Wide Range Of Capillary Numbers Research Articles

Influence of binder content on gas-water two-phase flow and displacement phase diagram in the gas diffusion layer of PEMFC: A pore network view

Understanding the gas-water flow dynamics in the gas diffusion layer (GDL) is one of the keys to improving the proton exchange membrane fuel cell's (PEMFC) overall performance and avoiding water flooding. Yet, the relationship between the two-phase flow and micro-scale GDL structures (including binder, PTFE, and fiber skeleton) is not well understood. In this study, three-dimensional GDL structures with different fractions of binder contents (φb=0%∼50%) and a fixed porosity of 75.6 % are confidently reconstructed based on high-resolution images from the confocal microscope, implying that the addition of binder will increase the number of large pores and cause a bimodal throat size distribution through morphology analysis. Thereafter, drainage simulations are performed under a wide range of capillary number (−9 < log Ca <0) and viscosity ratio (−3 < log M < 2) by the pore network model (PNM), which robustly predicts the displacement phase diagram of viscous fingering, capillary fingering, stable displacement, and transitional regime. In the viscous fingering and stable displacement regime, the nonwetting phase saturation (Snw) is nearly the same for different φb, implying the fluid invading pathway does not change much with the addition of binder. However, in the capillary fingering regime (refer to the actual operating conditions), Snw increases rapidly with φbat the breakthrough time and its transient value continues to increase until the steady state, which may be attributed to the increased fractions of pores above the capillary threshold attributed by the bimodal throat size distribution. In addition, the effective water permeability increases sharply with φb, whereas the gas permeability remains almost constant, which means such pore structure alteration by adding the binder is beneficial to water disposal in PEMFC. This research provides insights into delineating the effect of pore and throat size distribution alteration by adding binder on two-phase dynamics in GDL.

Effect of entry geometry on droplet dynamics in contraction microchannel

In droplet-based microfluidic systems, the movement and control of liquid droplets are primarily governed by microchannel geometry. The aim of this study is to examine droplet dynamics in contraction microchannels by using three-dimensional simulation and theoretical modeling. This work specifically describes three regimes of the droplet dynamics, including the trap, squeeze, and breakup regimes, and investigates the effects of capillary number (Ca), entry angle (α), and contraction channel ratio (C). Additionally, a theoretical model is proposed to describe the transition between squeeze and trap regimes, which depends on the entry angle. The critical value of capillary number (Ca1c) for this transition is observed to be Ca1c=a(CM−b/α), where a and b are fitted parameters. Meanwhile, the entry angle is found to have no influence on the transition from squeeze to breakup regime. The droplet deformations, retraction, and/or breakup position are quantitatively investigated for a wide range of capillary number and entry angle. The aforementioned findings would provide valuable recommendations for designing contraction micro channels.

Characteristics of fluid–fluid displacement in model mixed-wet porous media: patterns, pressures and scalings

We study numerically the characteristics of fluid–fluid displacement in simple mixed-wet porous micromodels using a dynamic pore network model. The porous micromodel consists of distinct water-wet and oil-wet regions, whose fractions are varied systematically to yield a variety of displacement patterns over a wide range of capillary numbers. We find that the impact of mixed-wettability is most prominent at low capillary numbers, and it depends on the complex interplay between wettability fraction and the intrinsic contact angle of the water-wet regions. For example, the fractal dimension of the displacement pattern is a monotonically increasing function of wettability fraction in flow cells with strongly water-wet clusters, but it becomes non-monotonic with respect to wettability fraction in flow cells with weakly water-wet clusters. Additionally, mixed-wettability also manifests itself in the injection pressure signature, which exhibits fluctuations especially at low wettability fraction. Specifically, preferential filling of water-wet regions leads to reduced effective permeability and higher injection pressure, even at vanishingly small capillary numbers. Finally, we demonstrate that scaling analyses based on a weighted average description of the overall wetting state of the mixed-wet system can effectively capture the variations in observed displacement pattern morphology.

Suppressing Viscous Fingering in Porous Media with Wetting Gradient.

The viscous fingering phenomenon often occurs when a low-viscosity fluid displaces a high-viscosity fluid in a homogeneous porous media, which is an undesirable displacement process in many engineering applications. The influence of wetting gradient on this process has been studied over a wide range of capillary numbers (7.5 × 10-6 to 1.8 × 10-4), viscosity ratios (0.0025 to 0.04), and porosities (0.48 to 0.68), employing the lattice Boltzmann method. Our results demonstrate that the flow front stability can be improved by the gradual increase in wettability of the porous media. When the capillary number is less than 3.5 × 10-5, the viscous fingering can be successfully suppressed and the transition from unstable to stable displacement can be achieved by the wetting gradient. Moreover, under the conditions of high viscosity ratio (M > 0.01) and large porosity (Φ > 0.58), wetting gradient improves the stability of the flow front more significantly.

Effect of mechanical properties of red blood cells on their equilibrium states in microchannels

The equilibrium positions of red blood cells (RBCs) and their steady motions in microchannel affect the hemodynamics in vivo and microfluidic applications on a cellular scale. However, the dynamic behavior of a single RBC in three-dimensional cylindrical microchannels still needs to be classified systematically. Here, with an immersed boundary method, the phase diagrams of the profiles and positions of RBCs under equilibrium states are illustrated in a wide range of Capillary numbers. The effects of initial positions are explored as well. Numerical results present that the profiles of RBCs at equilibrium states transform from snaking, tumbling to slipper, or parachute with the increase in flow rates, and whether RBCs finally approach slipper or parachute motion under large shear rates is dependent on their initial positions. With the increase in tube diameters, the equilibrium positions of RBCs are closer to tube walls relatively. Although both the increase in membrane shear modulus and the viscosity ratio are regarded as the stiffening of RBCs, the change of membrane property does not affect the dependence of the profiles and positions of RBCs at equilibrium states on the shear rates of the flow obviously, but with the increase in viscosity ratio, RBCs move further away from the centerline of the tube associating with more asymmetric characteristics in their stable profiles. The present results not only contribute to a better understanding of the dynamic behavior and multiple profiles of single RBC in microcirculation, but also provide fundamentals in a large range of Capillary numbers for cell sorting with microfluidic devices.

Coalescence of Growing Bubbles in Highly Viscous Liquids

AbstractBubble coalescence in ascending magma is a key process that controls the eruption violence and the texture of volcanic pyroclasts. In the present study, we performed in situ experiments to investigate the coalescence of two growing bubbles in highly viscous liquids (102 and 1,020 Pa ⋅ s). A new experimental apparatus enables us to directly observe the drainage of the film between growing bubbles in three dimensions. We combined the experimental results and a simple scaling analysis to reveal the dynamics of film drainage in terms of a capillary number depending on the liquid viscosity η, the bubble growth rate , and the surface tension σ. The capillary number represents the interplay between the viscous force arising from bubble growth and the capillary force. At Ca ≪ 1, two adjacent bubbles retain their spherical shapes until the film ruptures, and the capillary forces control the drainage timescale. In contrast, at Ca ≫ 1, bubbles largely flatten and bubble growth itself drives film drainage. We also provide a general formula for the drainage timescale over a wide range of capillary numbers (10−3 &lt; Ca &lt; 101). Our results highlight the importance of bubble growth in the coalescence process. The variations of bubble shape and number density during decompression can be explained by the capillary number.

An experimental study on the mobility of droplets in liquid-liquid Taylor flows within circular capillaries

Further development of microfluidics devices that reply on liquid-liquid droplet flows, requires a thorough understanding of the parameters influencing droplet velocity. This study provides greater insights into this subject through an analysis of parameters effecting droplet mobility in such flows. A novel, fully automated experimental setup was designed to accurately measure droplet velocity and length. Measurements were performed over a wide range of Capillary number (2×10−4 to 3.7×10−2), Bond number (0.05 to 3.2) and carrier to dispersed viscosity ratio (0.059 to 23.2) while also varying droplet length. Five different fluid combinations were examined within circular capillaries with inlet diameters ranging from 555μm to 1.70mm. Results reveal a complex relationship between droplet velocity and droplet length, viscosity ratio and Bond number. In all cases, as droplet length exceeds a threshold value, droplet velocity becomes independent of length and is shown to scale with ∼ Ca0.5. As the droplet length falls below the threshold, the droplet velocity faces a changeover zone in which the velocity initially declines and then rises by further increase in the length. For shorter droplets, higher Bond numbers cause the droplet phase to travel asymmetrically with respect to the channel centre line which substantially impacts the mobility of these droplets. Finally, a new expression has been developed to estimate the velocity of elongated droplets.

The Co-Moving Velocity in Immiscible Two-Phase Flow in Porous Media

We present a continuum (i.e., an effective) description of immiscible two-phase flow in porous media characterized by two fields, the pressure and the saturation. Gradients in these two fields are the driving forces that move the immiscible fluids around. The fluids are characterized by two seepage velocity fields, one for each fluid. Following Hansen et al. (Transport in Porous Media, 125, 565 (2018)), we construct a two-way transformation between the velocity couple consisting of the seepage velocity of each fluid, to a velocity couple consisting of the average seepage velocity of both fluids and a new velocity parameter, the co-moving velocity. The co-moving velocity is related but not equal to velocity difference between the two immiscible fluids. The two-way mapping, the mass conservation equation and the constitutive equations for the average seepage velocity and the co-moving velocity form a closed set of equations that determine the flow. There is growing experimental, computational and theoretical evidence that constitutive equation for the average seepage velocity has the form of a power law in the pressure gradient over a wide range of capillary numbers. Through the transformation between the two velocity couples, this constitutive equation may be taken directly into account in the equations describing the flow of each fluid. This is, e.g., not possible using relative permeability theory. By reverse engineering relative permeability data from the literature, we construct the constitutive equation for the co-moving velocity. We also calculate the co-moving constitutive equation using a dynamic pore network model over a wide range of parameters, from where the flow is viscosity dominated to where the capillary and viscous forces compete. Both the relative permeability data from the literature and the dynamic pore network model give the same very simple functional form for the constitutive equation over the whole range of parameters.

Observations on the impact of displacement properties on mobility and relative permeability

The accuracy of relative permeability and mobility data can strongly impact the uncertainty in predictions of production in reservoir models. It is of particular importance to identify the most practical conditions to perform relative permeability tests in order to mimic the difference between test and subsurface conditions. It is known that the details of a displacement test, such as capillary number, can immensely impact the characteristics of a displacement. Therefore, it is paramount to perform displacement tests representative of the reservoir conditions. To improve the general understanding and design of displacement tests this work presents an exploration of displacement parameters and their impact on results. A multiphase Lattice Boltzmann Method is used to digitally perform displacement tests for a range of relevant conditions. Direct simulations are performed on 3D models of pore spaces built from microCT images of rock. A parameter space consisting of capillary number, wetting condition, viscosity ratio and driving mechanism is explored on multiple sandstone rock images. Results showing the impact multiple displacement properties have on relative permeability and mobility are presented. Particular attention was paid to the role of capillary number on total mobility. A wide range of capillary numbers (1 × 10−7 to 1 × 10−4) was investigated. It was observed that a quantification of mobility, the minimum total mobility of both fluids, is largely constant for the lower most range of capillary numbers for a specific rock image. This plateau behavior holds when capillary number is below a critical threshold where capillary forces fully dominate the 2-phase flow topology. Above this threshold mobility increases monotonically with capillary number. The study also presents relationships for various wetting conditions, viscosity ratios and driving mechanisms. When using an alternate definition of capillary number which relates velocity and fluid properties at the point of minimum total mobility, broad similarity in mobility data was observed for the various viscosity ratios and driving mechanisms investigated. In contrast, the minimum total mobility was consistently higher for oil-wet displacements when compared to equivalent water-wet displacements.

The Drag Forces on a Taylor Bubble Rising Steadily in Vertical Pipes

By the adoption of a drag-buoyancy equality model, analytical solutions were obtained for the drag coefficients (CD) of Taylor bubbles rising steadily in pipes. The obtained solutions were functions of the geometry of the Taylor bubble and the gas volume fraction. The solutions were applicable at a wide range of Capillary numbers. The solution was validated by comparison with experimental data of other investigators. All derived drag formulas were subject to the condition that Bond number &gt;4, for air-water systems.

Liquid film thickness of two‐phase slug flows in capillary microchannels: A review paper

AbstractTwo‐phase Taylor flow has received considerable attention from researchers in recent decades due to its potential use in a wide variety of industrial and medical applications. A large number of experimental, analytical, and numerical efforts have been taken by researchers to understand the fundamental characteristics of two‐phase flows and the relevant transport phenomena. This paper presents a comprehensive review of the hydrodynamics, flow pattern, and liquid film thickness in two‐phase flows through mini‐ and microchannels with different cross‐sectional geometry. This paper also reviews correlations that predict liquid film thickness in microchannels for gas‐liquid and liquid‐liquid flows. The variations of liquid film thickness are plotted over a wide range of capillary numbers for both experimental and computational studies. This study shows that the effects of cross‐sectional area on the flow patterns and flow characteristics have not been sufficiently investigated by researchers, particularly for rectangular cross‐sectional areas with different aspect ratios.

Pore-scale effects during the transition from capillary- to viscosity-dominated flow dynamics within microfluidic porous-like domains

We perform a numerical and experimental study of immiscible two-phase flows within predominantly 2D transparent PDMS microfluidic domains with disordered pillar-like obstacles, that effectively serve as artificial porous structures. Using a high sensitivity pressure sensor at the flow inlet, we capture experimentally the pressure dynamics under fixed flow rate conditions as the fluid–fluid interface advances within the porous domain, while also monitoring the corresponding phase distribution patterns using optical microscopy. Our experimental study covers 4 orders of magnitude with respect to the injection flow rate and highlights the characteristics of immiscible displacement processes during the transition from the capillarity-controlled interface displacement regime at lower flow rates, where the pores are invaded sequentially in the form of Haines jumps, to the viscosity-dominated regime, where multiple pores are invaded simultaneously. In the capillary regime, we recover a clear correlation between the recorded inlet pressure and the pore-throat diameter invaded by the interface that follows the Young–Laplace equation, while during the transition to the viscous regime such a correlation is no longer evident due to multiple pore-throats being invaded simultaneously (but also due to significant viscous pressure drop along the inlet and outlet channels, that effectively mask capillary effects). The performed experimental study serves for the validation of a robust Level-Set model capable of explicitly tracking interfacial dynamics at sub-pore scale resolutions under identical flow conditions. The numerical model is validated against both well-established theoretical flow models, that account for the effects of viscous and capillary forces on interfacial dynamics, and the experimental results obtained using the developed microfluidic setup over a wide range of capillary numbers. Our results show that the proposed numerical model recovers very well the experimentally observed flow dynamics in terms of phase distribution patterns and inlet pressures, but also the effects of viscous flow on the apparent (i.e. dynamic) contact angles in the vicinity of the pore walls. For the first time in the literature, this work clearly shows that the proposed numerical approach has an undoubtable strong potential to simulate multiphase flow in porous domains over a wide range of Capillary numbers.

Shape evolutions of moving fluid threads under asymmetrical confinements

This paper presents a combined experimental and numerical investigation designed to improve our understanding of how the shape of moving fluid threads evolves under asymmetrical confinements in both circular and square microchannels. Microfluidic devices with two junctions are designed to control the length of the fluid thread at the first junction and the deformation of the fluid thread at the second junction. Three different flow modes: nonbreakup, loosely confined breakup, and tightly confined breakup, are identified for varying lengths of fluid threads and capillary number, and two boundaries are identified between the three modes. The deformation dynamics of the fluid threads evolving as difference modes are addressed to consider the effects of thread length and capillary number. Numerical simulations are carried out to determine how the curvature evolves for different flow modes in the square microchannel. The evolution of interface profiles is obtained numerically over a wide range of capillary number. Stop-flow simulations are then carried out to identify both the critical shape for the onset of the capillary instability during tightly confined breakup and the corresponding curvature distribution. This critical shape is found to be corresponding to the fluid thread with the critical length at the transitive boundary between the loosely confined and tightly confined situations.

Signatures of fluid–fluid displacement in porous media: wettability, patterns and pressures

We develop a novel ‘moving-capacitor’ dynamic network model to simulate immiscible fluid–fluid displacement in porous media. Traditional network models approximate the pore geometry as a network of fixed resistors, directly analogous to an electrical circuit. Our model additionally captures the motion of individual fluid–fluid interfaces through the pore geometry by completing this analogy, representing interfaces as a set of moving capacitors. By incorporating pore-scale invasion events, the model reproduces, for the first time, both the displacement pattern and the injection-pressure signal under a wide range of capillary numbers and substrate wettabilities. We show that at high capillary numbers the invading patterns advance symmetrically through viscous fingers. In contrast, at low capillary numbers the flow is governed by the wettability-dependent fluid–fluid interactions with the pore structure. The signature of the transition between the two regimes manifests itself in the fluctuations of the injection-pressure signal.

An Experimental Investigation of Flow Regimes in Imbibition and Drainage Using a Microfluidic Platform

Instabilities in immiscible displacement along fluid−fluid displacement fronts in porous media are undesirable in many natural and engineered displacement processes such as geological carbon sequestration and enhanced oil recovery. In this study, a series of immiscible displacement experiments are conducted using a microfluidic platform across a wide range of capillary numbers and viscosity ratios. The microfluidic device features a water-wet porous medium, which is a two-dimensional representation of a Berea sandstone. Data is captured using a high-resolution camera, enabling visualization of the entire domain, while being able to resolve features as small as 10 µm. The study reports a correlation between fractal dimensions of displacement fronts and displacement front patterns in the medium. Results are mapped on a two-dimensional parameter space of log M and log Ca, and stability diagrams proposed in literature for drainage processes are superimposed for comparison. Compared to recent reports in the literature, the results in this work suggest that transition regimes may constitute a slightly larger portion of the overall flow regime diagram. This two-phase immiscible displacement study helps elucidate macroscopic processes at the continuum scale and provides insights relevant to enhanced oil recovery processes and the design of engineered porous media such as exchange columns and membranes.

A Taylor analogy model for droplet dynamics in planar extensional flow

The dynamics of a droplet suspended in a medium fluid is determined by the hydrodynamic forces and surface tension force, and the Taylor analogy had been successfully employed to predict droplet deformation and breakup in a spray. This paper aims to extend the Taylor analogy for prediction of droplet dynamics in planar extensional flow which has great significance in droplet-based microfluidic systems. Performance of the proposed model is compared with the three-dimensional numerical simulation results over a wide range of capillary number and viscosity ratio. Experimental data available in the literature is also compared with the prediction results for verification purpose. The proposed model could describe both the time scale and the magnitude of droplet deformation accurately.

Phase-field modeling of an immiscible liquid-liquid displacement in a capillary.

We develop a numerical model for a two-phase flow of a pair of immiscible liquids within a capillary tube. We assume that a capillary is initially saturated with one liquid and the other liquid is injected via one of the capillary's ends. The governing equations are solved in the velocity-pressure formulation, so the pressure levels are imposed at the capillary inlet and outlet ends. We model the structure of the flow and the shape of the interface. We are able to reproduce the flow for a wide range of capillary numbers, when the meniscus preserves its shape moving together with the flow, and when the meniscus constantly stretches resembling the transport of a passive impurity. We demonstrate that the phase-field approach is capable of reproducing all features of the liquid-liquid displacement, including the motion of a contact line, the dynamic changes of the capillary pressure, and the dynamic changes of the apparent contact angle.

Electrostatic Assist of Liquid Transfer between Flat Surfaces.

Transfer of liquid from one surface to another plays a vital role in printing processes. During liquid transfer, a liquid bridge is formed and subjected to substantial extension but incomplete liquid transfer can produce defects that are detrimental to the operation of printed electronic devices. One strategy for minimizing these defects is to apply an electric field, a technique known as electrostatic assist (ESA). However, the physical mechanisms underlying ESA remain a mystery. To better understand these mechanisms, slender-jet models are developed for both perfect dielectric and leaky dielectric axisymmetric Newtonian liquid bridges with moving contact lines. Nonlinear partial differential equations describing the evolution of the bridge radius and interfacial charge are derived and then solved using finite element methods. For perfect dielectrics, application of an electric field enhances liquid transfer to the more wettable surface over a wide range of capillary numbers. The electric field modifies the pressure differences inside the liquid bridge and, as a consequence, drives liquid toward the more wettable surface. For leaky dielectrics, charge can accumulate at the liquid-air interface. Application of an electric field can augment or oppose the influence of wettability differences, depending on the direction of the electric field and the sign of the surface charge. Flow visualization experiments reveal that when an electric field is applied, more liquid is transferred to the more wettable surface because of a modified bridge shape that causes depinning of the contact line. The measured values of the amount of liquid transferred are in good agreement with predictions of the perfect dielectric model.

Capsule equilibrium positions near channel center in Poiseuille flow

A fundamental question in microfluidics is how capsules migrate laterally in microchannels. Because of formidable challenges in physics, no study has investigated capsule migration near the channel center at a wide range of Capillary numbers and Reynolds numbers. To fill this significant knowledge gap, we developed a 2D mathematical model, based on the front tracking method, to investigate the lateral migration of capsules near the channel center. The trajectory, shape, deformation, equilibrium position of capsules were studied at various capsule Capillary numbers (Ca=0.005–0.6) and Reynolds numbers (Re=1–20). At high Reynolds numbers and Capillary numbers (Ca>1.694Re-1.068), the equilibrium positions were at the channel center; whereas, at low Reynolds numbers and Capillary numbers, they were between the channel center and the wall. A region near the channel center where no capsule can equilibrate within the studied range of Reynolds numbers and Capillary numbers was discovered for the first time. This region of non-equilibrium position has never been identified in either 3D or 2D simulations, though it is unclear this region will exist in 3D simulations. We deciphered the underlying mechanism for this novel region as outlined below: First, both the lateral velocity and the resultant lift force increased. Second, the shape of capsule transformed from an ellipse to a bullet. Third, the relative velocity at the top of the capsule changed from the direction towards the channel outlet to the direction towards the inlet. Fourth, the velocity difference between the top and the bottom of the capsule decreased. Finally, the high pressure region on the top windward disappeared. This study has advanced our understanding of the fluid mechanics of capsule migration in microchannel.

Dynamic pore-scale network model (PNM) of water imbibition in porous media

A dynamic pore-scale network model is presented which simulates 2-phase oil/water displacement during water imbibition by explicitly modelling intra-pore dynamic bulk and film flows using a simple local model. A new dynamic switching parameter, λ, is proposed within this model which is able to simulate the competition between local capillary forces and viscous forces over a very wide range of flow conditions. This quantity (λ) determines the primary pore filling mechanism during imbibition; i.e. whether the dominant force is (i) piston-like displacement under viscous forces, (ii) film swelling/collapse and snap-off due to capillary forces, or (iii) some intermediate local combination of both mechanisms.A series of 2D dynamic pore network simulations is presented which shows that the λ-model can satisfactorily reproduce and explain different filling regimes of water imbibition over a wide range of capillary numbers (Ca) and viscosity ratios (M). These imbibition regimes are more complex than those presented under drainage by (Lenormand et al. (1983)), since they are determined by a wider group of control parameters. Our simulations show that there is a coupling between viscous and capillary forces that is much less important in drainage. The effects of viscosity ratio during imbibition are apparent even under conditions of very slow flow (low Ca)–displacements that would normally be expected to be completely capillary dominated. This occurs as a result of the wetting films having a much greater relative mobility in the higher M cases (e.g. M = 10) thus leading to a higher level of film swelling/snap-off, resulting in local oil cluster bypassing and trapping, and hence a poorer oil recovery. This deeper coupled viscous mechanism is the underlying reason why the microscopic displacement efficiency is lower for higher M cases in water imbibition processes.Additional results are presented from the dynamic model on the corresponding effluent fractional flows (fw) and global pressure drops (ΔP) as functions of capillary number and viscosity ratio. These results indicate that unsteady-state (USS) relatively permeabilities in imbibition should be inherently rate dependent.