bubble creation is a fragmentation process occurring when bubbles pinched against obstacles are split in two smaller bubbles. We infer the statistics of these individual and local fragmentation events from the experimental data and propose a fragmentation equation to relate that statistics to the evolution of the global size distribution. The predicted evolution shows very good agreement with direct experimental measurements of the bubble size distribution.

Noise-driven interfaces and their macroscopic representation.

We study the macroscopic representation of noise-driven interfaces in stochastic interface growth models in (1+1) dimensions. The interface is characterized macroscopically by saturation, which represents the fluctuating sharp interface by a smoothly varying phase field with values between 0 and 1. We determine the one-point interface height statistics for the Edwards-Wilkinson (EW) and Kadar-Paris-Zhang (KPZ) models in order to determine explicit deterministic equations for the phase saturation for each of them. While we obtain exact results for the EW model, we develop a Gaussian closure approximation for the KPZ model. We identify an interface compression term, which is related to mass transfer perpendicular to the growth direction, and a diffusion term that tends to increase the interface width. The interface compression rate depends on the mesoscopic mass transfer process along the interface and in this sense provides a relation between meso- and macroscopic interface dynamics. These results shed light on the relation between mesoscale and macroscale interface models, and provide a systematic framework for the upscaling of stochastic interface dynamics.

Influence of the elastic deformation of a foam on its mobility in channels of linearly varying width.

We study foam flow in an elementary model porous medium consisting of a convergent and a divergent channel positioned side by side and possessing a fixed joint porosity. Configurations of converging or diverging channels are ubiquitous at the pore scale in porous media, as all channels linking pores possess a converging and diverging part. The resulting flow kinematics imposes asymmetric bubble deformations in the two channels, which modulate foam-wall friction and strongly impact the flux distribution. We measure, as well as quantitatively predict, the ratio of the fluxes in the two channels as a function of the channel widths by modeling pressure drops of both viscous and capillary origins. This study reveals the crucial importance of boundary-induced bubble deformation on the mobility of a flowing foam, resulting in particular in flow irreversibility.

Mixing and reaction kinetics in porous media: an experimental pore scale quantification.

We propose a new experimental set up to characterize mixing and reactive transport in porous media with a high spatial resolution at the pore scale. The analogous porous medium consists of a Hele-Shaw cell containing a single layer of cylindrical solid grains built by soft lithography. On the one hand, the measurement of the local, intrapore, conservative concentration field is done using a fluorescent tracer. On the other hand, considering a fast bimolecular reaction A + B → C occurring as A displaces B, we quantify the rate of product formation from the spatially resolved measurement of the pore scale reaction rate, using a chemiluminescent reaction. The setup provides a dynamical measurement of the local concentration field over 3 orders of magnitude and allows investigating a wide range of Péclet and Damköhler numbers by varying the flow rate within the cell and the local reaction rate. We use it to study the kinetics of the reaction front between A and B. While the advection-dispersion (Fickian) theory, applied at the continuum scale, predicts a scaling of the cumulative mass of product C as MC ∝ √t, the experiments exhibit two distinct regimes in which the produced mass MC evolves faster than the Fickian behavior. In both regimes the front rate of product formation is controlled by the geometry of the mixing interface between the reactants. Initially, the invading solute is organized in stretched lamellae and the reaction is limited by mass transfer across the lamella boundaries. At longer times the front evolves into a second regime where lamellae coalesce and form a mixing zone whose temporal evolution controls the rate of product formation. In this second regime, the produced mass of C is directly proportional to the volume of the mixing zone defined from conservative species. This interesting property is indeed verified from a comparison of the reactive and conservative data. Hence, for both regimes, the direct measurement of the spatial distribution of the pore scale reaction rate and conservative component concentration is shown to be crucial to understanding the departure from the Fickian scaling as well as quantifying the basic mechanisms that govern the mixing and reaction dynamics at the pore scale.

Quick clay and landslides of clayey soils.

We study the rheology of quick clay, an unstable soil responsible for many landslides. We show that above a critical stress the material starts flowing abruptly with a very large viscosity decrease caused by the flow. This leads to avalanche behavior that accounts for the instability of quick clay soils. Reproducing landslides on a small scale in the laboratory shows that an additional factor that determines the violence of the slides is the inhomogeneity of the flow. We propose a simple yield stress model capable of reproducing the laboratory landslide data, allowing us to relate landslides to the measured rheology.

The isotropic-nematic interface in suspensions of Na-fluorohectorite synthetic clay.

Colloidal suspensions of Na-fluorohectorite synthetic clay platelets in saline water exhibit coexisting isotropic and nematic phases, due to gravitational separation of the polydisperse particles. We study the ordering of the platelets at the interfaces between various coexisting phases. Four different experimental techniques are employed: visual observation of birefringence, synchrotron wide angle and small-angle X-ray scattering, and magnetic resonance imaging. We find that at the narrow isotropic sol-nematic sol interface the platelets are lying horizontally, i.e. with their mean platelet normal along the vertical direction. The experiments indicate that the platelets align homeotropically both at the isotropic sol-nematic sol interface and at the nematic sol-wall interface. We further investigate the complex alignment effect of a horizontally applied magnetic field in the nematic sol, and we compare it with the adjacent nematic gel.

Growth activity during fingering in a porous Hele-Shaw cell.

We present in this paper an experimental study of the invasion activity during unstable drainage in a two-dimensional random porous medium, when the (wetting) displaced fluid has a high viscosity with respect to that of the (nonwetting) displacing fluid, and for a range of almost two decades in capillary numbers corresponding to the transition between capillary and viscous fingering. We show that the invasion process takes place in an active zone within a characteristic screening length lambda from the tip of the most advanced finger. The invasion probability density is found to only depend on the distance z to the latter tip and to be independent of the value for the capillary number Ca. The mass density along the flow direction is related analytically to the invasion probability density, and the scaling with respect to the capillary number is consistent with a power law. Other quantities characteristic of the displacement process, such as the speed of the most advanced finger tip or the characteristic finger width, are also consistent with power laws of the capillary number. The link between the growth probability and the pressure field is studied analytically and an expression for the pressure in the defending fluid along the cluster is derived. The measured pressure is then compared with the corresponding simulated pressure field using this expression for the boundary condition on the cluster.

Interface scaling in a two-dimensional porous medium under combined viscous, gravity, and capillary effects.

We have investigated experimentally the competition between viscous, capillary, and gravity forces during drainage in a two-dimensional synthetic porous medium. The displacement of a mixture of glycerol and water by air at constant withdrawal rate has been studied. The setup can be tilted to tune gravity, and pressure is recorded at the outlet of the model. Viscous forces tend to destabilize the displacement front into narrow fingers against the stabilizing effect of gravity. Subsequently, a viscous instability is observed for sufficiently large withdrawal speeds or sufficiently low gravity components on the model. We predict the scaling of the front width for stable situations and characterize it experimentally through analyses of the invasion front geometry and pressure recordings. The front width under stable displacement and the threshold for the instability are shown, both experimentally and theoretically, to be controlled by a dimensionless number F which is defined as the ratio of the effective fluid pressure drop (i.e., average hydrostatic pressure drop minus viscous pressure drop) at pore scale to the width of the fluctuations in the threshold capillary pressures.