# Fabrication technique for mixed hydrophobic-hydrophilic wettability micromodels: Experimental and numerical validation

Abdullah Alomier, Marwan Fahs, Hussein Hoteit

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Abdullah Alomier, Marwan Fahs, Hussein Hoteit. Fabrication technique for mixed hydrophobic-hydrophilic wettability micromodels: Experimental and numerical validation. Physics of Fluids, 2025, 37, 10.1063/5.0244023. insu-05082258

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# Fabrication technique for mixed hydrophobic-hydrophilic wettability micromodels: Experimental and numerical validation

Abdullah AlOmier ⚙️ ; Marwan Fahs ⚙️ ; Hussein Hoteit 🧮

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Physics of Fluids 37, 012108 (2025)

https://doi.org/10.1063/5.0244023

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# Fabrication technique for mixed hydrophobic-hydrophilic wettability micromodels: Experimental and numerical validation

Cite as: Phys. Fluids **37**, 012108 (2025); doi: 10.1063/5.0244023

Submitted: 15 October 2024 · Accepted: 6 December 2024 ·

Published Online: 8 January 2025

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Abdullah AlOmier,<fnref n="1" />,<fnref n="2" /> ID Marwan Fahs,<fnref n="3" /> ID and Hussein Hoteit<fnref n="1" />,ª ID

## AFFILIATIONS

## ABSTRACT

Subsurface reservoirs often display heterogeneous hydrophobic-hydrophilic wettability, known as mixed wettability, which significantly impacts the behavior of multiphase fluid flow and their entrapments. Microfluidic systems have emerged as a crucial tool for studying the impact of wettability on fluid flow at the pore scale. However, creating microfluidic devices with controlled spatial distribution of mixed wettability has been a challenge. This study investigates a novel technique for fabricating micromodels with controlled mixed wettability, using photolithography and molecular vapor deposition of perfluorodecyltrichlorosilane. The primary objective is to validate this technique through two-phase flow experiments and numerical simulations. Six different configurations of mixed wettability micromodels, including single channels with horizontal and vertical mixed wettability, Y-shaped channels with two and multiple mixed-wet branches, and mixed-wet pore-doublet models, were designed and fabricated to mimic the complex wettability variations found in natural porous media. Experimental observations, captured with a high-resolution microscope and high-speed camera, provided dynamic insights into the influence of mixed wettability on two-phase fluid flow. Pore-scale simulations, conducted using the phase-field approach in COMSOL Multiphysics®, were performed to replicate and validate the experimental findings. Simulations showed excellent agreement with the experimental results, affirming the effectiveness of the proposed fabrication technique, the robustness of the experimental setup, and the reliability of the numerical model.

© 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0244023

## I. INTRODUCTION

Optimized hydrocarbon recovery, carbon dioxide (CO₂) sequestration, and hydrogen (H₂) storage have become increasingly significant for various energy and environmental applications (Heinemann et al., 2021; Metz et al., 2005; Tabrizinejadas et al., 2023; and Thomas, 2008). Achieving success in these areas at the reservoir scale requires a comprehensive understanding of multiphase flow dynamics at the pore scale (Valvatne and Blunt, 2004). For instance, understanding interfacial forces within porous media is essential for enhancing oil extraction through water flooding and improving CO₂ storage efficiency in deep saline aquifers. These microscopic processes directly impact the macroscopic performance, influencing the overall efficiency and economic feasibility of field-scale operations.

In porous media, fluid-fluid displacement involves mobilizing one fluid by another in a confined space and is primarily controlled by the interplay between capillary and viscous forces (Alaamri et al., 2024). When two immiscible fluids come into contact, they form a curved interface. Capillary pressure arises due to this curvature, which is significantly influenced by the wettability of solid surface (de Gennes et al., 2004). Wettability, defined by the tendency of a solid surface to preferentially interact with one fluid over another, is a critical petrophysical property that directly impacts two-phase flow in porous media (Blunt, 2017). It plays a pivotal role in determining the efficiency of fluid phase mobilization and displacement processes (Lake et al., 2014). The affinity of a solid surface to a fluid varies significantly based on the pore material and fluids occupying the pores

<footnote n="1">¹Physical Science and Engineering Division (PSE), King Abdullah University of Science and Technology (KAUST), Thuwal 23955, Saudi Arabia</footnote>

<footnote n="2">²EXPEC Advanced Research Center, Saudi Aramco, Dhahran 31311, Saudi Arabia</footnote>

<footnote n="3">³Université de Strasbourg, CNRS, ENGEES, Institut Terre et Environnement de Strasbourg, UMR 7063, F-67000 Strasbourg, France</footnote>

<footnote>ª) Author to whom correspondence should be addressed: Hussein.hoteit@kaust.edu.sa</footnote>
(Morrow, 1990). Natural subsurface reservoirs often exhibit wettability heterogeneity, commonly referred to mixed wettability. In such systems, different hydrophobic and hydrophilic wettability states coexist within the porous media due to variations in mineral composition or the deposition of organic components, such as asphaltenes, from the contacting oil phase (Kovscek et al., 1993; Radke et al., 1992; and Salathiel, 1973). Despite its prevalence, the effect of mixed wettability on flow processes and capillary trapping in porous media is not well understood compared to homogenous wettability (Hu et al., 2018; Lei et al., 2022; Mascini et al., 2021; Trojer et al., 2015; and Zhao et al., 2016).

Several studies have utilized core-flooding experiments to investigate the impact of wettability on multiphase flow in porous media. These experiments often employ samples extracted directly from the reservoir to preserve natural conditions or synthetic samples that are treated and aged to replicate the mixed wettability characteristics of reservoir rocks (Anderson, 1986). Noticeable variations in flow dynamics were observed in mixed-wet rocks compared to the uniformly wet (Alhammadi et al., 2020; Al-Menhali et al., 2016; Al-Menhali and Krevor, 2016; Lin et al., 2019; Scanziani et al., 2020; and Zou et al., 2018). Despite their realistic representation of subsurface reservoirs, core-flooding experiments face limitations, primarily due to the opacity of the samples. This opacity hinders the observations of microscale mechanisms, which is constrained by the resolution and time limitations of imaging techniques such as micro-computed tomography (micro-CT) scanning. As a result, capillary pressures and relative permeabilities are typically derived from Darcy-scale core flood experiments, serving as indirect assessments of wettability (Rücker et al., 2019). Additionally, the core-sample complex structures with varying wettability conditions limit the capacity of the experiments to provide accurate interpretations of the impact of wettability on flow behaviors.

Microfluidics have emerged as a viable alternative for investigating multiphase flow in porous media, effectively addressing the limitations associated with the opacity of rocks (Sinton, 2014; Whitesides, 2006). Microfluidics utilize models with micrometer dimensions that mimic the connectivity and structure of porous media. These models are transparent, facilitating direct observation of fluid flow behavior in a controlled setting, offering significant value for industrial applications (Lifton, 2016; Song and Kovscek, 2016). Although many studies have explored the impact of homogenous wettability on pore-scale flow behavior (Cottin et al., 2011; Hu et al., 2017; Lei et al., 2022; and Zhao et al., 2016), classical microfluidic studies have largely overlooked the role of mixed wettability due to the challenges in fabricating microfluidic devices with controlled mixed-wet properties.

Several techniques have been developed to address this gap by creating heterogeneous wettability patterns in micromodels to study multiphase flow in porous media. For instance, Lee et al. introduced a method to construct polymeric microstructures with heterogeneous wetting properties in initially empty microchannels (Lee et al., 2015). While this technique successfully incorporated wetting heterogeneity, the flow primarily occurred around geometric features, which does not fully capture the complexity of mixed-wet surfaces typically found in natural rock systems. Similarly, Chang et al. introduced a mixed-wet system by injecting octadecyltrichlorosilane (OTS) diluted in hexane to coat the inner surface of glass micromodel (Chang et al., 2020). However, this approach lacked precise control over spatial wettability modification, as only the invaded regions were altered, making it

challenging to accurately replicate natural mixed-wettability characteristics observed in natural formations. Irannezhad et al. employed a method using high-energy ultraviolet (UV) radiation through a UV-blocking mask to locally modify the hydrophobic properties of photocurable polymer (NOA81) micromodels, creating hydrophilic clusters (Irannezhad et al., 2023). While effective in achieving localized wettability alterations, this technique faces durability challenges, with the altered wettability remaining stable for only a few days (Levaché et al., 2012; Masouminia et al., 2022). Sun and Torres-Verdín applied hydrophobic triethoxyoctylsilane to a vinyl stencil patterned sheet on a Hele-Shaw cell, enabling wettability patterning over large areas (Sun and Torres-Verdín, 2023). However, the limited resolution of this approach may not adequately reflect the complexities of mixed wettability at microscale. Despite these advancements, achieving precise spatial control of wettability distribution at high resolution remains a significant challenge. Recently, AlOmier et al. introduced a novel methodology to address these limitations by developing a robust technique for creating durable, well-controlled mixed-wettability micromodels (AlOmier et al., 2022, 2024). This method uses selective wettability modification through photolithography and the molecular vapor deposition (MVD) of perfluorodecyltrichlorosilane (FDTS), enabling precise surface wettability alteration of microfluidics.

This research explores the validity of the previous proposed technique to generate various mixed wettability configurations in different microfluidic systems. It also examines the effectiveness of this technique under two-phase flow conditions. To accomplish these objectives, this study utilizes both experimental and numerical simulations. The methodology includes: (i) fabricating different micromodels with various mixed wettability designs, (ii) performing two-phase flow experiments, and (iii) performing two-phase numerical simulations to mimic the experimental observations. Six different designs of mixed-wet micromodels (single capillary channels, Y-branching channels, and pore-doublet models) were fabricated. Experimental observations were captured with high-resolution microscope objective coupled with a high-speed camera. These observations were compared to numerical simulations performed using COMSOL Multiphysics®. The corresponding mathematical model was based on the phase field approach for fluid interface tracking. The mathematical model combined the Navier-Stokes equation for fluid flow within the phase field transport equation that allows for considering the presence of two fluids. The fluid properties used in the Navier-Stokes equations were calculated based on the phase field function. Wettability was modeled as a boundary condition in the phase field equation.

This work, which delineates the development and validation of a new fabrication technique for microfluidic devices with controlled mixed wettability, is organized as follows. We begin by reviewing the methodology using photolithography and MVD. Subsequent sections present a series of experimental setups and two-phase flow experiments designed to test the efficacy of the fabricated micromodels. These are complemented by numerical simulations that confirm experimental results and provide deeper insights into fluid dynamics at the pore scale. This approach enables the creation of mixed-wettability microfluidic devices with the flexibility to accommodate a wide range of designs, including complex geometries. This versatility provides a valuable platform for conducting advanced studies in applications involving multiphase flow in porous media.
## II. METHODOLOGY

### A. Developed technique for mixed wettability

The microfluidic devices were fully fabricated in-house using standard photolithography techniques, which enable the transfer of pre-designed geometric patterns onto a substrate. Silicon was selected as the primary material for the devices due to its well-established and reliable fabrication process. To enable the visualization of flow behavior, the microfluidic devices were designed with partial optical transparency. The fabrication process of mixed wettability micromodels utilized selective surface coating. The workflow, illustrated in Fig. 1, outlines the micromodels fabrication process, highlighting the surface modifications implemented to achieve the mixed wettability features (AlOmier et al., 2024). The process consisted of three main steps. First, two design layers were developed: layer-1 represents the flow patterns, while layer-2, applied on top, defines the location and shape of the wettability patterns. The two design layers were created using Clewin layout editor software, with all patterns converted into a full micromodel layout of size 2 × 1 cm². These layers were printed onto two 5-inch chromium-coated glass photomasks (Nanofilm, USA) using a high-resolution DWL 66+ laser lithography system (Heidelberg Instruments, Germany). The resulting photomasks were partially coated with chromium, providing transparency in specific areas to define both the micromodel features and wettability patterns. This allows light to pass through the unmasked transparent areas while being blocked in the chrome-covered areas, thus defining the required features.

In the second step, micromodels were fabricated using layer-1 photolithography. A 4-inch silicon wafer (MSE Supplies, USA) served as the substrate. The wafer was vapor-primed with hexamethyldisilazane (HMDS) to promote adhesion and then spin-coated with a 4 µm layer of AZ ECI-3027 positive photoresist (MicroChemicals GmbH, Germany). The designed flow patterns were transferred onto the wafer by exposing the transparent areas of the layer-1 mask to UV light using a high-resolution double-side mask aligner (EVG 6200, EV Group, Austria). The UV-exposed photoresist became soluble and was removed with AZ-726 MIF developer (MicroChemicals GmbH, Germany). The exposed surface was etched to engrave the patterns onto silicon using cyclic perfluorocyclobutane ($C_4F_8$) and sulfur hexafluoride ($SF_6$) plasma in a deep reactive-ion etching (DRIE) tool (Oxford Instruments, United Kingdom). Finally, the remaining photoresist was stripped off, and the wafer was cleaned in a piranha solution, composed of a 3:1 mixture of sulfuric acid ($H_2SO_4$) and hydrogen peroxide ($H_2O_2$), at 115 °C for 10 min.

In the third step, the alteration of the micromodel surface wettability was performed using layer-2 photolithography. The patterned wafer was spin-coated with a 6 µm layer of AZ ECI-3035 negative photoresist (MicroChemicals GmbH, Germany). Wettability patterns were precisely imprinted on top of the patterned wafer by exposing the layer-2 mask to UV light using high-resolution alignment marks. For the negative photoresist used, only the unexposed areas, which were covered by the wettability mask, were removed by the AZ-726 MIF developing solution. This exposed the micromodel surface areas

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<figure><img src="image_13.png" /><figcaption>**FIG. 1.** Workflow of the mixed-wettability microfluidic device fabrication process, beginning with (1) pattern design and mask writing, displaying the top view of the entire micromodel layout, sized 2 × 1 cm² on a 5-inch photomask. This is followed by (2) the first layer of photolithography and dry etching to engrave the flow pattern onto the silicon surface, and (3) the second layer of photolithography with selective coating guided by the second photomask to instill mixed wettability features. The process concludes with the dicing and bonding of the microfluidic devices.</figcaption></figure>
targeted for wettability alteration while protecting the rest with the resist. The wafer was then fully coated with hydrophobic FDTS in a vacuum chamber using an MVD 100 tool (Applied Microstructures, United States). Subsequently, the remaining photoresist was lifted off from the silicon surface using n-methylpyrrolidone (NMP) solvent, leaving the protected silicon surface uncoated with FDTS. Finally, the micromodels were diced and bonded with a thin layer of polydimethylsiloxane (PDMS) to create the final mixed-wet microfluidic chip.

## B. Experimental setup

All microfluidics flow experiments were conducted using a microscope setup to allow direct observations at pore-scale under dynamic conditions (Fig. 2). The setup comprised a high-resolution optical microscope (ZEISS Axio Examiner, Germany) equipped with an EC Epiplan-Neofluar 5× magnification objective. An ORYX 10GigE high-speed camera (FLIR Systems Inc., United States) was integrated with the microscope to enable direct flow observation and recording. This camera features a 7.1-megapixel resolution and is equipped with a Sony IMX420 color sensor, connected to a computer for data acquisition purposes. Visualization was achieved using the bright-field technique, where reflected light is imaged. The microfluidic chip was mounted on the stage directly below the observation lens to provide the necessary field of view. Flow was injected into the chip using a PHD ULTRA syringe pump (Harvard Apparatus, United States), with fluid transported through stiff 1/32-inch ID Teflon tubing. The injected fluid was de-ionized (DI) water colored for visualization purposes.

## C. Mathematical and numerical models

The simulation of the two-phase flow through the channels of the micromodels accounted for fluid-fluid and fluid-solid interfacial

<figure><img src="image_14.png" /><figcaption>FIG. 2. Experimental setup for the flow experiments, including a high-resolution optical microscope with a magnification objective, integrated with a high-speed camera for flow observation. A syringe pump is used for fluid injection into the microfluidic chip.</figcaption></figure>

forces while tracking the propagation of the fluid-fluid interface. Different computational fluid dynamics (CFD) methods using Navier-Stokes equation coupled with fluid-fluid interface tracking have been proposed in the literature, such as the volume of fluid method (Ambekar et al., 2021; Zhu et al., 2021), level-set method (Jettestuen et al., 2013; Verma et al., 2018), and phase-field method (Cueto-Felgueroso and Juanes, 2014; Rokhforouz and Akhlaghi Amiri, 2017; and Shi et al., 2023).

In this work, the phase-field approach was used for modeling the dynamics of two-phase flow through the channels of the micromodels. With this approach, a mathematical function representing the phase field was used to track the two propagating fluids. This phase-field variable ranges between +1 and -1, with the extreme values corresponding to the pure fluids and the intermediate values indicating the mixture of the two fluids. The interface between the fluids was represented by a narrow diffusive zone, corresponding to the isoline zero of the phase-field function. The interface displacement was modeled using the advection-diffusion equation of the phase-field function (Jain, 2022). The capillary processes were simulated by incorporating the surface tension between the fluids. These equations are given as follows:

$$ \frac{\partial \varphi}{\partial t} + u \cdot \nabla \varphi = \nabla \cdot \left( \frac{\gamma \lambda}{\varepsilon_{pf}^2} \nabla \Psi \right), \quad (1) $$

where $\varphi[-]$ is the phase-field function ranging between 1 and -1, $u(m/s)$ is the flow velocity, and $\varepsilon_{pf}(m)$ is a numerical parameter controlling the interface thickness. As $\varepsilon_{pf}$ tends to zero, the diffusive interface converges to a sharp interface (Feng, 2006). The parameters $\gamma(m^3 s kg^{-1})$ and $\lambda(N)$ are defined as follows:

$$ \gamma = \chi \varepsilon_{pf}^2, \quad (2) $$

$$ \lambda = \frac{3 \varepsilon_{pf} \sigma}{\sqrt{8}}, \quad (3) $$

where $\chi(m s kg^{-1})$ is a mobility tuning parameter and $\sigma(N m^{-1})$ is the surface tension.

The term $(\frac{\gamma \lambda}{\varepsilon_{pf}^2})$ represents a diffusion coefficient, and the function $\Psi[-]$ represents the chemical potential, defined by

$$ \Psi = -\nabla \cdot \left( \varepsilon_{pf}^2 \nabla \varphi \right) + (\varphi^2 - 1) \varphi + \frac{\varepsilon_{pf}^2}{\lambda} \frac{\partial f}{\partial \varphi}. \quad (4) $$

In Eq. (4), $\partial f / \partial \varphi(J/m^3)$ is a parameter expressing the derivative of the free external energy with respect to the phase field function.

The flow of the fluids in the domain was simulated using the mass conservation and the Navier-Stokes equations for incompressible fluids. Under steady-state conditions, these equations are given by

$$ \rho u \cdot \nabla u = -\nabla p + \nabla \cdot (\mu(\nabla u + \nabla u^T)) + \rho g + F_{st}, \quad (5) $$

where $u(m s^{-1})$ is the velocity field, $\rho(Pa)$ is the pressure, $\rho(kg m^{-3})$ and $\mu(Pa s)$ are, respectively, the density and viscosity of the fluid, $g(m s^{-2})$ is the gravitational acceleration, and $F_{st}(N)$ is the surface tension force.

The velocity field is specific to each phase. For instance, in any part of the domain, if the phase-field function is equal to 1, $u$ will represent the velocity of the first phase, and where the phase field function
is equal to -1, u will represent the velocity of the second phase. The properties of the fluids (i.e., density and viscosity) at the interface were approximated as an average of the properties of the two fluids weighted by the phase-field, that is,

$$ \rho = \rho_1 \left( \frac{1 - \varphi}{2} \right) + \rho_2 \left( \frac{1 + \varphi}{2} \right), \qquad (6) $$

$$ \mu = \mu_1 \left( \frac{1 - \varphi}{2} \right) + \mu_2 \left( \frac{1 + \varphi}{2} \right). \qquad (7) $$

The surface tension was expressed as a function of the gradient of the phase-field,

$$ F_{st} = \left( \frac{\lambda}{\varepsilon_{pf}^2} \Psi - \frac{\partial f}{\partial \varphi} \right) \nabla \varphi. \qquad (8) $$

The contact angle with the solid wall was modeled as a boundary condition, given by

$$ n \cdot \frac{\gamma \lambda}{\varepsilon_{pf}^2} \nabla \Psi = 0, \qquad (9) $$

$$ n \cdot \frac{\nabla \varphi}{|\nabla \varphi|} = \cos(\theta), \qquad (10) $$

where $\theta$(rd) is the contact angle with the solid boundary and n is the outward normal vector at the boundary.

Equation (9) indicates that the diffusive flux of the phase-field function over the surface is zero, while Eq. (10) specifies that the angle between the outward normal of the interface ($\nabla\varphi/|\nabla\varphi|$) and the outward normal of the wall (n) is the contact angle ($\theta$) (Fig. 3). As the experiments were conducted at low and almost constant pressure, both fluid phases were assumed to be incompressible and immiscible at isothermal and laminar conditions. Given the size of the model, the gravity is neglected.

### III. RESULTS AND DISCUSSION

In this study, six micromodels with varying wettability configurations were designed to validate the fabrication methodology and to further explore the impact of mixed wettability on two-phase flow at the

<figure><img src="image_15.png" /><figcaption>FIG. 3. Boundary conditions representing the surface forces by imposing the contact angle ($\theta$) that varies spatially depending on the wettability of the solid boundary.</figcaption></figure>

pore level. Each configuration was specifically designed to simulate common features observed in subsurface porous media, allowing for a systematic study of the effects of varying wettability and pore-scale geometries on fluid flow behavior. These included flow through pores with heterogeneous wettability surfaces, flow through branches with differing wettability states, and parallel pore-throats with variations in both wettability and size. Together, presented in increasing order of complexity, these configurations offer a structured approach to studying the impact of mixed wettability on displacement processes under controlled conditions.

Figure 4 shows the flow units of the six micromodels with heterogeneous wettability patterns highlighted in different colors, where blue represents hydrophilic wettability and red represents hydrophobic wettability. The micromodels were initially hydrophilic (i.e., all blue, $\theta$ = 50°). The wettability, highlighted in red, was then altered by applying a hydrophobic coating ($\theta$ = 113°) on the solid surface. Figure 5 shows the fabricated 2 × 1 cm² microfluidic chip made from silicon, featuring channels with mixed wettability configurations.

To assess the fabrication effectiveness, scanning electron microscopy (SEM) images were captured throughout the fabrication process, as shown in Fig. 6. Figure 6(a) illustrates the selective opening of the designated areas of the channels by removing the photoresist. The image clearly shows the regions where the photoresist remains intact, protecting the surface during the coating process, while other parts reveal a clean silicon surface ready for coating. This demonstrates the precision of the layer-2 photolithography in creating selective hydrophilic and hydrophobic regions on the micromodel surface. Figure 6(b) presents a top view of the fabricated single mixed-wet channel with a width of 100 µm. The image shows the channel half-coated, indicated by the different gray color contrast, which demonstrates the precise application of the coating. The areas between the “X” marks highlight the distinct regions of hydrophobic and hydrophilic surfaces. Figure 6(c) shows a Y-shaped channel with a width of 50 µm, where one branch is coated and the other remains uncoated. Figure 6(d) presents a 40° tilted image of an etched flow channel with a depth of 30 µm. This image indicates the precise and sharp etching process used to create vertical walls, which is critical for maintaining the capillary forces that control flow behavior based on channel width. Additionally, it highlights the uniform coating applied to both the surface and walls of the selected channel, ensuring consistent wettability properties throughout the structure. Different coating configurations applied to the doublet model are confirmed for the first time to achieve mixed wettability. In Fig. 6(e), the smaller upper channel is coated, while the one in Fig. 6(f), the larger lower channel is coated. Overall, the color difference between the coated and uncoated regions also demonstrates the reliability of the fabrication process in producing well-defined wettability patterns. The ability to accurately coat these regions is essential for representing controlled wettability conditions found in subsurface porous media.

A set of two-phase flow experiments were conducted to investigate the effects of surface mixed wettability on various factors, including interface behavior, preferential flow paths, and displacement mechanisms. In these experiments, water (fluid 2, displacing phase) displaced air (fluid 1, resident phase). In the experiments, the yellow color denotes water, while the white color denotes air. The flow direction is from left to right. The pump flow rate was kept constant at 0.5 µl/min. In all experiments, this injection rate was maintained at a
<figure><img src="image_16.png" /><figcaption>**FIG. 4.** Illustration of the six micromodels designs with various mixed wettability configurations achieved through selective hydrophilic (blue, $\theta = 50^{\circ}$) and hydrophobic (red, $\theta = 113^{\circ}$) coating. (a) A single mixed-wet channel with a hydrophobic coating applied from the left half side, transitioning to a hydrophilic surface in the right half side. (b) A single mixed-wet channel with a hydrophobic coating applied to the bottom half along the channel, resulting in a vertical gradient of wettability. (c) Y-shaped mixed-wet micromodel with channel branching into two channels with lower sizes. One branch hydrophilic, and the other hydrophobic. (d) Y-shaped mixed-wet micromodel with a network of branching channels with different widths and wettability properties. (e) and (f) Mixed-wet pore-doublet models with two connected channels of different sizes and wettability, where in (e) the smaller upper channel is hydrophilic, while the larger lower channel is hydrophobic, and in (f) an inverse configuration where the smaller upper channel is hydrophobic, and the larger lower channel is hydrophilic.</figcaption></figure>

low level, ensuring that the flow regime in each design was dominated by capillary forces.

Simulations were then conducted to replicate the same experimental conditions. As the micromodels have repeated flow patterns, simulations were performed for some representative patterns and not

for the whole model as the patterns exhibited repeated flow behaviors. This allowed optimizing the computational requirements of the simulations. For the simulated patterns, fluid pressure and flow velocity were imposed as initial and boundary conditions. The outlet pressure was maintained at ambient conditions, similar to the experiments. Constant velocity was imposed at the inlet of the simulated domains as boundary conditions, corresponding to the experimental conditions. The fluid properties and parameters used in the simulations are summarized in Table I.

## A. Experiment 1: Single channel with two sequentially placed wettability

In this experiment, a single capillary channel was designed with two distinct wettability arranged sequentially. The left half of the channel from the inlet was hydrophobic, while the right half was hydrophilic, creating a wettability step transition within the channel [see Fig. 4(a)]. This configuration was used to investigate how fluid interfaces interact and how transitions occur between regions with different wettability. Such variations in wettability can be found in porous media due to mineralogical changes, like the

<figure><img src="image_17.png" /><figcaption>**FIG. 5.** View of an actual microfluidic chip ($2 \times 1 \text{ cm}^2$) fabricated on a silicon substrate, featuring channels with varying mixed wettability.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>FIG. 6. SEM images of the fabricated mixed-wet microfluidics chips. (a) Selective opening of the target area of photoresist during fabrication targeted for wettability alteration. (b) Half-coated single channel. (c) Y-shaped channel with one channel coated and another uncoated. (d) Tilted image of an etched flow channel with vertical walls showing coating on the channel surface and walls. (e) Mixed-wet pore-doublet model where smaller upper channel coated. (f) Mixed-wet pore-doublet model where larger lower channel coated.</figcaption></figure>

presence of organic matter (kerogen, which is oil-wet) in inorganic silica-based shale (water-wet). Figure 7(a) illustrates the fluid front (highlighted in yellow) as it advanced into the hydrophobic section from the left side. Observations were recorded at various time intervals during the displacement process to assess the impact of the single wettability within each zone and the transition between them.

<table><caption>TABLE I. Fluid properties and parameters used in the simulations.</caption><thead><tr><th>Parameter</th><th>Value</th></tr></thead><tbody><tr><td>ρ<sub>1</sub> (kg m<sup>-3</sup>)</td><td>1.2032</td></tr><tr><td>ρ<sub>2</sub> (kg m<sup>-3</sup>)</td><td>998.06</td></tr><tr><td>μ<sub>1</sub> (Pa s)</td><td>1.81 × 10<sup>-5</sup></td></tr><tr><td>μ<sub>2</sub> (Pa s)</td><td>9.99 × 10<sup>-4</sup></td></tr><tr><td>ε<sub>pf</sub> (m)</td><td>6.5 × 10<sup>-6</sup></td></tr><tr><td>χ (m s kg<sup>-1</sup>)</td><td>1</td></tr><tr><td>σ (N m<sup>-1</sup>)</td><td>0.0726</td></tr><tr><td>∂f/∂φ (J/m<sup>3</sup>)</td><td>0</td></tr></tbody></table>

In stage I, when the fluid was within the hydrophobic region, the meniscus exhibited a dynamic contact angle of $\theta = 120^{\circ}$, typical of a non-wetting phase. At the interface between the hydrophobic and hydrophilic regions, the meniscus underwent an instantaneous shape transition due to the change in wettability. This transition was marked by a nearly flat interface with a contact angle of $\theta = 90^{\circ}$ at the boundary between the coated and uncoated areas, shifting from a convex shape in the hydrophobic region to a concave shape with a dynamic contact angle of $\theta = 60^{\circ}$ in the hydrophilic region. Notably, this transition did not result in a perfectly concave shape immediately; one side of the interface crossed first, followed by the other, to balance the surface forces, as observed in stage III. To our knowledge, this dynamic of the meniscus shape is demonstrated for the first time.

Simulations were conducted to assess the observed flow behavior. The simulated channel had a length of 860 µm and a width of 100 µm, as depicted in Fig. 4. Initially, the simulated domain was initialized with air at ambient conditions. The water inflow velocity at the inlet was specified as, $u = 0.042$ m/s, matching the experimental conditions. No-slip boundary conditions were applied to the walls of the flow domain. The phase-field model incorporated different contact angles as boundary conditions, such that $\theta = 120^{\circ}$ for the hydrophobic surface, while $\theta = 60^{\circ}$ for the hydrophilic surface. A computational mesh
<figure><img src="image_19.png" /><figcaption>FIG. 7. Comparison of experimental and simulated fluid front progression at different time intervals in a single capillary channel with sequential wettability transition. (a) Experimental observations of the fluid front showing the transition of contact angles at three different times: $\theta = 120^{\circ}$ at t₁, $\theta = 90^{\circ}$ at t₂, and $\theta = 60^{\circ}$ at t₃. The direction of fluid flow is indicated by the arrow. (b) Corresponding simulation results with volume fraction of displacing fluid represented by a color gradient: blue indicates air (0) and red indicates water (1). The simulation captures the dynamic transitions of the contact angles and validates the experimental approach.</figcaption></figure>

consisting of approximately 2700 nodes was generated in COMSOL. The obtained simulation results showed an excellent match with the experimental observations, shown at different time intervals: $t_1 = 8.5$, $t_2 = 10.85$, and $t_3 = 11.24$ ms. Figure 7(b) depicts the progression of the fluid front from the simulations. The fluid distribution is represented by a color gradient, ranging from blue (air phase) to red (water phase), corresponding to the volume fraction of displacing fluid (e.g., water). The simulation effectively captured the interface behavior and the transition of contact angles, consistent with the experimental observations.

The calculated pressure behavior, as illustrated in Fig. 8, aligns with theoretical expectations of wettability impacts on fluid flow within a capillary channel. The transition from a hydrophobic to a hydrophilic surface within the microfluidic channel influences the pressure profile required to propagate the displacing phase. In the hydrophobic section of the channel, positive pressures are necessary to overcome the resistance against the non-wetting phase, as appears at $t = 2.3–9.3$ s in Fig. 8. As the interface reaches the hydrophilic section, the pressure

requirement shifts dramatically to negative pressures resulting from a succession force, aiding the imbibition process.

These pressure profiles are consistent with the analytical analysis presented by Lake et al. 2014 (Lake et al., 2014; Fig. 3.13), where they discuss how wettability can influence capillary pressure, which can lead to complex fluid displacement behaviors, necessitating varied pressure regimes to maintain flow. Our experimental data and simulations corroborate these findings, demonstrating a clear demarcation in pressure requirements corresponding to the wettability transition, which underscores the significant role of surface properties on flow mechanisms in microscale fluidic environments.

## B. Experiment 2: Single channel with two parallel wettability zones

In this experiment, a channel with a 100 µm width and 30 µm depth was fabricated to incorporate a mixed hydrophilic and a hydrophobic section extending parallel along the center of the channel,

<figure><img src="image_20.png" /><figcaption>FIG. 8. The profiles of the pressure difference ($\Delta p = p - p_{initial}$) along the length of the single capillary channel with wettability transition from hydrophobic to hydrophilic at the middle of the channel (position = 0). The x-axis represents the distance from the channel origin, at 0 µm, where the transition between wettability occurs. The jump in the pressure at the interface represents the capillary pressure. Initially, a positive injection pressure is required to propagate the nonwetting phase (displacing phase) through the hydrophobic zone (during times 2.3–9.3 s). As the displacement front enters the hydrophilic zone, the inlet pressure becomes negative, facilitating fluid imbibition due to supportive capillary forces (during times 12.9–19.9 s).</figcaption></figure>
<figure><img src="image_21.png" /><figcaption>FIG. 9. Water injection displacing air (left to right) in a single mixed-wet channel consisting of a hydrophilic upper half and a hydrophobic bottom half. (a) Experiment showing the fluid interface resemble S-shape in a mixed-wet channel. (b) Numerical simulation showing a two-dimensional S-shape fluid-fluid interface (volume fraction of displacing fluid). (c) Numerical simulation showing a three-dimensional visualization of fluid-fluid interface showing unique saddle-shaped.</figcaption></figure>

establishing two distinct wettability zones [see Fig. 4(b)]. This configuration was designed to assess the fluid dynamics as fluids simultaneously interact with surfaces of varying wettability. As depicted in Fig. 9(a), the fluid interface formed an S-shape around the bisect line where the mixed-wet surfaces meet. The interface exhibited dynamic contact angles of $\theta = 60^{\circ}$ against the hydrophilic wall and $\theta = 120^{\circ}$ against the hydrophobic wall. This pattern emerges as the invading fluid advances through the wetting region and retracts within the non-wetting region, resulting in a bending of the fluid interface. This distinctive behavior of the fluid-fluid interface differs from those observed in uniform-wet configurations. This observation is consistent with the findings by (Bauters et al., 2000; Irannezhad et al., 2023), which is attributed to the establishment of near-zero mean curvatures. Additionally, a saddle-shaped fluid-fluid interface was observed in a waterflooded oil-saturated sandstone core sample using x-ray CT imaging (Lin et al., 2019).

Due to the spatial variability of the boundary conditions, this test case was modeled in three dimensional (3D). The simulation domain was designed to match the exact width and depth of the flow unit used in the experiment. The length of the simulated domain was 730 µm. The computational mesh consisted of approximately 15 500 nodes, ensuring sufficient resolution for capturing detailed fluid dynamics. Surface wettability was assigned to the boundary walls within the phase-field model, replicating the experimental conditions with contact angles of $\theta = 120^{\circ}$ for the hydrophobic surfaces and $\theta = 60^{\circ}$ for the hydrophilic surfaces. All other simulation parameters were kept consistent with those used in case 1. As for the previous test case, the inlet velocity was set to 0.042 m/s. Simulations showed that a similar S-shape interface was captured in the simulation during the water displacement in the mixed-wet channel, as depicted in Fig. 9(b). Figure 9(c) illustrates the formation of the saddle-shaped interface, closely matching the

experimental observations. The 3D model effectively captures the bending in the fluid interface due to the hydrophobic top layer sealing the channel, which results in more pronounced spreading along the bottom surface of the channel. This behavior was also observed in the experiments, where a thicker interface was noted in the hydrophilic section when viewed from the top. These consistent observations confirm the validity of the simulation model in accurately capturing the impact of mixed wettability on fluid behavior.

### C. Experiment 3: Y-shaped micromodel with two mixed-wet branches

This case presented a Y-shaped branched channel design with mixed-wettability branches. The main channel had a width of 150 µm and split into two branches, each 100 µm wide [see Fig. 4(c)]. This configuration ensured sufficient downstream volume for the fluid to flow freely. One branch was hydrophilic, while the other was hydrophobic, creating a junction where the two different wettability surfaces meet. The presence of both hydrophilic and hydrophobic capillary throats mimicked conditions commonly found in natural porous media. This configuration has been used in previous studies to examine bubble and droplet dynamics at junctions (Wang et al., 2016); however, those studies did not address the impact of mixed wettability. Figure 10(a) displays the injected fluid at different time frames, corresponding to $t_1 = 6$, $t_2 = 138$, and $t_3 = 140$ s. As the fluid approached the junction, it was directed into the hydrophilic branch, avoiding the hydrophobic one, rather than splitting. This clearly demonstrates how wettability perturbation controls the flow direction by affecting the capillary entry pressure.

Simulation was conducted to mimic the same configurations of the experiment. The simulation domain was created by importing the computer-aided design (CAD) file to replicate the exact geometry and dimensions of the micromodel. The wettability conditions were
<figure><img src="image_22.png" /><figcaption>**FIG. 10.** Water injection displacing air in a mixed-wet Y-shaped micromodel. (a) Injected water moving from left to right at three different times, displacing air in a Y-shaped micromodel with splitting branches under different wettability conditions; the top branch is hydrophilic, and the bottom branch is hydrophobic. Water diverts entirely to the hydrophilic branch. (b) The corresponding simulation results (volume fraction of displacing fluid), demonstrating fluid displacement dynamics in the same mixed-wet Y-shaped configuration as the experiments.</figcaption></figure>

defined with contact angles of $\theta = 120^{\circ}$ for the hydrophobic branch and $\theta = 60^{\circ}$ for the hydrophilic branch. All other simulation parameters remained consistent with the previous cases. A finite-element unstructured triangular mesh consisting of 5300 nodes was employed. The outputs simulations were compared with observations at $t_1 = 29$, $t_2 = 42$, and $t_3 = 108$ ms. The simulations successfully captured the precise fluid behavior and flow direction preferences, as illustrated in Fig. 10(b). These consistent observations give more confidence in the ability of the simulation to capture the role of mixed wettability and demonstrate how mixed wettability can dictate the preferential flow direction at microscale.

**Figure 11** presents the simulation results for the pressure distribution (a) and velocity field (b) in the Y-shaped micromodel. The pressure distribution plot [Fig. 11(a)] shows a significant pressure gradient at the junction, with higher pressure drop observed in the hydrophilic branch compared to the hydrophobic one. Despite the lower pressure in the hydrophobic branch, the fluid preferentially flows into the hydrophilic branch, as illustrated by the velocity field in Fig. 11(b). This behavior is attributed to the higher capillary entry pressure in the hydrophobic channel, which acts as a barrier to fluid entry. The hydrophilic channel, by contrast, offers lower capillary resistance, allowing for faster fluid advancement.

<figure><img src="image_23.png" /><figcaption>**FIG. 11.** Simulation results illustrating the (a) pressure difference ($\Delta p = p - p_{\text{initial}}$) distribution (in Pa) and (b) velocity field (in m/s) during water injection displacing air in a Y-shaped micromodel with mixed wettability branches. The hydrophilic top branch exhibits a higher pressure and a higher fluid velocity, while the hydrophobic bottom branch shows a higher resistance to flow caused by capillarity.</figcaption></figure>
## D. Experiment 4: Y-shaped mixed-wet micromodel with multiple branches

A network of channels with varying widths and wettability was introduced in this design to create a more complex flow environment. Similar to the previous case, the main channel started with a width of 100 µm and splits into two branches, each with a width reduced by 50%, resulting in 50 µm wide branches at the first stage [see Fig. 4(d)]. These branches further split into additional branches with widths reduced by another 50%, creating 25 µm wide branches at the second stage. Each branch in both stages was designated as either hydrophilic or hydrophobic to decouple the impact of channel size in each stage. This resulted in a complex network with varying channel sizes and wettability properties. Figure 12(a) illustrates the fluid distribution within the channel network following the complete injection process and breakthrough. It is observed that water exclusively followed the hydrophilic channels, entirely bypassing the hydrophobic ones. Despite the size reduction, water showed a preference for invading the smaller hydrophilic channels in the second stage over the larger hydrophobic channels in the first stage. The hydrophilic and hydrophobic regions influenced the preferential flow path, with capillary forces and wettability contrast causing the fluid to predominantly flow through specific channels. This behavior indicates the significant impact of mixed wettability on overall fluid displacement and capillary entrapments within a complex matrix.

Figure 12(b) presents the results of the numerical simulation conducted using a simulation domain that replicates the experimental design. The simulation parameters were kept the same as in the previous cases. The inlet velocity was set at 0.005 m/s, consistent with the experiment conditions. The mesh used in the simulation consisted of 6600 nodes. The simulation results revealed an identical match of fluid distribution as observed in the experiments. The simulation confirmed that water preferentially follows the hydrophilic channels while bypassing the hydrophobic ones, mirroring the experimental observations.

## E. Experiments 5 and 6: Mixed-wet pore-doublet models

In this section, pore-doublet model was utilized to represent fluid flow within the pores of porous media. Recognizing that in real

reservoir rocks, many small pores are bypassed by capillary forces when located outside the main flow path, this model consisted of two connected channels with different sizes. This approach aimed to represent fluid flow and entrapments by accounting for pore tortuosity and competing flow pathways. Originally proposed by Chatzis and Dullien (1983) to study displacement and entrapment mechanisms, this configuration has been employed in various experimental and numerical studies (Alizadeh and Fatemi, 2021; Zamula et al., 2019). However, the effect of mixed wettability has not been tested. Therefore, this work introduces pore-doublet models, featuring mixed wettability for the first time.

The design, as shown in Figs. 4(e) and 4(f), consisted of two connected channels with sizes of 15 and 45 µm. Mixed wettability was assigned in two configurations: in Fig. 4(e), the narrow upper pore was hydrophilic, while the wide lower pore was hydrophobic. Figure 4(f) illustrates the inverse arrangement, where the narrow upper channel is hydrophobic, and the wide lower channel is hydrophilic.

Fluid was injected from the left side and progressively flowed through the channel network over time, as illustrated in Fig. 13(a). This figure shows the fluids displacement process at $t_1 = 24.4$ and $t_2 = 29.8$ s, $t_3 = 33.2$ and $t_4 = 38.8$ s. The initial stages of the experiment demonstrated that the fluid preferentially invaded the narrow hydrophilic upper pore, bypassing the hydrophobic wide pore due to the significant capillary forces present in the hydrophilic channel. Once the smaller pore was fully swept, the water flow shifted into the larger pore. The fluid front in the small pore remained stationary until the displacing front in the larger pore reached the end. As the fluid reached the end of the narrow hydrophilic pore, the capillary forces began to decrease due to the expansion in the channel size. This reduction in capillarity at the larger junction allowed the viscous forces to take over fluid to invade the wide hydrophobic pore. At this point, the fronts in both the small and large pores merged, and the water eventually broke through the outlet of the model, resulting in full displacement.

This experimental case was further assessed using numerical simulation. The simulation domain was generated by importing the same experimental design. At the inlet, the velocity was set to $u = 0.001$ m/s, while the outlet pressure was maintained at ambient conditions. No-slip conditions were applied to the walls of the flow unit. Contact

<figure><img src="image_24.png" /><figcaption>FIG. 12. Water injection displacing air (left to right), entering the main channel and subsequently splitting into two branches at the first stage. Each branch further splits into additional branches at the second stage. (a) Experiments. (b) Numerical simulations (volume fraction of displacing fluid).</figcaption></figure>
<figure><img src="image_25.png" /><figcaption>FIG. 13. Water injection displacing air (left to right), sequence of events over time, in mixed-wet pore-doublet model where the narrow upper pore is hydrophilic, while the wide lower pore is hydrophobic. (a) Experiments. (b) Numerical simulations (volume fraction of displacing fluid).</figcaption></figure>

angles were assigned as boundary conditions according to the experimental design specifications. An unstructured triangular mesh, consisting of 2400 nodes, was used. The simulation results are shown in Fig. 13(b). The benchmarking with the observations is shown at time intervals $t_1 = 38.5$, $t_2 = 74.5$, $t_3 = 116.5$, and $t_4 = 217$ ms. The fluid distribution patterns in the simulations closely mirrored those observed in the experiments, validating the accuracy of the numerical model. The simulation confirmed the preferential invasion of the hydrophilic upper narrow pore and the avoidance of the hydrophobic lower wide pore due to the high capillary forces.

The observations from the previous case were anticipated due to the enhanced capillary effect driven by both hydrophilicity and the smaller channel size in the upper channel. This resulted in capillary forces dominating over competing viscous forces. In contrast, fluid displacement exhibited different behavior when the wettability configuration was altered, as depicted in Fig. 14(a). The figure shows the fluid displacement at $t_1 = 33.2$ and $t_2 = 37$ s, $t_3 = 38.4$ and $t_4 = 48.6$ s. In this altered configuration, the fluid avoided the narrow upper pore due to its hydrophobic nature, which caused resistance to flow. Instead, the fluid invaded the wide hydrophilic pore, where both capillary and viscous forces directed the fluid movement preferentially. This led to the narrow pore being completely bypassed, resulting in the entrapment of the other fluid phase.

Simulations accurately captured this behavior, as illustrated in Fig. 14(b), compared at time intervals $t_1 = 76.5$, $t_2 = 167$, $t_3 = 313$, and $t_4 = 399$ ms. This consistency between the experimental and simulation results further validated the capability of numerical to replicate complex flow dynamics in heterogeneous porous media with mixed wettability. The findings highlight the significant influence of wettability and channel size on fluid displacement and entrapment mechanisms.

The capillary pressures in both pores were calculated to further validate the experimental observations. Assuming each pore behaves like a circular duct with a radius $r$ (m), the capillary pressure can be described using the Young–Laplace equation,

$$p_c = p_1 - p_2 = \frac{2 \sigma \cos(\theta)}{r}, \quad (11)$$

where $p_1$ and $p_2$ represent the pressures of fluid 1 and fluid 2, respectively. In experiment 5, the narrow pore was hydrophilic with a diameter $d = 15$ µm and contact angle $\theta = 60^\circ$. For this pore, $p_c = 1.404$ psi. This positive capillary pressure indicates favorable imbibition due to capillary forces. Conversely, the wide pore is hydrophobic with a diameter $d = 45$ µm and $\theta = 120^\circ$. Considering the etching depth of 30 µm as the effective pore depth, $p_c = -0.702$ psi. The negative capillary pressure here suggests an invading process contrary to capillarity.

<figure><img src="image_26.png" /><figcaption>FIG. 14. Water injection displacing air (left to right), sequence of events over time, in mixed-wet pore-doublet model where the narrow upper pore is hydrophobic, while the wide lower pore is hydrophilic. (a) Experiments. (b) Numerical simulations (volume fraction of displacing fluid).</figcaption></figure>
Therefore, the narrow pore exhibits a more favorable capillary behavior under these conditions. In experiment 6, the roles of the pores were reversed. The narrow pore was hydrophobic with a diameter *d* = 15 µm and contact angle θ = 120°, while the wide pore was hydrophilic, with a diameter *d* = 45 µm, an effective depth of 30 µm, and θ = 60°. In this case, the calculated capillary pressures were -1.404 and 0.702 psi, respectively. These results indicate that, in this configuration, the wide hydrophilic pore was more favorable for fluid imbibition, as the positive capillary pressure in the wide pore promotes fluid displacement into this pore. This contrasts with experiment 5, where the narrow pore was more favorable. In experiment 6, the larger negative capillary pressure in the narrow hydrophobic pore prevented fluid invasion, resulting in the small pore being completely bypassed, as observed during the experiment. The change in wettability and pore size between the two experiments clearly demonstrated the importance of pore geometry and surface properties on fluid behavior in porous media.

## IV. CONCLUSIONS

This study investigated the effectiveness of a novel technique for fabricating micromodels with mixed hydrophobic–hydrophilic wettability. The approach, which combines photolithography and thin film deposition via MVD, enabled precise selective wettability alteration on silicon surfaces. Six different configurations of variable wettability were examined, demonstrating the versatility of this fabrication method. Some of these experimental models with mixed wettability, including the single channel with two sequentially placed wettability and the mixed-wet pore-doublet models, are presented here for the first time.

Experimental observations revealed a significant impact of mixed wettability on two-phase fluid behavior. Notably, meniscus shapes transitioned from convex to concave as fluids moved between hydrophobic and hydrophilic areas. In channels with vertical mixed wettability variations, the fluid interface adopted a distinctive S-shape. In Y-shaped micromodels, the fluid showed a preference for hydrophilic channels, bypassing hydrophobic ones entirely. The mixed-wet pore-doublet models demonstrated that fluid initially invaded the narrow hydrophilic pore due to a higher capillarity, while the reverse configuration caused the fluid to invade the wide hydrophilic pore, trapping the other phase in the narrow hydrophobic pore.

Both the Navier–Stokes equations for air/water two-phase flow and the phase-field technique for tracking fluid–fluid interfaces were implemented in COMSOL Multiphysics to simulate the experiments. These simulations accurately replicated the experimental findings across various wettability configurations, confirming the validity of our approach. The results provide robust validation for using this fabrication technique in controlled experiments to replicate reservoir-representative mixed-wet conditions, advancing pore-scale numerical modeling.

This study established an integrated experimental and simulation platform to control and observe the effects of mixed wettability at the pore scale, providing a reliable and controlled experimental setup for systematic investigations of mixed wettability in porous media. While scaling findings from micromodel studies to actual porous media or reservoir conditions poses challenges, including the complexity of natural geometries, heterogeneities, and the influence of elevated pressure and temperature, this technique offers significant potential for further development and applications. It can be extended to replicate actual rock-type geometries with complex wettability patterns and conduct experiments under elevated pressures and temperatures to better

simulate reservoir conditions. Insights gained from well-characterized porous matrices with controlled wettability states can support and validate pore-scale modeling, particularly in scenarios where individual pore behavior strongly influences flow dynamics. Incorporating mixed wettability into pore network models, guided by representative experimental data, is crucial for reducing uncertainties and improving the predictive accuracy of pore-scale simulations.

The integration of validated numerical models with experimental data from these advanced micromodels provides a robust framework for scaling findings to more realistic scenarios. This comprehensive approach bridges the gap between controlled micromodel studies and field-scale applications, enhancing the understanding and predictive capabilities of multiphase flow behavior in heterogeneous porous media with mixed wettability. The developed platform enables extended analyses and diverse applications, including enhanced oil recovery, CO₂ sequestration, and groundwater management.

## ACKNOWLEDGMENTS

The authors would like to acknowledge Martin Hoecherl for his valuable assistance in the preparation of Fig. 6. The authors would like to extend their acknowledgment to Nano Fabrication and Thin Film Core Labs at KAUST for providing the necessary facilities to perform fabrication.

## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

### Author Contributions

**Abdullah AlOmier:** Data curation (equal); Formal analysis (equal); Methodology (equal); Software (equal); Visualization (equal); Writing – original draft (equal). **Marwan Fahs:** Investigation (equal); Software (equal); Validation (equal); Writing – review & editing (equal).

**Hussein Hoteit:** Conceptualization (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal).

## DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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