Spontaneous imbibition has been receiving much attention due to its significance in many subsurface and industrial applications. Unveiling pore-scale wetting dynamics, and particularly its upscaling to the Darcy scale are still unresolved. In this work, we conduct image-based pore-network modeling of cocurrent spontaneous imbibition and the corresponding quasi-static imbibition, in homogeneous sintered glass beads as well as heterogeneous Estaillades. A wide range of viscosity ratios and wettability conditions are taken into account. Based on our pore-scale results, we show the influence of pore-scale heterogeneity on imbibition dynamics and nonwetting entrapment. We elucidate different pore-filling mechanisms in imbibition, which helps us understand wetting dynamics. Most importantly, we develop a non-equilibrium model for relative permeability of the wetting phase, which adequately incorporates wetting dynamics. This is crucial to the final goal of developing a two-phase imbibition model with measurable material properties such as capillary pressure and relative permeability. Finally, we propose some future work on both numerical and experimental verifications of the developed non-equilibrium permeability model.
A deep understanding of two-phase displacement in porous media with permeability contrast is essential for the design and optimisation of enhanced oil recovery processes. In this paper, we investigate the forced imbibition behaviour in two dual-permeability geometries that are of equal permeability contrast. First, a mathematical model is developed for the imbibition in a pore doublet, which shows that the imbibition dynamics can be fully described by the viscosity ratio $λ$ and capillary number $Ca_m$ which creatively incorporates the influence of channel width and length. Through the finite …
During spontaneous imbibition a wetting liquid is drawn into a porous medium by capillary forces. In systems with comparable pore length and diameter, such as paper and sand, the front of the propagating liquid forms a continuous interface. Sections of this interface advance in a highly correlated manner due to an effective surface tension, which restricts front broadening. Here we investigate water imbibition in a nanoporous glass (Vycor) in which the pores are much longer than they are wide. In this case, no continuous liquid-vapor interface with coalesced menisci can form. Anomalously fast …
We present gravimetrical and optical imaging experiments on the capillarity-driven imbibition of silicone oils in monolithic silica glasses traversed by 3D networks of pores (mesoporous Vycor glass with 6.5 nm or 10 nm pore diameters). As evidenced by a robust square-root-of-time Lucas-Washburn (L-W) filling kinetics, the capillary rise is governed by a balance of capillarity and viscous drag forces in the absence of inertia and gravitational effects over the entire experimental times studied, ranging from a few seconds up to 10 days. A video on the infiltration process corroborates a collecti…
We present a scaling theory for the long time behavior of spontaneous imbibition in porous media consisting of interconnected pores with a large length-to-width ratio. At pore junctions the meniscus propagation in one or more branches can come to a halt when the Laplace pressure of the meniscus exceeds the hydrostatic pressure within the junction. We derive the scaling relations for the emerging arrest time distribution and show that the average front width is proportional to the height, yielding a roughness exponent of exactly beta=1/2 and explaining recent experimental results for nano-porou…
We present gravimetrical, optical, and neutron imaging measurements of the capillarity-driven infiltration of mesoporous silica glass by hydrocarbons. Square-root-of-time Lucas-Washburn invasion kinetics are found for linear alkanes from n-decane (C10) to n-hexacontane (C60) and for squalane, a branched alkane, in porous Vycor with 6.5 nm or 10 nm pore diameter, respectively. Humidity-dependent experiments allow us to study the influence on the imbibition kinetics of water layers adsorbed on the pore walls. Except for the longest molecule studied, C60, the invasion kinetics can be described by…
Recently anomalous scaling properties of front broadening during spontaneous imbibition of water in Vycor glass, a nano-porous medium, were reported: the mean height and the width of the propagating front increase with time $t$ both proportional to $t^{1/2}$. Here we propose a simple lattice imbibition model and elucidate quantitatively how the correlation range of the hydrostatic pressure and the disorder strength of the pore radii affect the scaling properties of the imbibition front. We introduce an effective tension of liquid across neighboring pores, which depends on the aspect ratio of e…
We present, along with some fundamental concepts regarding imbibition of liquids in porous hosts, an experimental, gravimetric study on the capillarity-driven invasion dynamics of water and of the rod-like liquid crystal octyloxycyanobiphenyl (8OCB) in networks of pores a few nanometers across in monolithic silica glass (Vycor). We observe, in agreement with theoretical predictions, square root of time invasion dynamics and a sticky velocity boundary condition for both liquids investigated. Temperature-dependent spontaneous imbibition experiments on 8OCB reveal the existence of a paranematic p…
Capillary filling dynamics of liquid n-tetracosane (n-C24H50) in a network of cylindrical pores with 7 and 10 nm mean diameter in monolithic silica glass (Vycor) exhibit an abrupt temperature-slope change at Ts=54 deg C, ~4 deg C above bulk and ~16 deg C, 8 deg C, respectively, above pore freezing. It can be traced to a sudden inversion of the surface tension's T slope, and thus to a decrease in surface entropy at the advancing pore menisci, characteristic of the formation of a single solid monolayer of rectified molecules, known as surface freezing from macroscopic, quiescent tetracosane melt…
We establish a comprehensive description of the patterns formed when a wetting liquid displaces a viscous fluid confined in a porous medium. Building on model microfluidic experiments, we evidence four imbibition scenarios all yielding different large-scale morphologies. Combining high-resolution imaging and confocal microscopy, we show that they originate from two liquid-entrainment transitions and a Rayleigh-Plateau instability at the pore scale. Finally, we demonstrate and explain the long-time coarsening of the resulting patterns.
We study the spatio-temporal dynamics of water uptake by capillary condensation from unsaturated vapor in mesoporous silicon layers (pore radius $r_\mathrm{p} \simeq 2$ nm), taking advantage of the local changes in optical reflectance as a function of water saturation. Our experiments elucidate two qualitatively different regimes as a function of the imposed external vapor pressure: for low saturations, equilibration occurs via a diffusion-like process; for high saturations, an imbibition-like wetting front results in fast equilibration towards a fully saturated sample. We show that the imbibi…
Imbibition plays a central role in diverse energy, environmental, and industrial processes. In many cases, the medium has multiple parallel strata of different permeabilities; however, how this stratification impacts imbibition is poorly understood. We address this gap in knowledge by directly visualizing forced imbibition in three-dimensional (3D) porous media with two parallel strata. We find that imbibition is spatially heterogeneous: for small capillary number Ca, the wetting fluid preferentially invades the fine stratum, while for Ca above a threshold value, the fluid instead preferential…
A stochastic approach to the filling dynamics of an open topology porous structure permeated with a perfectly wetting fluid is presented. From the discrete structure of the disordered voids network with only nearest neighbors links, we derive the "microscopic" (at the pores scale) dynamical equations governing the filling dynamics of the coupled pores and the fluid pressure dynamics. The model yields two fundamental consequences. The first consequence regards the emergence of Darcy's law and the dependence of the predicted permeability with the voids network topology. The second one is the pre…
Theoretical analysis and fully atomistic molecular dynamics simulations reveal a Brownian ratchet mechanism by which thermal fluctuations drive the net displacement of immiscible liquids confined in channels or pores with micro- or nanoscale dimensions. The thermally-driven displacement is induced by surface nanostructures with directional asymmetry and can occur against the direction of action of wetting or capillary forces. Mean displacement rates in molecular dynamics simulations are predicted via analytical solution of a Smoluchowski diffusion equation for the position probability density.…
Liquid flow propelled by capillary forces is one of the most important transport mechanisms in porous environments. It is governed by a fascinating interplay of interfacial, viscous drag as well as gravitational forces which liquids encounter upon invasion into geometries with often complex topologies, such as capillary networks of trees or interconnected fractures in soils and ice. Here, we present fundamentals, concepts and an experimental, gravimetric study on the capillarity-driven invasion dynamics of liquids in networks of pores a few nanometers across in monolithic, nanoporous silica gl…
We present measurements on the spontaneous imbibition (capillary rise) of water, a linear hydrocarbon (n-C16H34) and a liquid crystal (8OCB) into the pore space of monolithic, nanoporous Vycor glass (mean pore radius 5 nm). Measurements on the mass uptake of the porous hosts as a function of time, m(t), are in good agreement with the Lucas-Washburn square root of time prediction, typical of imbibition of liquids into porous hosts. The relative capillary rise velocities scale as expected from the bulk fluid parameters.
Imbibition dynamics under dissolution-driven fluid thickening
Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa（里斯本大学理学院理论与计算物理中心）；Debye Institute for Nanomaterials Science, Utrecht University（乌得勒支大学德拜纳米科学研究所）；Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；Departamento de Física, Faculdade de Ciências, Universidade de Lisboa（里斯本大学理学院物理系）
Imbibition, the displacement of a nonwetting fluid by a wetting fluid, plays a central role in diverse energy, environmental, and industrial processes. While this process is typically studied in homogeneous porous media with uniform permeabilities, in many cases, the media have multiple parallel strata of different permeabilities. How such stratification impacts the fluid dynamics of imbibition, as well as the fluid saturation after the wetting fluid breaks through to the end of a given medium, is poorly understood. We address this gap in knowledge by developing an analytical model of imbibiti…
We report an approach to fully visualize the flow of two immiscible fluids through a model three-dimensional (3D) porous medium at pore-scale resolution. Using confocal microscopy, we directly image the drainage of the medium by the non-wetting oil and subsequent imbibition by the wetting fluid. During imbibition, the wetting fluid pinches off threads of oil in the narrow crevices of the medium, forming disconnected oil ganglia. Some of these ganglia remain trapped within the medium. By resolving the full 3D structure of the trapped ganglia, we show that the typical ganglion size, and the tota…
Two-fluid interfaces in porous media, an example of driven disordered systems, were studied by a real time three-dimensional imaging technique with pore scale resolution for a less viscous fluid displacing a more viscous one. With increasing flow rate the interface transforms from flat to fingers and thence to droplets for both drainage and imbibition. The results compare and contrast the effects of randomness, both physical (geometry of the pore space) and chemical (wettability of the fluids), on the dynamical instability and identify the origin of the pore-scale processes that govern them.
Continuum models of porous media use macroscopic parameters and state variables to capture essential features of pore-scale physics. We propose a macroscopic property "accessivity" ($α$) to characterize the network connectivity of different sized pores in a porous medium, and macroscopic state descriptors "radius-resolved saturations" ($ψ_w(F),ψ_n(F)$) to characterize the distribution of fluid phases within. Small accessivity ($α\to0$) implies serial connections between different sized pores, while large accessivity ($α\to1$) corresponds to more parallel arrangements, as the classical capillar…
We report on the capillary rise of water in three-dimensional networks of hydrophilic silica pores with 3.5nm and 5nm mean radii, respectively (porous Vycor monoliths). We find classical square root of time Lucas-Washburn laws for the imbibition dynamics over the entire capillary rise times of up to 16h investigated. Provided we assume two preadsorbed strongly bound layers of water molecules resting at the silica walls, which corresponds to a negative velocity slip length of -0.5nm for water flow in silica nanopores, we can describe the filling process by a retained fluidity and capillarity of…
Wetting phenomena play a key role in flows through porous media. Relative permeability and capillary pressure-saturation functions show a high sensitivity to wettability, which has different definitions at the continuum- and pore-scale. At the continuum-scale, the state of wetting is defined as Amott-Harvey or USBM (United States Bureau of Mines) by capillary pressure drainage and imbibition cycles. At the pore-scale, the concept of contact angle is used, which until recently was not experimentally possible to determine within an opaque porous medium. Recent progress on measurements of pore-sc…
The behaviour of two dimensional binary and ternary amphiphilic fluids under flow conditions is investigated using a hydrodynamic lattice gas model. After the validation of the model in simple cases (Poiseuille flow, Darcy's law for single component fluids), attention is focussed on the properties of binary immiscible fluids in porous media. An extension of Darcy's law which explicitly admits a viscous coupling between the fluids is verified, and evidence of capillary effects are described. The influence of a third component, namely surfactant, is studied in the same context. Invasion simulati…
Diffusion of colored dye on water saturated paper substrates has been traditionally exploited with great skill by renowned water color artists. The same physics finds more recent practical applications in paper based diagnostic devices deploying chemicals that react with a bodily fluid yielding colorimetric signals for disease detection. During spontaneous imbibition through the tortuous pathways of a porous electrolyte saturated paper matrix, a dye molecule undergoes diffusion in a complex network of pores. The advancing front forms a strongly correlated interface that propagates diffusively …
A poromechanical model of partially saturated deformable porous media is proposed based on a phase field approach at modeling the behavior of the mixture of liquid water and wet air, which saturates the pore space, the phase field being the saturation (ratio). While the standard retention curve is expected still to provide the intrinsic retention properties of the porous skeleton, depending on the porous texture, an enhanced description of surface tension between the wetting (liquid water) and the non-wetting (wet air) fluid, occupying the pore space, is stated considering a regularization of …
Hypothesis Control of capillary flow through porous media has broad practical implications. However, achieving accurate and reliable control of such processes by tuning the pore size or by modification of interface wettability remains challenging. Here we propose that the flow of liquid by capillary penetration can be accurately adjusted by tuning the geometry of porous media and develop numerical method to achieve this. Methodologies On the basis of Darcys law, a general framework is proposed to facilitate the control of capillary flow in porous systems by tailoring the geometric shape of por…
