Low Capillary Numbers Research Articles

Numerical simulation of the bubble dynamics in a bifurcated micro-channel using the lattice Boltzmann method

The dynamics behavior of a bubble passing through a bifurcated microchannel is studied numerically by using the lattice Boltzmann model. The effects of channel wettability, the viscosity ratio, the capillary number (Ca), the initial bubble size, and the flow flux ratio on the interface dynamic behavior, breakup mechanism, and residual mass of the bubble through the bifurcated microchannel are studied systematically. The simulation result indicates that these factors have significant influence on the bubble motion behavior. The bubble splits into two sub-bubbles and flow out of the channel completely when the channel surface is hydrophilic. However, some mass residuals of the bubble are observed when the channel surface is hydrophobic and the residual mass increases with the contact angle. On the other hand, as the viscous ratio of gas-liquid increases, the bubble is more likely to break up and to flow out of the channel. In addition, for the case of low capillary number and small bubble size, the bubble cannot break up, so it finally strands in the main channel. Besides, as capillary number increases, the flow flux ratio required for the bubble to flow out of subchannels increases. Eventually, we establish the relation for the critical flow flux ratio Qc as Qc=0.604e13.44Ca and Qc=1.985e5.53Ca to describe whether the bubble breaks up or not for different bubble radii.

Capillary Sorting of Particles by Dip Coating

In this letter, we describe the capillary sorting of particles by size based on dip coating. A substrate withdrawn from a liquid bath entrains a coating whose thickness depends on the withdrawal speed and the liquid properties. If the coating material contains particles, they will only be entrained when the viscous force pulling them with the substrate overcomes the opposing capillary force at the deformable meniscus. This force threshold occurs at different liquid thicknesses for particles of different sizes. Here, we show that this difference can be used to separate small particles from a mixed suspension through capillary filtration. In a bidisperse suspension, we observe three distinct filtration regimes. At low capillary numbers, Ca, no particles are entrained in the liquid coating. At high Ca, all particle sizes are entrained. For a range of capillary numbers between these two extremes, only the smallest particles are entrained while the larger ones remain in the reservoir. We explain how this technique can be applied to polydisperse suspension. We also provide an estimate of the range of capillary number to separate particles of given sizes. The combination of this technique with the scalability and robustness of dip coating makes it a promising candidate for high-throughput separation or purification of industrial and biomedical suspensions.

In-situ pore-scale imaging and image-based modelling of capillary trapping for geological storage of CO2

We describe an imaging and pore-scale modelling study of capillary trapping in the Paaratte Sandstone formation in the Otway Basin, Australia. Three-dimensional X-ray computed tomography (micro-CT) was used to characterize the pore structure of the reservoir core. We obtain in-situ pore-scale images of the distribution of CO2:brine analogue fluid pairs (octane:brine) within reservoir samples during low capillary number drainage and imbibition flooding experiments. The images were recorded using time-lapse X-ray micro-tomography at elevated pressure. The observed two-phase fluid distributions are consistent with a water wet system. The micro-CT images are used directly as input to a geometrically accurate quasi-static pore-scale simulation model. The validity of the quasi-static assumption is investigated by comparing on a pore-by-pore basis the simulated and imaged fluid distributions. The pore filling states are in good agreement both for drainage and imbibition displacements and the computed capillary trapping curve agrees with experimental data. This indicate that quasi-static pore-scale physics can be used to obtain averaged or continuum flow properties for low capillary number displacements. We perform a sensitivity study of the impact of the advancing contact angle on capillary trapping. The magnitude of residual trapping increases with decreasing contact angle. Land's trapping coefficient increases with increasing contact angle. We compute capillary pressure and relative permeability scanning curves. Simulated relative permeability hysteresis is compared with that predicted by the industry-standard Carlson's and Killough's models. Killough's model reproduces the simulated data more accurately.

Characterization of Transport-Enhanced Phase Separation in Porous Media Using a Lattice-Boltzmann Method

Phase separation of formation fluids in the subsurface introduces hydrodynamic perturbations which are critical for mass and energy transport of geofluids. Here, we present pore-scale lattice-Boltzmann simulations to investigate the hydrodynamical response of a porous system to the emergence of non-wetting droplets under background hydraulic gradients. A wide parameter space of capillary number and fluid saturation is explored to characterize the droplet evolution, the droplet size and shape distribution, and the capillary-clogging patterns. We find that clogging is favored by high capillary stress; nonetheless, clogging occurs at high non-wetting saturation (larger than 0.3), denoting the importance of convective transport on droplet growth and permeability. Moreover, droplets are more sheared at low capillary number; however, solid matrix plays a key role on droplet’s volume-to-surface ratio.

Damped interfacial oscillation of a particle-embedded viscous drop

This article describes how a drop with an embedded particle exhibits interfacial waves with transient decay due to the interplay between capillary and viscous effects. To reveal the damped oscillation of the system properly, the deformation and pressure fields inside the domain are described in terms of complete sets of basis functions. Such representation leads to a matrix formulation which enforces no-slip condition at the solid-liquid interface and ensures correct discontinuity in normal stress due to surface tension at the drop periphery. The resulting characteristic equation involving the natural frequencies and the decay constants is solved numerically to determine these quantities. The matrix expression implies a block-diagonalized structure with two uncoupled blocks corresponding to two distinctly different dynamics. The first of these is related to pure rotational velocities on spherical surfaces which monotonically decay in time without any fluctuation in the absence of any peripheral deformation. By contrast, the second block is associated with the undulation in shape. Due to the restoring features of surface tension, the latter can exhibit underdamped oscillatory modes, if the capillary number Ca is below a critical value. However, even these waves would become overdamped if the critical number is exceeded. These values of Ca for a few most relevant modes are plotted in this paper as functions of particle-to-drop size ratio. Also, the natural frequencies for the underdamped cases as well as the damping constants for all considered modes are presented for different size ratios and capillary numbers. The findings are verified by matching the computed results to a novel boundary layer theory under low capillary number limit. Under the limiting condition, both sets of independent calculations yield the same decay constants and natural frequencies providing mutual validations.

Immiscible fluid displacement in porous media with spatially correlated particle sizes

Immiscible fluid displacement in porous media is fundamental for many environmental processes, including infiltration of water in soils, groundwater remediation, enhanced recovery of hydrocarbons and CO2 geosequestration. Microstructural heterogeneity, in particular of particle sizes, can significantly impact immiscible displacement. For instance, it may lead to unstable flow and preferential displacement patterns. We present a systematic, quantitative pore-scale study of the impact of spatial correlations in particle sizes on the drainage of a partially-wetting fluid. We perform pore-network simulations with varying flow rates and different degrees of spatial correlation, complemented with microfluidic experiments. Simulated and experimental displacement patterns show that spatial correlation leads to more preferential invasion, with reduced trapping of the defending fluid, especially at low flow rates. Numerically, we find that increasing the correlation length reduces the fluid-fluid interfacial area and the trapping of the defending fluid, and increases the invasion pattern asymmetry and selectivity. Our experiments, conducted for low capillary numbers, support these findings. Our results delineate the significant effect of spatial correlations on fluid displacement in porous media, of relevance to a wide range of natural and engineered processes.

CO2 storage potential during CO2 enhanced oil recovery in sandstone reservoirs

CO2 can be sequestered in hydrocarbon reservoirs when it is injected for enhanced oil recovery (EOR) purpose. This study aims to experimentally evaluate the CO2 sequestration potential in sandstone reservoirs during CO2-EOR projects with a focus on the effect of active forces in the reservoir. To do so, a series of core flooding experiments at reservoir conditions were conducted using horizontal and vertical systems. A real light crude oil sample together with two native sandstone cores used here that were taken from a Malaysian oil field. The experiments were performed at near-miscible condition. Four secondary CO2 flooding tests were conducted through a composite core arrangement at various flow rates in a horizontal system to investigate the effect of viscous forces on the oil recovery and also the CO2 storage. Additionally, the gravity force effect was studied by conducting a gas (CO2) assisted gravity drainage (GAGD) test in a vertical system. The results showed that the highest oil recovery at all stages of CO2 flooding was obtained during the GAGD test. Considering flooding in the horizontal system, the ultimate recovery factor (RF) was significantly improved by increasing the CO2 injection rate. Furthermore, by investigating the interplay between the governing forces during CO2 injection, it was found that a higher oil RF was obtained at a lower capillary number at early stages of the test, while the CO2 injection rate (viscous forces) should be increased after breakthrough to overcome the capillary forces and recover more oil. In terms of CO2 storage, it was useful to quantify CO2 storage efficiency and CO2 trapping mechanisms which was mainly solubility trapping. Therefore, CO2 solubility in crude oil was also measured at various pressures. The gravitational effect in the GAGD test resulted in the highest CO2 storage percentage. While in the horizontal system, the storage efficiency of CO2 decreased with increasing the injection rate. Furthermore, a dimensionless number was proposed to investigate the combined effect of active forces in addition to CO2 diffusion during CO2 flooding operations. Finally, two correlations based on the combined dimensionless number were introduced to predict oil RF and CO2 storage efficiency for near-miscible CO2 flooding processes.

Dynamic pore-network modeling of air-water flow through thin porous layers

Thin porous layers, that have large aspect ratios, are seen in many applications such as hydrogen fuel cells and hygiene products, in which air-water immiscible flow is of great interest. Direct numerical simulations based on Navier-Stokes equation are computationally expensive, and even prohibitive for low capillary number flow such as water flooding in low-temperature polymer electrolyte fuel cells. Alternatively, the pore-network modeling needs much less computational resources, while still retaining essentials of the pore-structure information. In this work, a dynamic pore-network model of air-water flow with phase change has been developed. We focus on drainage processes through thin porous layers, in which liquid water is the nonwetting phase. Three test cases are conducted, namely, air-water flow through a thin porous layer, air-water flow through a bilayer of fine and coarse thin porous layers, and water flooding in the gas diffusion layer of a polymer electrolyte fuel cell with phase change between water and its vapor. Using these test cases, we aim to demonstrate the application of dynamic pore-network modeling in thin porous media studies. In particular, we discuss the challenge of modeling thin porous media at the average scale, and highlight the role of phase change in removing liquid water from the cathode gas diffusion layer.

A CutFEM method for two-phase flow problems

In this article, we present a cut finite element method for two-phase Navier–Stokes flows. The main feature of the method is the formulation of a unified continuous interior penalty stabilisation approach for the stabilisation of the advection and the pressure–velocity coupling, on the one hand, and the stabilisation of the cut region on the other hand. The accuracy of the algorithm is enhanced by the development of extended fictitious domains to guarantee a well defined velocity from previous time steps in the current domains. Finally, the robustness of the moving-interface algorithm is further improved by the introduction of a curvature smoothing technique that reduces spurious velocities. The algorithm is shown to perform remarkably well for low capillary number flows, and is a first step towards flexible and robust CutFEM algorithms for the simulation of flows in microfluidic devices.

Experimental characterization of a micro cross-junction as generator of Newtonian and non-Newtonian droplets in silicone oil flow at low Capillary numbers

In this paper the generation of Newtonian and non-Newtonian droplets in a continuous silicone oil flow through a micro cross-junction has been studied experimentally. The results obtained by using, as dispersed phase, pure water, water with Tween 20 and different concentrations of Xanthan gum aqueous solutions with the addition of Tween 20 are presented and discussed with the aim to put spotlight on the effect of properties of the involved immiscible liquids on the droplet regimes. A commercial micro cross-junction based on two glass microchannels having a stadium-shaped cross-section and inner hydrophobic walls has been employed. A wide range of volumetric flow rates of the continuous and dispersed phase has been imposed at the inlets of the micro cross-junction by two independent syringe pumps. The main droplet regimes have been correlated to the Capillary number linked to the continuous phase (Cac) and the volumetric flow rate ratio (α). The role of the viscosity ratio (λ) and of the shear-thinning nature of Xanthan gum aqueous solutions on the droplet regime is discussed. The results evidence that the tested micro cross-junction is able to generate very uniform monodispersed droplets with low polydispersity values (P < 6%) at low Capillary numbers (Cac < 0.02) in presence of both Newtonian and non-Newtonian dispersed phases.

Relationship between endothelial dysfunction, videocapillaroscopy and circulating CD3+CD31+CXCR4+ lymphocytes in systemic lupus erythematosus without cardiovascular risk factors.

The objective of this paper is to analyse whether digital capillary morphology, analysed by nailfold videocapillaroscopy (NVC), and the number of circulating CD3 + CD31 + CXCR4 + lymphocytes (angiogenic T cells) could be markers of endothelial dysfunction (ED) in systemic lupus erythematosus (SLE) without cardiovascular disease (CVD) and CV risk factors. Nineteen consecutive SLE patients, according to Systemic Lupus International Collaborating Clinics Classification Criteria, with a disease duration less than five years, low disease activity, without CVD and CV risk factors (diabetes, chronic renal disease, uncontrolled systemic arterial hypertension, smoking, hypercholesterolemia, obesity), statin or beta-blocker use were enrolled. Each patient and sex- and age-matched healthy control (HC) underwent Doppler echocardiogram, an endothelial function study by peripheral arterial tonometry technique, NVC and peripheral blood immunophenotyping. SLE ED+ more frequently showed NVC abnormalities compared with HCs ( p < 0.0001) in terms of minor alterations ( p = 0.017), lower capillary numbers ( p = 0.0035) and major alterations. SLE ED + showed a higher rate of CD3 + CD31 + CXCR4 + lymphocytes compared with SLE ED- and with HCs. NVC + SLE showed a significantly reduced rate of total CD3 + cells, but a higher rate and absolute number of CD3 + CD31 + CXCR4 + , compared with NVC- SLE. NVC alterations are frequent in SLE without any CV risk factors and CVD. They are associated with ED and increased circulating CD3 + CD31 + CXCR4 + lymphocytes. These findings demonstrate a clear microvascular perturbation in patients with short disease duration, low disease activity and no CV risk factors.

Viscoelastic displacement and anomalously enhanced oil recovery of a novel star-like amphiphilic polyacrylamide

Star-like amphiphilic polyacrylamide (SHPAM), consisting of nano-SiO2 as the core and a layer of amphiphilic chains as the shell, having two gradient molecular weights, was prepared via a facile method. To elucidate its enhanced oil recovery (EOR) potential, the viscoelastic flow and displacement efficiency of SHPAM were studied using geological rock-core samples. The results showed that the core-shell microstructure and intermolecular interactions imparted viscoelasticity to SHPAM in a lower-concentration region. The elasticity mechanism of SHPAM solutions in porous media was determined by quantifying the relaxation time. Low-field nuclear magnetic resonance experiments suggested that SHPAM flowed through the dominant porous media followed by intermediate porous media having radii of 0.08–10.0μm. The thickness of the adsorbed layer was independent of the shear rate, demonstrating that SHPAM was compatible with porous media owing to the reversibly viscoelastic flow. The core flooding tests demonstrated that even after hydrolyzed polyacrylamide flooding, 3.0% oil saturation was further recovered by SHPAM flooding even in a region with low capillary number (<10−5). Moreover, over 27% oil recovery with 70% cumulative oil recovery was achieved with a SHPAM pore volume of 0.3 and concentration of 1500mg/L. The displacement efficiency tests confirmed that the high viscoelasticity of SHPAM imparted anomalous enhanced oil recovery efficiency to the HPAM.

Kinematic and dynamic forcing strategies for predicting the transport of inertial capsules via a combined lattice Boltzmann – Immersed Boundary method

Modeling the transport of deformable capsules under different flow regimens is crucial in a variety of fields, including oil rheology, blood flow and the dispersion of pollutants. The aim of this study is twofold. Firstly, a combined Lattice Boltzmann – Immersed Boundary (LBM – IB) approach is developed for predicting the transport of inertial deformable capsules. A Moving Least Squares (MLS) scheme has been implemented to correlate the pressure, velocity and force fields of the fluid domain with the capsule dynamics. This computational strategy has been named LBM – Dynamic IB. Secondly, this strategy is directly compared with a more conventional approach, named LBM – Kinematic IB, where capsules move with the same velocity of the surrounding fluid. Multiple test cases have been considered for assessing the accuracy and efficiency of the Dynamic over Kinematic IB scheme, including the stretching of circular capsules in shear flow, the transport in a plane Poiseuille flow of circular and biconcave capsules, with and without inertia. By monitoring the capsule geometry over time, the two schemes have been documented to be in excellent agreement, especially for low Capillary numbers (Ca ≤ 10−2), in the case of non-inertial capsules. Despite a moderate increase in computational burden, the presented LBM – Dynamic IB scheme is the sole capable of predicting the dynamics of both non-inertial and inertial deformable capsules. The proposed approach can be efficiently employed for studying the transport of blood cells, cancer cells and nano/micro capsules within a capillary flow.

Effects of grain size and shape distribution on pore-scale numerical simulation of two-phase flow in a heterogeneous porous medium

Series of numerical simulations were done to quantify the effects of pore structure approximations on micro-scale displacement mechanisms. Coupled Cahn–Hilliard phase field and Navier–Stokes equations were solved using finite element method to simulate two-phase flow in a heterogeneous model -having a real pore network- as the base case, compared to two other approximated models; in one of those, the complex grain geometries were simplified to circular shapes; while in the other one, only the sizes of the real-shaped grains were gently (less than ±10%) modified. In both approximated models, the medium porosity and absolute permeability were kept unchanged, compared to the base case. The simplification of the grain shapes changed the morphologies of the formed fingers and the trapped oil volumes. The general trends of the oil recovery factor and macro-scale capillary pressure variations were similar during displacement at different medium wettabilities for the base and the simplified models. However, the simplified model showed higher displacement efficiency at water-wet conditions and lower capillary pressures at oil-wet conditions; due to less complexity of its pore network geometry. Different micro-scale events were captured similarly in both models, including reverse displacement, interface coalescence, water bursting and stick-slip motion. But the oil trapping mechanisms were totally different. Slight modification of the grain sizes resulted in different displacement profiles, especially at neutral and oil-wetting conditions and low capillary numbers (log Ca < −3.69), due to modification of capillarity in the medium, hence variation of the preferred paths of the displacing phase finger(s).

Deformation of a biconcave-discoid capsule in extensional flow and electric field

Natural (red blood cells) and artificial biconcave-discoid-shaped capsules have immense biological (a cellular component of blood) and technological (as drug carrier) relevance, respectively. Their low reduced volume allows significant shape changes under external fields such as extensional flows (encountered at junctions and size-varying capillaries in biological flows) and electric fields (in applications such as electroporation and dielectrophoresis). This work demonstrates biconcave-discoid to capped-cylindrical and prolate-spheroid shape transitions of a capsule in uniaxial extensional flow as well as in DC and AC electric fields. The shape changes of a stress-free biconcave-discoid capsule in external fields are important in determining the momentum and mass transfer between the capsule and the medium fluid as well as dielectrophoresis and electroporation phenomena of a capsule in an electric field. The biconcave-discoid to capped-cylindrical/prolate-spheroid shape transition is demonstrated for both a capsule (with parameters relevant to drug delivery) as well as for a red blood cell (physiological conditions). However, significant differences are observed in this shape transition depending upon the applied external fields. In an extensional flow, the pressure-driven transition shows the equator being squeezed in and the poles being pulled out to deform into a capped cylinder at low capillary number and a prolate spheroid at high capillary number. On the other hand, in the transition driven by electric fields, the shoulders of the capsule seem to play a significant role in the dynamics. The shape transition in the electric fields depends upon the relative magnitude of the electric and the hydrodynamic response times, particularly relevant for the dynamics of red blood cells in physiological conditions. A new method of analysing the shape transition of red blood cells in AC electric fields is suggested, where a large separation of time scales is observed between the hydrodynamic and electric responses.

Wettability-mediated dynamics of two-phase flow in microfluidic T-junction

Fundamental understanding of two-phase flow and the concomitant implications of wall wettability and viscosity are critical in areas like microfluidics and lab on chip applications. In this work, numerical investigation of the displacement of two immiscible fluids in a T-junction is presented. The study reveals the interplay of critical physicochemical determinants like capillarity, viscosity, and wettability on the dynamics of two-phase flow. Temporal evolution of the displacement of dispersed phase resulting into different regimes like squeezing, dripping, necking, droplet formation, and jetting for a combination of capillary numbers, viscosity ratios, and wettability scenarios is furnished in detail in order to elucidate the mechanism of droplet formation through the displacement behavior of two-phase flow. The findings establish the surface wettability to be the dominating factor in determining the time evolution of the dispersed liquid interface at a lower capillary number. With the increase in the hydrophobicity of the surface, the liquid interface transits from squeezing to dripping and then to droplet formation at a low capillary number. However, irrespective of wettability, the regime changes from jetting to parallel flows due to an increase in capillary number beyond a critical limit. Furthermore, the phenomenon of squeezing, necking, and breakage occurs relatively earlier with the increase in viscosity ratio and hydrophobicity of the surface. These results may bear significant implications toward designing of droplet dispensing systems with the substrate wettability as a critical controlling parameter.

Thermocapillary flows on heated substrates with sinusoidal topography

Two-dimensional steady thermocapillary flows in a liquid layer over a substrate, which has a uniform temperature and sinusoidal topography, are investigated by asymptotic theory. Here, the buoyancy effect is negligible and the interface is not significantly disturbed under low Marangoni number and low capillary number. A temperature gradient along the gas/liquid interface causes recirculating flows. For a small aspect ratio, which yields a sinusoidal topography with a long wavelength relative to the mean depth of the liquid layer, the second-order solutions are obtained analytically. The basic solutions show vertical diffusion of heat and vorticity from the substrate and interface, respectively. In the second corrections, the horizontal diffusion of heat weakens the overall flow and the convection of heat intensifies it.

Breakup versus coalescence of closely packed fluid drops in simple shear flows

Using computational fluid dynamic (CFD) simulations, based on an improved conservative level set method we investigated the dynamics of mechanically interacting fluid drops in closely packed drop systems under simple shear flow. Our 2D simulations show drop concentration (ψ) as a key factor, in addition to capillary number (Ca) in controlling the two competing processes: breakup and coalescence. For a given ψ, the breakup process governs the drop dynamics when Ca exceeds a critical value (Cac); this is replaced by the coalescence process as Ca < Cac. The Cac value is found to increase non-linearly with ψ. We observed varying modes of breakup as a function of ψ for different Ca values. Low concentrations (ψ ∼ 0) give rise to drop breakup by mid-point pinching, forming smaller daughter drops of nearly equal size. Increasing ψ transforms this breakup mode into another mode characterized by asymmetric capillary instability at the drop edges. On the other hand, high Ca promotes the capillary instability to develop uniformly in strongly flattened drops, resulting in their homogeneous breakup. We demonstrate that these three modes: mid-point pinching, edge breakup and homogeneous breakup yield characteristic drop size distributions (DSDs). Our multiple drop models provide a concentration limit (ψ < 0.4) for the breakup process; this is taken over by coalescence drop dynamics as ψ exceeds this limit. It is shown that two contrasting mechanisms: tension-driven interfacial burst and compression-driven interfacial wave instability operate in the coalescence processes under low (Ca < 0.2) and high (Ca > 0.2) capillary numbers, respectively under high concentrations (ψ > 0.4). The first coalescence mechanism develops a single bridge between two adjoining drops, which grows in diameter non-linearly with time. We predict distinctive non-linear relations for collision and pull-apart drop configurations. We finally synthesize the breakup and coalescence mechanisms in a ψ – Ca space.

Multiscale simulations of sliding droplets

We study—through numerical simulations—a droplet sliding over a solid substrate as a result of a simple shear flow. We use a free-energy lattice Boltzmann (LB) scheme and compare its results with those of molecular dynamics (MD) simulations. According to the MD, at sufficiently low Reynolds and capillary numbers, the dimensionless sliding speed is a unique function of the equilibrium contact angle. Reproducing the MD results with LB simulations requires the use of a non-equilibrium boundary condition at the substrate and tuning a free parameter in the boundary condition.

Influence of wettability on phase connectivity and electrical resistivity

Experimental results have shown that resistivity index can deviate from Archie's law at low conductive phase saturation. Previous works have claimed that wettability and flow history are the two main factors causing this phenomenon. Herein, we investigate how the underlying fluid morphology influences electrical resistivity. We start from digital synchrotron x-ray microcomputed tomography images at different conductive phase saturations. We then simulate two-phase flow at different Capillary numbers and wettabilities to investigate deviations in resistivity index. We discover that other than water saturation the connectivity of water quantified by Euler characteristic is an important parameter in determining electrical resistivity for intermediate to purely oil-wet conditions. Deviations in electrical resistivity are found to start at low Capillary number ($\mathrm{Ca}\ensuremath{\sim}{10}^{\ensuremath{-}5}$) for intermediate and oil-wet conditions for the full range of water saturations. We study correlations between resistivity index, saturation, and Euler characteristic by using the Pearson product-moment correlation and a linear regression model. We find a strong correlation between water saturation and resistivity index for the water-wet case while for the intermediate and oil-wet cases a strong correlation between Euler characteristic and resistivity index was observed. The results are explained in terms of percolation theory and a general relationship for resistivity index is proposed for intermediate-wet to oil-wet systems whereby the percolation parameter is normalized Euler characteristic. The findings explain previously observed deviations in resistivity index measurements and allow for a means to predict Euler characteristic from laboratory core-scale experiments using the proposed percolation model.