Range Of Capillary Numbers Research Articles

Fluid dynamics of gas–liquid slug flow under the expansion effect in a microchannel

The expansion of bubbles in viscous fluids in microchannels is normally overlooked. The bubble dynamics in liquids with varying viscosities (1.15 ∼ 101.47 mPa·s) and contact angles (29.3 ∼ 137.6°) in a microchannel were investigated under various inlet pressure drops (8 ∼ 202 kPa). The findings indicate that bubble formation occurs within a squeezing-shearing regime over a wide Capillary number range of 0.0023–0.43. Interestingly, the wettability affects the bubble length rather than the bubble shape, and the poor wettability can hinders the decrease of length in higher viscosity fluids. Bubble expansion causes decreasing curvature radii of bubble caps, and non-linear rapid increases in its length and velocity along the microchannel. The bubble’s pressure–volume relation at the inlet and outlet confirms the validation of Boyle’s law in slug flow. A linear decline in pressure along the microchannel was deduced from this law. Further analysis suggests that besides the friction of the liquid slug, the pressure drop is influenced by the interface effect, film flow, and liquid circulation. Finally, a model for total pressure drop was developed, which effectively predicted the length and velocity of bubbles in the expansion process. This study offers valuable insights for a deeper understanding of bubble expansion behaviors in microchannels.

Taylor droplet breakup in T-type microchannels: A detailed flow analysis

The study of droplet break-up in microchannels can be used to improve designs for both biological or chemical microreactors and microfluidic devices e.g., heat exchangers and microchips. In this study, 3D computer simulations were carried out to investigate the detailed behavior of droplet breakup in a T-junction microchannel using the Volume of Fluid (VOF) and Level Set (LS) coupling methods (S-CLSVOF) implemented in OpenFoam. The evolution of droplet morphology and the rupture regimens were analyzed considering pressure results, velocity neck thickness, and tunnel width. The results show four rupture regimes for a range of capillary numbers and dimensionless initial droplet length of 0.005≤Ca≤0.055 and 1≤l0/w≤5. The stages of each rupture were also analyzed and compared with experimental and numerical results from literature. A detailed description of each step in the droplet breakup is also given, including analyses of the influence that the local pressure field and Laplace pressure have on the rupture processes. The 3D results reveal that the Laplace pressure decreases in the main channel due to continuous flux at the top and bottom of the 3D channel. This in turn, leads to a slight change in the rear curvature of the bubble. Laplace pressure is an important parameter that can be used to predict the opening tunnel point, large changes in curvature, and whether the droplet will breakup or not. Just before breakup, the 3D simulations captured a backflow near the neck, a region, characterized by pressure drops, and thus smaller breakup times.

Mechanism study and formula development by numerical simulation and visualization experiment in a microfluidic system for enhanced oil recovery

In this study, microfluidic system was adopted to investigate the effects of hydrodynamic factors on chemical flooding. The combination of visualization experiments and computational fluid dynamics (CFD) simulations was used to evaluate the effects of flow rate, interfacial tension (IFT), viscosity, density, contact angle and porosity on EOR (enhanced oil recovery). The chemical flooding regulation model was built through dimensional analysis of hydrodynamic factors, affording oil displacement empirical formula for oil displacement by fitting EOR data. The empirical formula displayed high applicability within a certain range of capillary number (Ca), oil–water density ratio and porosity. In addition, the empirical formula was expected to guide the development of a cardanol-based surfactant, whose preparation process was optimized in the microreactor. These findings would provide useful references for understanding the EOR mechanism of chemical flooding at micro-scale.

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.

Pore‐Scale Modeling of Carbon Dioxide and Hydrogen Transport During Geologic Gas Storage

AbstractGeologic storage of CO2 and H2 are climate‐positive techniques for meeting the energy transition. While similar formations could be considered for both gases, the flow dynamics could differ due to differences in their thermophysical properties. We conduct a rigorous pore‐scale study of water/CO2 and water/H2 systems at relevant reservoir conditions in a Bentheimer rock sample using the lattice Boltzmann method to quantify the effects of capillary, viscous, inertial, and wetting forces during gas invasion. At similar conditions, H2 invasion is weaker compared to CO2 due to unfavorable viscosity ratios. Increasing flow rate, however, increases the breakthrough saturation for both gas systems in the range of capillary numbers studied. At isolated conditions of flow rate, viscosity ratio, and wettability, local inertial effects are found to be critical and show consistent increase in the invaded gas saturation. The effect of inertial forces persits for both gases across all field conditions tested.

Experimental visualization of mass transfer from a slug bubble during co-current flow in a conventional channel

Process intensification during gas–liquid flows is of paramount importance to optimize the size of the chemical reactors. This paper results from an investigation of the mass transfer visualization in a millimetric tube by using the colorimetric technique. A slug bubble train has been established in a 3.8 mm diameter tube for different gas superficial velocities and a constant liquid superficial velocity resulting in the low capillary number range between 0.0004<Ca<0.0006. Color-inducing dye Resazurin solution interacts with the Oxygen bubble to induce the pink color in the solution which has been captured by a high-speed camera. The liquid slug entrapped between the bubbles has three distinct regions namely, the central stem which has a stagnation point ahead of the bubble, the wall lubrication layer, and an entrapped Taylor vortex between the central stem and wall lubrication layer. Flow visualization results have been correlated with the penetration theory-based mass transfer models.

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.

Pore‐Scale Modeling of Coupled CO2 Flow and Dissolution in 3D Porous Media for Geological Carbon Storage

AbstractDissolution trapping is one of the crucial trapping mechanisms for geological carbon storage in deep saline aquifers. The injected supercritical CO2 (scCO2) flow and dissolution processes are coupled and interact with each other. Therefore, we performed direct numerical simulations in three‐dimensional micro‐CT images of sandstones using the volume of fluid and continuous species transfer method. We investigated the coupled scCO2 flow and dissolution processes at pore‐scale under different rock structures, capillary numbers, and rock wettability conditions. The dynamic evolution of the scCO2/brine phase distribution and scCO2 concentration distribution occurring during the injection period were presented and analyzed. Complicated coupling mechanisms between scCO2‐brine two‐phase flow and interphase mass transfer were also revealed. Our results showed that the scCO2 dissolution was highly dependent on the local distribution of scCO2 clusters. The rock with relatively high porosity and permeability would have more capacity for scCO2 injection resulting in a faster and greater dissolution of scCO2 in brine. The effect of capillary number on the scCO2 dissolution process was related to the range of capillary number. The effective upscaled (macro‐scale) mass transfer coefficient (kA) during scCO2 dissolution was evaluated, and the power‐law relationship between kA and Péclet number was obtained. Rock wettability was found to be another factor controlling the scCO2 dissolution process by affecting the scCO2‐brine interfacial area. Our pore‐scale study provides a deep understanding of the scCO2 dissolution trapping mechanism, which is important to enhance the prediction of sequestration risk and improve sequestration efficiency.

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.

Droplet impact dynamics over a range of capillary numbers and surface wettability: Assessment of moving contact line models and energy budget analysis

Bouncing and non-bouncing impact dynamics of a droplet on a solid surface are studied experimentally and numerically. High-speed visualization and an in-house dual-grid level-set method based solver are employed. Two established contact angle models, namely, Kistler and Fukai models, are implemented in the solver. While the Kistler model employs a time-varying dynamic contact angle, the Fukai model accounts for a quasi-dynamic contact angle based on contact line velocity. Better agreement between the present numerical result and present as well as published experimental results of a dynamic contact angle is found for the Kistler model, specifically for more transient contact angle variations cases that correspond to the less viscous droplets on the hydrophilic surfaces (Ca = 0.005–0.037 and θeq = 22°–90°). This is because the Kistler model can replicate more dynamic variations of the contact angles during spreading and receding as compared to the Fukai model, while both the Fukai and Kistler models numerical results are found in good agreement with the measurements for less transient contact angle variations cases that correspond to the high viscous droplets on the hydrophilic/hydrophobic surfaces (Ca = 7.596 and θeq = 86°–125°). Finally, the coupled effects of liquid surface tension, liquid viscosity, substrate wettability, and impact velocity during droplet bouncing and non-bouncing are presented through an energy budget analysis. At a given impact velocity, for less-viscous and less-surface tension liquids, the viscous dissipation is substantial irrespective of the surface wettability, whereas for less-viscous and high-surface tension liquids, the viscous dissipation is smaller on hydrophobic surfaces as compared to that on hydrophilic surfaces.

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.

Lattice Boltzmann simulation of binary three-dimensional droplet coalescence in a confined shear flow

Small-scale microscopic phenomena determine the behavior of large-scale droplets, which brings great challenges to accurately simulate the droplet coalescence process. In this paper, the mesoscopic lattice Boltzmann method based on the phase field theory is used to simulate the collision and coalescence of binary three-dimensional droplets in a confined shear flow. The numerical prediction of droplet coalescence behavior was first compared with the experimental result, and good agreement was reported. Then, we investigated the influences of a comprehensive range of capillary numbers (0.01≤Ca≤0.5) and Reynolds numbers (0.01≤Re≤10) on the shearing dynamics of binary droplets and also provided a quantitative description of droplet behavior in terms of the droplet deformation parameter and relative trajectory. A shearing regime diagram is further constructed based on the coupling effect of Ca and Re, which reveals three distinct types of droplet behaviors, including coalescence, breakup after the coalescence, and non-coalescence. Concretely, three different patterns of droplets can be completely captured with the variation of Ca at low Re; only two types of coalescence and non-coalescence can be observed for a medium Re, and two droplets just slide over each other without the occurrence of the coalescence when Re is sufficiently large. Also, we identified two critical capillary numbers in the lower Re region and one critical capillary number in the middle Re region, respectively, characterizing flow type transitions from the coalescence to breakup, from the breakup to the non-coalescence, and from the coalescence to the non-coalescence. It is found that all the capillary numbers decrease with Re.

Wrinkling and multiplicity in the dynamics of deformable sheets in uniaxial extensional flow

The processing of thin-structured materials in a fluidic environment, from nearly inextensible but flexible graphene sheets to highly extensible polymer films, arises in many applications. So far, little is known about the dynamics of such thin sheets freely suspended in fluid. In this work, we study the dynamics of freely suspended soft sheets in uniaxial extensional flow. Elastic sheets are modeled with a continuum model that accounts for in-plane deformation and out-of-plane bending, and the fluid motion is computed using the method of regularized Stokeslets. We explore two types of sheets: "stiff" sheets that strongly resist bending deformations and always stay flat, and "flexible" sheets with both in-plane and out-of plane deformability that can wrinkle. For stiff sheets, we observe a coil-stretch-like transition, similar to what has been observed for long-chain linear polymers under extension as well as elastic sheets under planar extension: in a certain range of capillary number (flow strength relative to in-plane deformability), the sheets exhibit either a compact or a highly stretched conformation, depending on deformation history. For flexible sheets, sheets with sufficiently small bending stiffness wrinkle to form various conformations. Here, the compact-stretched bistability still occurs, but is strongly modified by the wrinkling instability: a highly-stretched planar state can become unstable and wrinkle, after which it may dramatically shrink in length due to hydrodynamic screening associated with wrinkling. Therefore, wrinkling renders a shift in the bistability regime. In addition, we can predict and understand the nonlinear long-term dynamics for some parameter regimes with linear stability analysis of the flat steady states.

Surface Charge Affecting Fluid–Fluid Displacement at Pore Scale

AbstractEfficiency in fluid–fluid displacement is drastically reduced by viscous fingering, limiting the overall effectiveness in enhanced oil recovery, membrane science, and lateral flow devices used in biomedical applications. Local instabilities at the fluid–fluid interface lead to finger‐like patterns when a less viscous fluid displaces an immiscible fluid of higher viscosity. This widely observed phenomenon in multiphase flow inside porous media is infamously intricate to control, especially for given geometry and viscosity ratio. The presented study uses a highly controlled microfluidic porous network structure with tailored ionic surface strength. The direct correlation of viscous fingering evolution on the porous structure's zeta potential at a pore‐scale level is demonstrated via polyelectrolyte coatings using a layer‐by‐layer technique. Displacement patterns are tuned from vigorous viscous fingering over stable displacement to corner flow events across a broad range of capillary numbers depending on the applied coatings. The experimental data show an increasing trend of oil recovery with increasing surface wettability, consistent with several previous findings. Furthermore, the results reveal that surface zeta potential correlates positively with recovery rate but negatively with the displacement stability quantified by the fractal dimension. These insights enable a more targeted porous media design to obtain optimal multiphase flow control.

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.