Fluid Transport Phenomena Research Articles

Confined mass transport in two-dimensional capillary

Abstract Over the past decade, nanofluidics has undergone significant expansion, propelled by advances in crafting artificial channels at nanometric and sub-nanometric scales with diverse geometries. Central to this domain, two-dimensional capillaries have risen as a pivotal research platform, marked by their angstrom-level precision, unparalleled wall surface smoothness, and clearly defined surface charge states. Their advent has profoundly deepened our understanding of mass transport dynamics, spanning gases, water molecules, and ions, shedding light on the complex interactions among various influencing factors and revealing a range of previously undiscovered physical phenomena. This review delves into the development of 2D capillaries, the principal fluid transport phenomena observed within, and the critical elements that affect these processes. We also touch on a fascinating discovery - the quantum liquid friction seen in water moving over carbon surfaces. In anticipation of future explorations in nanofluidics, we envision a trajectory aimed at emulating the efficiency levels of biological protein channels, setting the stage for a new era of scientific inquiry and technological innovation.

Comprehensive numerical prototyping of paper-based microfluidic devices using open-source tools

Paper-based microfluidics has emerged as a promising field with diverse applications ranging from medical diagnostics to environmental monitoring. Despite significant progress in research and development, the translation of paper-based prototypes into practical end-user devices remains limited. This limitation stems from challenges related to devices not being sufficiently portable and autonomous, which paper-based microfluidics is expected to overcome. Yet for this purpose, we note the lack of comprehensive numerical modeling tools capable of simulating the intricate physicochemical phenomena involved in order to optimize the development process; hence, in this study, we introduce porousMicroTransport, a novel simulation package integrated with the open-source platform OpenFOAM®, designed to address these challenges. porousMicroTransport offers efficient solvers for fluid flow and transport phenomena in microfluidic porous media, including capillarity models and (bio)chemical reactions. Moreover, under horizontal flow conditions, porousMicroTransport application field can be extended to any porous media. We demonstrate the software’s effectiveness in two example cases, showcasing its ability to accurately reproduce complex phenomena involved in paper-based devices. By virtue of being an easy-to-use and computationally efficient tool, porousMicroTransport facilitates the design and optimization of devices, potentially enabling more devices to meet the WHO’s REASSURED criteria for point-of-care testing. We anticipate that this tool will accelerate the development and deployment of robust and portable diagnostic devices, bridging the gap between research and practical applications.

Influence of sedimentary structure and pore-size distribution on upscaling permeability and flow enhancement due to liquid boundary slip: A pore-scale computational study

Low-permeability sedimentary formations, such as tight sandstones, exhibit fluid flow and transport phenomena distinct from those in conventional porous systems due to the dominance of micro- to nanometer-sized pores and variable amounts of boundary slip. The widely used traditional no-slip boundary condition often fails to accurately describe fluid behavior in these formations. A knowledge gap exists in understanding how liquid slip influences fluid dynamics in complex, heterogeneous sedimentary structures, as previous studies have primarily focused on simplified, homogeneous pore geometries. In this study, we investigated the impact of boundary slip on low-Reynolds number fluid dynamics within synthetically designed two-dimensional graded and random pore networks with varying pore-size distributions to account for heterogeneity. Our results showed that velocity variance increased with increasing heterogeneity, following a power-law relationship. The power-law exponents decreased with boundary slip, quantifying how boundary slip mitigated the impact of heterogeneity on velocity variance. We developed a theoretical model to predict asymptotic flow enhancement and derived constitutive relations to estimate the coefficient C and maximum flow enhancement (ΔE) based on the pore-to-grain size ratio and porosity. Energy dissipation increased with both heterogeneity and boundary slip, which we identified as the primary mechanism contributing to asymptotic flow enhancement. This relationship was illustrated by a 1:1 linear correlation between maximum energy dissipation and maximum flow enhancement, regardless of heterogeneity, indicating that energy dissipation due to boundary slip entirely controls the emerging fluid dynamics. The presented theoretical model and constitutive equations offer practical applications for optimizing fluid dynamics in heterogeneous formations.

Impact of nanopore confinement on phase behavior and enriched gas minimum miscibility pressure in asphaltenic tight oil reservoirs

Miscible gas injection in tight/shale oil reservoirs presents a complex problem due to various factors, including the presence of a large number of nanopores in the rock structure and asphaltene and heavy components in crude oil. This method performs best when the gas injection pressure exceeds the minimum miscibility pressure (MMP). Accordingly, accurate calculation of the MMP is of special importance. A critical issue that needs to be considered is that the phase behavior of the fluid in confined nanopores is substantially different from that of conventional reservoirs. The confinement effect may significantly affect fluid properties, flow, and transport phenomena characteristics in pore space, e.g., considerably changing the critical properties and enhancing fluid adsorption on the pore wall. In this study, we have investigated the MMP between an asphaltenic crude oil and enriched natural gas using Peng-Robinson (PR) and cubic-plus-association (CPA) equations of state (EoSs) by considering the effect of confinement, adsorption, the shift of critical properties, and the presence of asphaltene. According to the best of our knowledge, this is the first time a model has been developed considering all these factors for use in porous media. We used the vanishing interfacial tension (VIT) method and slim tube test data to calculate the MMP and examined the effects of pore radius, type/composition of injected gas, and asphaltene type on the computed MMP. The results showed that the MMP increased with an increasing radius of up to 100 nm and then remained almost constant. This is while the gas enrichment reduced the MMP. Asphaltene presence changed the trend of IFT reduction and delayed the miscibility achievement so that it was about 61% different from the model without the asphaltene precipitation effect. However, the type of asphaltene had little impact on the MMP, and the controlling factor was the amount of asphaltene in the oil. Moreover, although cubic EoSs are particularly popular for their simplicity and accuracy in predicting the behavior of hydrocarbon fluids, the CPA EoS is more accurate for asphaltenic oils, especially when the operating pressure is within the asphaltene precipitation range.

Effect of pH on Spontaneous Imbibition in Calcareous Rocks

AbstractReactive transport in porous media exhibits multifaceted interactions that are dependent on the matrix and fluid properties, and which ultimately alter these properties. A set of calcareous rock samples with unique mineralogy and varying petrophysical properties are selected for this study. A capillary rise experiment is performed in each sample, first with deionized water and then with a dilute, pH 2, HCl solution. Pre‐ and post‐acid petrophysical properties such as porosity, permeability, pore size distribution, and contact angle are measured for each sample along with the capillary rise profile. The latter is tracked by applying image analysis on video recording. The rock mineralogy significantly affects the acidic fluid intrusion into the rock samples. Calcite dissolution is the main reaction that results in the opening of the pore space. This is more prominent in all the carbonate samples where a higher proportion of calcite minerals is present. A higher capillary rise is consistently observed compared to the neutral fluid along with an increase in porosity and the mean pore size. The contact angle also undergoes changes making the carbonate matrix from oil‐wet to neutral‐wet. Coupling capillary interactions with fluid reactivity is often neglected in fluid transport phenomena. This study offers new insights into the relative importance of reactivity at the timescale of spontaneous imbibition. This is important in understanding dissolution and precipitation processes during capillary flow.

Direct numerical simulation of electrokinetic transport phenomena in fluids: Variational multi-scale stabilization and octree-based mesh refinement

Computational modeling of charged species transport has enabled the analysis, design, and optimization of a diverse array of electrochemical and electrokinetic devices. These systems are represented by the Poisson-Nernst-Planck (PNP) equations coupled with the Navier-Stokes (NS) equation. Direct numerical simulation (DNS) to accurately capture the spatio-temporal variation of ion concentration and current flux remains challenging due to the (a) small critical dimension of the diffuse charge layer (DCL), (b) stiff coupling due to fast charge relaxation times, large advective effects, and steep gradients close to boundaries, and (c) complex geometries exhibited by electrochemical devices.In the current study, we address these challenges by presenting a direct numerical simulation framework that incorporates (a) a variational multiscale (VMS) treatment, (b) a block-iterative strategy in conjunction with semi-implicit (for NS) and implicit (for PNP) time integrators, and (c) octree based adaptive mesh refinement. The VMS formulation provides numerical stabilization critical for capturing the electro-convective flows often observed in engineered devices. The block-iterative strategy decouples the difficulty of non-linear coupling between the NS and PNP equations and allows the use of tailored numerical schemes separately for NS and PNP equations. The carefully designed second-order, hybrid implicit methods circumvent the harsh timestep requirements of explicit time steppers, thus enabling simulations over longer time horizons. Finally, the octree-based meshing allows efficient and targeted spatial resolution of the DCL. These features are incorporated into a massively parallel computational framework, enabling the simulation of realistic engineering electrochemical devices. The numerical framework is illustrated using several challenging canonical examples.

Nonlinear and Anisotropic Ion Transport in Black Phosphorus Nanochannels.

Two-dimensional material nanochannels with molecular-scale confinement can be constructed by Van der Waals assembly and show unexpected fluid transport phenomena. The crystal structure of the channel surface plays a key role in controlling fluid transportation, and many strange properties are explored in these confined channels. Here, we use black phosphorus as the channel surface to enable ion transport along a specific crystal orientation. We observed a significant nonlinear and anisotropic ion transport phenomenon in the black phosphorus nanochannels. Theoretical results revealed an anisotropy of ion transport energy barrier on the black phosphorus surface, with the minimum energy barrier along the armchair direction approximately ten times larger than that along the zigzag direction. This difference in energy barrier affects the electrophoretic and electroosmotic transport of ions in the channel. This anisotropic transport, which depends on the orientation of the crystal, may provide new approaches to controlling the transport of fluids.

Using mesoporous thin films as nano-micro-fluidic tools

Achieving active control on small amounts of liquids represents a substantial challenge in both scientific and engineering aspects. Imbibition of fluids in bodies with nanoscale dimensions enables the spontaneous propelling of nano-flows because of the powerful capillarity at small-length scales. Peculiarities of nanopore imbibition at the thin film level lead to distinctive capillary transport phenomena of fluids across the nanopore matrix. This particular imbibition also impacts on the behavior of the in-contact liquid micro-volumes. These both features add versatile alternatives to the high interest in the management of femtolitre to microlitres amounts of liquids. Herein, we show a brief discussion-outlook based on recent advances in the design of versatile tools to attain programmable nano/microfluidics using mesoporous thin film platforms. Cited as: Berli, C. L. A., Bellino, M. G. Using mesoporous thin films as nano-micro-fluidic tools. Capillarity, 2022, 5(6): 123-127. https://doi.org/10.46690/capi.2022.06.03

A new methodology for measuring solid/liquid interfacial energy

HypothesisThe interfacial energy γsl between a solid and a liquid designates the affinity between these two phases, and in turn, the macroscopic wettability of the surface by the fluid. This property is needed for precise control of fluid-transport phenomena that affect the operation/quality of commercial devices/products. Although several indirect or theoretical approaches can quantify the solid/liquid interfacial energy, no direct experimental procedure exists to measure this property for realistic (i.e. rough) surfaces. Makkonen hypothesized that the frictional resistance force per unit contact-line length is equal to the interfacial energy on smooth surfaces, which, however, are rarely found in practice. Consequently, the hypothesis that Makkonen’s assumption may also hold for rough surfaces (which are far more common in practice) arises naturally. If so, a reliable and simple experimental methodology of obtaining γsl for rough surfaces can be put forth. This is accomplished by performing dynamic contact-angle experiments on rough surfaces that quantify the relationship between the frictional resistance force per unit contact-line length acting on an advancing liquid (Fp,a) and the surface roughness in wetting configurations. ExperimentWe perform static and advancing contact-line experiments with aqueous and organic liquids on different hydrophilic surfaces (Al, Cu, Si) with varying Wenzel roughnesses in the range 1-2. These parameters are combined with the liquid’s known surface tension to determine Fp,a. FindingsFp,a rises linearly with the surface roughness. Analysis based on existing theories of wetting and contact-angle hysteresis reveals that the slope of Fp,a vs.Wenzel roughness is equal to the solid/liquid interfacial energy, which is thus determined experimentally with the present measurements. Interfacial energies obtained with this experimental approach are within 12% of theoretically predicted values for several solid/liquid pairs, thereby validating this methodology.

Perspectives of the extra corporeal membrane oxygenation – Key insights from mathematical analysis

Extracorporeal membrane oxygenator is a life-saving critical medical equipment for cardio-pulmonary support, for treatment of severe chronic respiratory distress. The equipment performance is dependent on the type of membrane, flow configuration, and blood physiology. Lot of research efforts are focused on the development of novel membrane. However, the cardiovascular pulsations and blood physiological conditions on the flow and associated transport is important, which was not explored significantly. Here, we investigate the impact of the frequency of flow oscillations on the oxygenation profile. The physiological parameters which affect the blood oxygenation profile is investigated in detail. The oscillations in the oxygen transfer rate profiles are suppressed, as the blood flow rate is reduced, and the oxygen saturation is completely out-of-phase with the flow rhythm (saturation is maximum when the flow is minimum). We present the phase space to easily decide on the required combination of process variables or design specifications, needed to achieve the target oxygen saturation, based on the patient blood physiology. The present effort in understanding the process, can lead to improved performance and design of this life-supporting equipment. The results provide clear recommendations from the clinical perspectives. The outcome of the work will be useful to the engineering (biomedical) community in realizing the role of fluid flow and transport phenomena in extracorporeal oxygenation, under varied physiological conditions.

Variational multiscale reinforcement learning for discovering reduced order closure models of nonlinear spatiotemporal transport systems

A central challenge in the computational modeling and simulation of a multitude of science applications is to achieve robust and accurate closures for their coarse-grained representations due to underlying highly nonlinear multiscale interactions. These closure models are common in many nonlinear spatiotemporal systems to account for losses due to reduced order representations, including many transport phenomena in fluids. Previous data-driven closure modeling efforts have mostly focused on supervised learning approaches using high fidelity simulation data. On the other hand, reinforcement learning (RL) is a powerful yet relatively uncharted method in spatiotemporally extended systems. In this study, we put forth a modular dynamic closure modeling and discovery framework to stabilize the Galerkin projection based reduced order models that may arise in many nonlinear spatiotemporal dynamical systems with quadratic nonlinearity. However, a key element in creating a robust RL agent is to introduce a feasible reward function, which can be constituted of any difference metrics between the RL model and high fidelity simulation data. First, we introduce a multi-modal RL to discover mode-dependant closure policies that utilize the high fidelity data in rewarding our RL agent. We then formulate a variational multiscale RL (VMRL) approach to discover closure models without requiring access to the high fidelity data in designing the reward function. Specifically, our chief innovation is to leverage variational multiscale formalism to quantify the difference between modal interactions in Galerkin systems. Our results in simulating the viscous Burgers equation indicate that the proposed VMRL method leads to robust and accurate closure parameterizations, and it may potentially be used to discover scale-aware closure models for complex dynamical systems.

Electro-elastic instability in electroosmotic flows of viscoelastic fluids through a model porous system

Electrokinetic transport phenomena in porous media are encountered in many practical applications such as electro-chromatography, micro-pumping, chemical remediation of contaminated soil, etc. These applications often deal with various complex viscoelastic fluids (such as polymers, emulsions, suspensions, different kinds of biofluids, etc.) along with simple Newtonian ones. This study presents a detailed numerical investigation on this electrokinetic transport of both Newtonian and viscoelastic fluids in a model porous system consisting of a long micropore with step expansion and contraction. Over the whole range of conditions encompassed in this study, a steady and symmetric flow field is observed for a Newtonian fluid. However, for a viscoelastic fluid, we observe a transition in the flow field from steady and symmetric to unsteady and asymmetric once the Weissenberg number (ratio of the elastic to that of the viscous forces) exceeds a critical value. We show that this transition is caused due to the onset of an electro-elastic instability in the system. The critical value of this Weissenberg number (at which this transition occurs) depends on various factors. In particular, we find that this value increases with the polymer viscosity ratio and expansion and contraction lengths of the micropore. At fixed values of the electric field strength, polymer viscosity ratio, contraction and expansion lengths of the micropore, we observe the existence of different vortex dynamics within this model porous system as the Weissenberg number gradually increases, such as the emergence of the entrant and re-entrant lip vortices, oscillating lip vortices, multi vortices, etc. Therefore, the electrokinetic flow dynamics of viscoelastic fluids in a porous system is much more complex than that of simple Newtonian fluids. We hope this study for a model porous system would facilitate a better understanding of the electrokinetic transport phenomena of viscoelastic fluids in an actual porous media. Furthermore, we show how this model system of a long micropore with step expansion and contraction could also be successfully utilized for other practical applications such as mixing two viscoelastic fluids.

Suitability of Bronchoscopic Spraying for Fluid Deposition in Lower Airway Regions: Fluorescence Analysis on a Transparent In Vitro Airway Model.

Introduction: Bronchoscopic spraying has potential for the application of therapeutic drugs in distal regions of the lung by bypassing the upper airways. However, there is a lack of understanding about the underlying fluid transport phenomena that are responsible for the intrapulmonary propagation of applied liquid. Methods: By using a transparent airway model, this study provides first experimental insights into relevant transport phenomena of bronchoscopic spraying. Furthermore, the penetration depth of the application is quantitatively evaluated. Laser-induced fluorescence is used to analyze fluid propagation in the transparent channels. Potential influencing factors such as the positioning in different airways, application number, breathing pattern, and lung obstructions are varied within this study to determine their influence on liquid deposition. Findings: This study shows that the method of bronchoscopic spraying allows the application of liquid in distal regions of the airway model. The position of the bronchoscope is a key influencing factor in increasing the penetration depth. We found that fluid transport along the distal airways essentially occurs by the film and plug flow phenomenon during application, which is similar to the transport mechanisms during instillation. Liquid plugs in lower airways are responsible for the reorganization of liquid during proximal movements and thereby influence the penetration depth in subsequent applications.

Molecular Simulation Study and Analytical Model for Oil–Water Two-Phase Fluid Transport in Shale Inorganic Nanopores

Shale reservoirs contain omnipresent nanopores. The fluid transport phenomena on the nanoscale are significantly different from that on the macroscale. The understandings of fluid transport behavior, especially multiphase flow, are still ambiguous on the nanoscale and the traditional hydrodynamic models are insufficient to describe the fluid flow in shale. In this work, we firstly use a molecular dynamics simulation to study the oil–water two-phase flow in shale inorganic quartz nanopores and investigated the unique interfacial phenomena and their influences on fluid transport in a confined nanospace. The results of the molecular simulation revealed that the water-oil-water layered structure was formed in quartz nanopores. There is no-slip boundary condition between water and quartz surface. The density dip and the extremely low apparent viscosity of the oil–water interface region were observed. The liquid–liquid slip effect happened at the oil–water interface. Based on the nano-effects obtained by the molecular simulation, two mathematical models were proposed to describe the nanoscale oil–water two-phase flow, considering both the solid–liquid and liquid–liquid interfacial phenomena, and the performances of two mathematical models were validated. This study shed light on the flow behaviors of oil and water on the nanoscale, and provides the theoretical basis for scale-upgrading, from the nanoscale to the macroscale.

Reconstruction of 3D Porous Geometry for Coupled FEM-CFD Simulation

Porous materials can be found in numerous areas of life (e. g., applied science, material science), however, the simulation of the fluid flow and transport phenomena through porous media is a significant challenge nowadays. Numerical simulations can help to analyze and understand physical processes and different phenomena in the porous structure, as well as to determine certain parameters that are difficult or impossible to measure directly or can only be determined by expensive and time-consuming experiments. The basic condition for the numerical simulations is the 3D geometric model of the porous material sample, which is the input parameter of the simulation. For this reason, geometry reconstruction is highly critical for pore-scale analysis. This paper introduces a complex process for the preparation of the microstructure's geometry in connection with a coupled FEM-CFD two-way fluid-structure interaction simulation. Micro-CT has been successfully applied to reconstruct both the fluid and solid phases of the used porous material.

Impact of liquid coolant subcooling on boiling heat transfer and dryout in heat-generating porous media

The present article discusses the impact of liquid coolant subcooling on multiphase fluid flow and boiling heat transfer in porous media with internal heat generation. Although extremely relevant and important, only limited studies are available in the open literature on the effects of coolant subcooling in heat-generating porous media and hence, this requires a detailed analysis. The present analysis is carried out using a validated computational model of multiphase fluid flow through clear fluid and porous media considering the relevant fluid transport, heat transfer and mass transfer phenomena. Results suggest that the qualitative nature of boiling heat transfer from the heat-generating porous body, with subcooled coolants, remain similar to that observed with a saturated coolant. Quantitative differences are, however, observed as a result of solid–liquid convective heat transfer, and competing mechanisms of boiling and condensation heat transfer, when subcooled liquid coolant is present. It is observed that a substantially larger heating power density is required - as coolant subcooling is increased - for achieving the same temperature rise in the porous body. Dryout power density at different coolant subcooling is also observed to follow a similar trend. The thermal energy removal limit is, hence, observed to be substantially enhanced in presence of subcooled coolants. Further, the dryout region within the porous body is observed to gradually shift towards its interior as the coolant subcooling is increased.

Coupling mesoscale transport to catalytic surface reactions in a hybrid model.

In heterogeneous catalysis, reactivity and selectivity are not only influenced by chemical processes occurring on catalytic surfaces but also by physical transport phenomena in the bulk fluid and fluid near the reactive surfaces. Because these processes take place at a large range of time and length scales, it is a challenge to model catalytic reactors, especially when dealing with complex surface reactions that cannot be reduced to simple mean-field boundary conditions. As a particle-based mesoscale method, Stochastic Rotation Dynamics (SRD) is well suited for studying problems that include both microscale effects on surfaces and transport phenomena in fluids. In this work, we demonstrate how to simulate heterogeneous catalytic reactors by coupling an SRD fluid with a catalytic surface on which complex surface reactions are explicitly modeled. We provide a theoretical background for modeling different stages of heterogeneous surface reactions. After validating the simulation method for surface reactions with mean-field assumptions, we apply the method to non-mean-field reactions in which surface species interact with each other through a Monte Carlo scheme, leading to island formation on the catalytic surface. We show the potential of the method by simulating a more complex three-step reaction mechanism with reactant dissociation.

Thermal investigation of peristaltic pumping of modified hybrid nanofluid (Al2O3−TiO2−Cu)/H2O) through a complex wavy convergent channel with electro-magneto-hydrodynamic phenomenon

This research analytically investigates the mathematical study of unsteady peristaltic motion of a modified hybrid nanofluid (containing dissimilar nanoparticles) in a convergent channel. This flow of modified hybrid nanofluids is controlled by the combined effects of magnetic and electric devices. In the current analysis, hybrid fluid with three distinct nano particles (titania oxide, alumina oxide and copper metallic nanoparticles) are considered to observe the performance of hybrid nanofluids along with water as a base fluid. The flow analysis is carried out under creeping phenomena and long wavelength approximations. Additionally, this mathematical invention is intended to examine the transport phenomena of biological fluids through the large to the small intestine. The Debye-Hückel theory (i.e. wall zeta potential ≤ 25 mV) is also used to remove the non-linearity of the Poisson-Boltzmann equation, which is assumed to become a simplified model of an electrolyte solution. The close-formed solutions are obtained for a system of non-dimensional boundary value problem. The effects of the physical parameters on the rheological phenomena are depicted graphically using Mathematica 11 software. Applications of the mathematical model include transport of complex biological fluids and control the transportation of fluids by using electro-kinetic modulate devices. Additionally, this study is productive to design a complex peristaltic pump which is used to control the motion of bio-fluids.

Rational Design of Multimodal Porous Carbon for the Interfacial Microporous Layer of Fuel Cell Oxygen Electrodes.

Accumulation of water at the interface of the cathode catalyst layer (CCL) and the diffusion media is a major cause of performance loss in H2/air fuel cells. Proper engineering of the interface by the use of advanced materials and preparation methods can effectively reduce the extent of this loss by improving the transport of water and gas across this interface. Herein, we present detailed modeling results of water and gas transport across this interface for in-house synthesized carbon material with multiple levels of porosity and by considering the interfacial properties of the carbon material and the microporous layer (MPL). The oxygen reduction reaction and the counter-flow transport of oxygen and water within the CCL and MPL pores were modeled considering a partially flooded interface. Well-characterized multimodal porous carbon was chosen as a candidate material for this study, and the effects of all the various levels of porosity in the MPL, wettability, permeability, and the quality of contact between the MPL and CCL on the transport phenomena of fluids were investigated. This study provides new insights into the balance of opposing transport phenomena on the local and overall performance of the catalyst layer and rationalizes the design parameters for an MPL material based on both the material and interfacial properties.

Mathematical Model of Macromolecular Drug Transport in a Partially Liquefied Vitreous Humor.

The purpose of this study is to investigate the effect of partial liquefaction (due to ageing) of the vitreous humor on the transport of ocular drugs. In our model, the gel part of the vitreous is treated as a Darcy-type porous medium. A spherical region within the porous part of vitreous is in a liquid state which, for computational purposes, is also treated as a porous medium but with a much higher permeability. Using the finite element method, a time-dependent, three-dimensional model has been developed to computationally simulate (using the Petrov-Galerkin method) the transport of intravitreally injected macromolecules where both convection and diffusion are present. From a fluid physics and transport phenomena perspective, the results show many interesting features. For pressure-driven flow across the vitreous, the flow streamlines converge into the liquefied region as the flow seeks the fastest path of travel. Furthermore, as expected, with increased level of liquefaction, the overall flow rate increases for a given pressure drop. We have quantified this effect for various geometrical considerations. The flow convergence into the liquefied region has important implication for convective transport. One effect is the clear diversion of the drug as it reaches the liquefied region. In some instances, the entry point of the drug in the retinal region gets slightly shifted due to liquefaction. While the model has many approximations and assumptions, the focus is illustrating the effect of liquefaction as one of the building blocks toward a fully comprehensive model.