Emergence of Power-Law Particle Size Distribution in Microfluidic Calcium Carbonate Precipitation: An Extended Yule Process with a Ripening Effect.

Precipitation of calcium carbonate in bulk solutions is well known to result in a bell-shaped or bimodal particle size distribution. However, it is unclear how the distribution behaves if precipitation occurs in a small, confined volume. In this Letter, we conduct microfluidic experiments where sodium carbonate and calcium chloride solutions are continuously injected into a microchannel to precipitate calcium carbonate particles. Results show that, regardless of the variations in reagent concentrations, mixing schemes, flow rates, and precipitation time, sizes of precipitated particles in the channel are power law distributed, with an exponent of 1.4. The data are described by an extended Yule process with the introduction of a ripening term. Since the Yule process is a general mechanism for power law generation, the extended Yule process proposed here provides a general model for systems where growth and ripening simultaneously present.

Surface-active compounds induce time-dependent and non-monotonic fluid-fluid displacement during low-salinity water flooding.

HYPOTHESIS: In a porous medium saturated with oil (containing oleic surfactant) and saline water, salinity reduction alters the thermodynamic equilibrium and induces spatial redistribution of surfactants, changing the local fluid configuration. During fluid-fluid displacement, this local change reshapes global fluid flows, and thus results in improved oil displacement. EXPERIMENTS: We performed microfluidic experiments in a centimeter-long pore-network model with a fracture and a dead-end model to observe both the macroscale flows and microscopic fluid configuration evolution. Water with different salinities and model oils with different surfactant concentrations are used. FINDINGS: When oil contacts low salinity water, we observe (1) the solid surface becomes more water-wet, and (2) water-in-oil emulsion spontaneously emerges near the oil-water interface. At the macroscale, the fluid distribution remains unchanged in short term but dramatically changes after tens of hours, which appears as improved oil recovery. Two modes are identified during fluid redistribution: gradual imbibition and sudden collapse. The displacement efficiency is a non-monotonic function of surfactant concentration. This is attributed to the interplay between two opposing effects by adding surfactant: (1) enhancing initial hydrophobicity which negatively affects the displacement, and (2) allowing stronger oil swelling which is beneficial for displacement.

Dissolution-After-Precipitation (DAP): a simple microfluidic approach for studying carbonate rock dissolution and multiphase reactive transport mechanisms.

We propose a simple microfluidic approach: Dissolution-After-Precipitation (DAP), to investigate regimes of carbonate rock dissolution and multiphase reactive transport. In this method, a carbonate porous medium is created in a glass microchannel via calcium carbonate precipitation, after which an acid is injected into the channel to dissolve the precipitated porous medium. Utilizing the DAP method, for the first time we realized all five classical single-phase carbonate rock dissolution regimes (uniform, compact, conical, wormhole, ramified wormholes) in a microfluidic chip. The results are validated against the established theoretical dissolution diagram, which shows good agreement. Detailed analysis of these single-phase dissolutions suggests that the heterogeneity of the porous medium may significantly impact how the dissolution patterns evolve over time. Furthermore, DAP is utilized to investigate multiphase dissolution. As examples we tested the cases of an oleic phase (tetradecane) and a gaseous phase (CO2). Results show that the presence of a nonaqueous phase in pore spaces induces the formation of wormholes despite weak advection, and these wormholes ultimately become pathways for nonaqueous phase transport. However, the transport of tetradecane in the wormhole is very slow, causing acid breakthrough into neighboring regions. This mechanism enhances lateral connectivity between wormholes and may lead to a wormhole network. In contrast, CO2 moves rapidly and continuously seeks to enter a widening wormhole from a narrower wormhole or the porous regions, generating phenomena such as ganglia redistribution and counterflow (flow of gas opposite to acid flow). Extensive independent experiments are conducted to verify the reproducibility of the observed phenomena/mechanisms and further analyze them. Real-time monitoring of fluid pressure drop during dissolution is implemented to complement microscopy image analysis. Our method can be implemented repeatedly on the same chip, which offers a convenient and inexpensive option to study pore-scale reactive transport mechanisms.

Oscillative Trapping of a Droplet in a Converging Channel Induced by Elastic Instability.

Permanent trapping of an oscillating, nonwetting droplet is observed in a converging-diverging microchannel when aqueous, viscoelastic fluids are injected. Classical theories based on the balance between capillary and viscous forces suggest that the droplet size should decrease with increasing flow rates of a displacing Newtonian fluid, and the droplet should be completely displaced at high injection rates. However, droplets in viscoelastic fluids cannot be removed by increasing flow rates due to the oscillation. The oscillation amplitude linearly increases with the Deborah number (De), which further inhibits the droplet's passing through the constriction, "permanently." Our microfluidic experiments show that the onset of oscillation is determined by a critical De, which is near 1. We derive a linear relationship for the trapped droplet length with Ec^{1/3}, where Ec is the elastocapillary number, by introducing the elastic force into the force balance in addition to the capillary and viscous forces.

Fluid-driven fractures in granular media: Insights from numerical investigations.

We investigate the mechanisms of opening-mode fracture initiation in granular media. The study is based on a simulation of grain-scale fluid-grain interactions through a coupled numerical approach in which the discrete element method is used to solve for the mechanics of a solid granular medium, and computational fluid dynamics is used to model fluid flow and drag forces. We present benchmark problems with analytical solutions and validate this numerical model against experiments on a viscous-drag-driven cavity in the literature. Additional simulation results show fracture initiation mechanisms in a random granular packing subjected to constant boundary stresses and to fluid injection with a localized source. The dimensionless variable F_{s}/F_{sk} (ratio of seepage force F_{s} and skeletal force F_{sk}) incorporates the impacts of physical properties and injection parameters including fluid viscosity, injection velocity, grain size, and effective stresses, and it has been used as a criterion separating regimes of fluid invasion and drag-driven fracture opening. Our simulation results show that F_{s}/F_{sk} in combination with τ_{1} (ratio of diffusion time from hydromechanical coupling and injection time) serves as a prediction of fracture opening within granular packing. We suggest a simple criterion (F_{s}/F_{sk}>1 or τ_{1}>0.17) that is valid for various types of granular media and injection conditions to determine if fracture opening will occur. Among other applications, this study is useful to predict the initiation and propagation of fractures in natural sediments.

Influences of polarity and hydration cycles on imbibition hysteresis in silica nanochannels.

Spontaneous liquid imbibition is a dominant mechanism for moving fluids in confinements with extremely high hydrodynamic resistance; i.e. nanopores. We demonstrate the impact of hydrophilicity and liquid polarity on nanoscale imbibition with dynamic measurements of the uptake of water-isopropanol (polar) and heptane (nonpolar) within 2D glass-silica nanochannels exposed to varied drying conditions and rehydration (rehydroxylation) cycles. The Lucas-Washburn equation, which does not consider interfacial fluidity effects, predicts that water-IPA and heptane should imbibe at similar speeds. However, we observed stymied and hysteretic water-IPA imbibition trends explained by extremely large contact line friction and increased effective viscosity, both surface chemistry-dependent, whereupon the results match a modified version of the Lucas-Washburn equation that accounts for dynamic wetting. In contrast, heptane imbibition, though still slower than the Lucas-Washburn equation prediction, was fairly insensitive to drying history and an order of magnitude faster than the polar mixture. The imbibition of aqueous solutions in analogous siliceous nanoporous materials and structures, ubiquitous in earth science and nanotechnology, may also be subject to hysteretic and large energy dissipation at contact lines and interfaces on account of hydrophilicity.

Spontaneous and Flow-Driven Interfacial Phase Change: Dynamics of Microemulsion Formation at the Pore Scale.

The dynamic behavior of microemulsion-forming water-oil-amphiphiles mixtures is investigated in a 2.5D micromodel. The equilibrium phase behavior of such mixtures is well-understood in terms of macroscopic phase transitions. However, what is less understood and where experimental data are lacking is the coupling between the phase change and the bulk flow. Herein, we study the flow of an aqueous surfactant solution-oil mixture in porous media and analyze the dependence of phase formation and spatial phase configurations on the bulk flow rate. We find that a microemulsion forms instantaneously as a boundary layer at the initial surface of contact between the surfactant solution and oil. The boundary layer is temporally continuous because of the imposed convection. In addition to the imposed flow, we observe spontaneous pulsed Marangoni flows that drag the microemulsion and surfactant solution into the oil stream, forming large (macro)emulsion droplets. The formation of the microemulsion phase at the interface distinguishes the situation from that of the more common Marangoni flow with only two phases present. Additionally, an emulsion forms via liquid-liquid nucleation or the Ouzo effect (i.e., spontaneous emulsification) at low flow rates and via mechanical mixing at high flow rates. With regard to multiphase flow, contrary to the common belief that the microemulsion is the wetting liquid, we observe that the minor oil phase wets the solid surface. We show that a layered flow pattern is formed because of the out-of-equilibrium phase behavior at high volumetric flow rates (order of 2 m/day) where advection is much faster than the diffusive interfacial mass transfer and transverse mixing, which promote equilibrium behavior. At lower flow rates (order of 30 cm/day), however, the dynamic and equilibrium phase behaviors are well-correlated. These results clearly show that the phase change influences the macroscale flow behavior.

A 2.5-D glass micromodel for investigation of multi-phase flow in porous media.

We developed a novel method for fabrication of glass micromodels with varying depth (2.5-D) with no additional complexity over the 2-D micromodels' fabrication. Compared to a 2-D micromodel, the 2.5-D micromodel can better represent the 3-D features of multi-phase flow in real porous media, as demonstrated in this paper with three different examples. Physically realistic capillary snap-off and the formation of isolated residual oil droplets were realized, which is not possible in 2-D micromodels. Droplet size variation during an emulsion flooding was investigated on the 2.5-D micromodel, showing that the droplet size decreases sharply at the inlet, with little change in size downstream of the micromodel. Displacement of light oil with ultra-low interfacial tension (IFT) surfactant was conducted in the 2.5-D micromodel, where we were able to visualize the generation and flowing of a microemulsion phase, which agrees with, and explains observations in experiments of more complex porous media.

Egalitarianism among Bubbles in Porous Media: An Ostwald Ripening Derived Anticoarsening Phenomenon.

We show that smaller gas bubbles grow at the expense of larger bubbles and all bubbles approach the same surface curvature after long times in porous media. This anticoarsening effect is contrary to typical Ostwald ripening and leads to uniformly sized bubbles in a homogeneous medium. Evolution dynamics of bubble populations were measured, and mathematical models were developed that fit the experimental data well. Ostwald ripening is shown to be the driving mechanism in this anticoarsening phenomenon; however, the relationship between surface curvature and bubble size determined by the pore-throat geometric confinement reverses the ripening direction.

Subsurface to substrate: dual-scale micro/nanofluidic networks for investigating transport anomalies in tight porous media.

Micro/nanofluidic experiments in synthetic representations of tight porous media, often referred to as "reservoir-on-a-chip" devices, are an emerging approach to researching anomalous fluid transport trends in energy-bearing and fluid-sequestering geologic porous media. We detail, for the first time, the construction of dual-scale micro/nanofluidic devices that are relatively large-scale, two-dimensional network representations of granular and fractured nanoporous media. The fabrication scheme used in the development of the networks on quartz substrates (master patterns) is facile and replicable: transmission electron microscopy (TEM) grids with lacey carbon support film were used as shadow masks in thermal evaporation/deposition and reactive ion etch (RIE) was used for hardmask pattern transfer. The reported nanoscale network geometries are heterogeneous and composed of hydraulically resistive paths (throats) meeting at junctures (pores) to mimic the low topological connectivity of nanoporous sedimentary rocks such as shale. The geometry also includes homogenous microscale grid patterns that border the nanoscale networks and represent microfracture pathways. Master patterns were successfully replicated with a sequence of polydimethylsiloxane (PDMS) and Norland Optical Adhesive (NOA) 63 polymers. The functionality of the fabricated quartz and polymer nanofluidic devices was validated with aqueous imbibition experiments and differential interference contrast microscopy. These dual-scale fluidic devices are promising predictive tools for hypothesis testing and calibration against bulk fluid measurements in tight geologic, biologic, and synthetic porous material of similar dual-scale pore structure. Applications to shale/mudrock transport studies in particular are focused on herein.

Anomalous liquid imbibition at the nanoscale: the critical role of interfacial deformations.

We observed that imbibition of various Rhodamine B-doped wetting liquids in an array of different-sized, horizontal, two-dimensional silica nanochannels terminated within the channels as a function of hydraulic diameter and liquid type. This front termination is not predicted by the classic Washburn equation for capillary flow, which establishes diffusive dynamics in horizontal channels. Various explanations for the anomalous static imbibition measurements were negated; hydrodynamics, thermodynamics, surface chemistry and mechanics were all taken into consideration for this analysis. The atypical imbibition data are explained by deformed menisci and decreased effective channel diameters. These occurrences are due to the enhanced influence of the following phenomena at the nanoscale: surface forces at fluid-solid boundaries, the presence of quasi-crystalline thin films or boundary regions, and potential solid surface or boundary layer deformation due to meniscus-induced negative pressures (suction). We introduce a phenomenological model which demonstrates how van der Waals forces, common to all interfaces, lead to local menisci deformation and an average reduction in capillary pressure. An expression for the approximate capillary pressure of a symmetric nanoscale meniscus in a cylindrical pore space is derived; its difference from the macroscopic capillary pressure can be expressed by an effective contact angle. Precursor films, adsorbed films and elastocapillary deformation decrease effective diameter, exacerbating meniscus deformation and increases in effective viscosity; we also describe local models and effective values for these phenomena. The findings can be scaled to imbibition and two-phase flow in nanoporous media.

Microfluidic Investigation of Nanoparticles' Role in Mobilizing Trapped Oil Droplets in Porous Media.

The flow of multiple fluid phases in porous media often results in trapped droplets of the nonwetting phase. Recent experimental and theoretical studies have suggested that nanoparticle aqueous dispersions may be effective at mobilizing trapped droplets of nonwetting fluid (oil) in porous media. Hypotheses to explain the observation include the nanoparticles' modification of solid wettability, droplet stabilization, and changes in interfacial tension and interface rheology. However, because it is difficult to observe droplet behavior on the pore scale, how those factors contribute to oil droplet mobilization has not been fully understood. In this work, we investigated the nanoparticles' role in nanoparticle-based improved recovery of the nonwetting phase through the direct observation of the mobilization of trapped oil droplets in microfluidic structures that mimic pore-throat geometries. A microfluidic platform was constructed for this study, on which different displacing liquids including aqueous surfactant solutions and nanoparticle suspensions were tested. We found that the nanoparticle concentration is positively related to the oil mobilization efficiency. An approximate mathematical model for calculating the maximum size of an oil droplet trapped in a pore-throat geometry for a fixed flow rate matches the experiment result for displacing liquid with no nanoparticles. The model still holds when the nanoparticle suspension is a displacing liquid. We concluded that nanoparticles mobilize oil in these geometries in a mechanism similar to that for surfactants, which is an increase in capillary number rather than an effect of other fluidic or interfacial properties such as the dynamics adsorption of nanoparticle or dilational rheology of a nanoparticle-adsorbed interface.

Quantification of bulk solution limits for liquid and interfacial transport in nanoconfinements.

Liquid imbibition, the capillary-pressure-driven flow of a liquid into a gas, provides a mechanism for studying the effects of solid-liquid and solid-liquid-gas interfaces on nanoscale transport. Deviations from the classic Washburn equation for imbibition are generally observed for nanoscale imbibition, but the identification of the origin of these irregularities in terms of transport variables varies greatly among investigators. We present an experimental method and corresponding image and data analysis scheme that enable the determination of independent effective values of nanoscale capillary pressure, liquid viscosity, and interfacial gas partitioning coefficients, all critical transport variables, from imbibition within nanochannels. Experiments documented herein are performed within two-dimensional siliceous nanochannels of varying size and as small as 30 nm × 60 nm in cross section. The wetting fluid used is the organic solvent isopropanol and the nonwetting fluid is air, but investigations are not limited to these fluids. Optical data of dynamic flow are rare in geometries that are nanoscale in two dimensions due to the limited resolution of optical microscopy. We are able to capture tracer-free liquid imbibition with reflected differential interference contrast microscopy. Results with isopropanol show a significant departure from bulk transport values in the nanochannels: reduced capillary pressures, increased liquid viscosity, and nonconstant interfacial mass-transfer coefficients. The findings equate to the nucleation of structured, quasi-crystalline boundary layers consistently ∼10-25 nm in extent. This length is far thicker than the boundary layer range prescribed by long-range intermolecular force interactions. Slower but linear imbibition in some experimental cases suggests that structured boundary layers may inhibit viscous drag at confinement walls for critical nanochannel dimensions. Probing the effects of nanoconfinement on the definitions of capillary pressure, viscosity, and interfacial mass transfer is critical in determining and improving the functionality and fluid transport efficacy of geological, biological, and synthetic nanoporous media and materials.