Effect Of Capillary Number Research Articles

Droplet dynamics in confinement

This study is to understand confinement effect on the dynamical behaviour of a droplet immersed in an immiscible liquid subjected to a simple shear flow. The lattice Boltzmann method, which uses a forcing term and a recolouring algorithm to realize the interfacial tension effect and phase separation respectively, is adopted to systematically study droplet deformation and breakup in confined conditions. The effects of capillary number, viscosity ratio of the droplet to the carrier liquid, and confinement ratio are studied. The simulation results are compared against the theoretical predictions, experimental and numerical data available in literature. We find that increasing confinement ratio will enhance deformation, and the maximum deformation occurs at the viscosity ratio of unity. The droplet is found to orient more towards the flow direction with increasing viscosity ratio or confinement ratio. Also, it is noticed that the wall effect becomes more significant for the confinement ratios larger than 0.4. Finally, the critical capillary number, above which the droplet breakup occurs, is found to be mildly affected by the confinement for the viscosity ratio of unity. Upon increasing the confinement ratio, the critical capillary number increases for the viscosity ratios less than unity, but decreases for the viscosity ratios more than unity.

Evolution of Free Surface in the Formation of Thermo-Solutocapillary Convection Within an Open Cavity

In order to understand the characteristics of free surface evolution in thermo-solutocapillary convection formation, a set of two-dimensional numerical simulations is conducted using level set method for thermo-solutocapillary convection in a rectangular cavity. The opposing thermocapillary effects equivalent to solutocapillary effects is considered. The computational results show that, the vortices first appear at the right side and travel to the left side gradually, and the flow field forms two comparable size vortices at final state. Meanwhile, the free surface deformation first increases and then decreases, and finally keeps a small constant deformation. Moreover, the effects of Marangoni number, Lewis number, Capillary number, aspect ratio and Prandtl number on the free surface evolution are analyzed.

樹脂構造体と3次元LBMを用いたPEFCガス拡散層内の水輸送解析

In a polymer electrolyte fuel cell (PEFC), it is necessary to optimize water and reactant gas flow in the cell to supply oxygen efficiently to the reaction zone. The water produced in the catalyst layer transports through micro-porous layer (MPL), gas diffusion layer (GDL), and then reach to the channel. All of the layers are important for the water management, and this study focuses on the water transport behavior in the GDL with complex fiber structure. For observation of the water behavior, a new experiment method using an enlarged scale model was developed. In the experiment method, silicone oil and water were applied to reduce Bond number. The GDL structure of the enlarged scale model was fabricated with a 3D printer. With the enlarged scale model, the effect of Capillary number was investigated. In the result, the liquid behavior is dominated by capillary force like the actual behavior of liquid water in the GDL and the liquid distribution is similar independently of the Capillary numbers at lower Capillary number.

Experimental and numerical investigations of local condensation heat transfer in a single square microchannel under variable heat flux

This paper presents an experimental investigation on the local and average condensation heat transfer in a single noncircular microchannel. Furthermore, it develops one dimensional model for annular condensation flow in a microchannel under variable heat flux condition. The condensate film thickness is calculated for each location in a microchannel including the effects of capillary number, Boiling number, contact angle, heat flux, vapor pressure, and hydraulic diameter. A comparative study shows that the present model well predicts the experimental data concerning local condensation heat transfer coefficient. The mean deviation between the local predictions of the theoretical model with the measurements for local heat transfer coefficient is 20%. It is found that the correlation of Quan et al. (2008) [19] gives the good predictions of the measurements with maximum deviation of 13% at high Reynolds number.

Effect of tube diameter and capillary number on platelet margination and near-wall dynamics

The effect of tube diameter $D$ and capillary number $Ca$ on platelet margination in blood flow at $\approx 37\%$ tube haematocrit is investigated. The system is modelled as three-dimensional suspension of deformable red blood cells and nearly rigid platelets using a combination of the lattice-Boltzmann, immersed boundary and finite element methods. Results show that margination is facilitated by a non-diffusive radial platelet transport. This effect is important near the edge of the cell-free layer, but it is only observed for $Ca > 0.2$, when red blood cells are tank-treading rather than tumbling. It is also shown that platelet trapping in the cell-free layer is reversible for $Ca \leq 0.2$. Only for the smallest investigated tube ($D = 10 \mu\text{m}$) margination is essentially independent of $Ca$. Once platelets have reached the cell-free layer, they tend to slide rather than tumble. The tumbling rate is essentially independent of $Ca$ but increases with $D$. Tumbling is suppressed by the strong confinement due to the relatively small cell-free layer thickness at $\approx 37\%$ tube haematocrit.

Quantitative prediction of residual wetting film generated in mobilizing a two-phase liquid in a capillary model

This research studies the motion of immiscible two-phase liquid flow in a capillary tube through a numerical approach employing the volume of fluid method, for simulating the core-annular flow and water flooding in oil reservoirs of porous media. More specifically, the simulations are a representation of water flooding at a pore scale. A capillary tube model is established with ANSYS Fluent and verified. The numerical results matches well with the existing data available in the literature. Penetration of a less viscous liquid in a liquid of higher viscosity and the development of a residual wetting film of the higher viscosity liquid are thoroughly investigated. The effects of Capillary number, Reynolds Number and Viscosity ratio on the residual wetting film are studied in detail, as the thickness is directly related to the residual oil left in the porous media after water flooding. It should be noticed that the liquids considered in this research can be any liquids of different viscosity not necessarily oil and water. The results of this study can be used as guidance in the field of water flooding.

Influence of dynamic factors on nonwetting fluid snap‐off in pores

AbstractSnap‐off is an important dynamic multiphase flow phenomenon which occurs in porous media. It plays a dominant role in the residual trapping and mobilization/immobilization of nonwetting fluids such as hydrocarbons or CO2. Current studies, applications, and threshold criteria of snap‐off are mostly based on static or equilibrium conditions. Thus, the dynamics of snap‐off which is relevant for many real world applications has rarely been systematically studied. While a static criterion indicates the snap‐off potential for nonwetting fluids, the competition between the time required for snap‐off and the local pore throat capillary number determines whether snap‐off actually occurs. Using a theoretical model to couple the wetting film thickness to the local capillary number at the pore throat, we analyzed the dynamics of the wetting/nonwetting interface instability in sinusoidally constricted capillary tubes. The influence of dynamic factors as encapsulated by the effect of local capillary number on nonwetting fluid snap‐off time were investigated for varying pore throat to pore body aspect ratio and pore body distances. The analysis showed that snap‐off can be inhibited by a sufficiently large local capillary number even in cases where the static snap‐off criterion has been met.

Investigation into the effect of capillary number on productivity of a lean gas condensate reservoir

The main objective of this study is to provide a comprehensive investigation into the effect of Capillary number (NCa) on production from the lean gas condensate reservoirs and to show the importance of NCa in these types of reservoirs. In the current study a gas condensate reservoir has been simulated and validated using field and PVT data. The effect of NCa on the parameters such as producing gas flow rate, bottom-hole pressure, average reservoir pressure, the amount of condensate in the reservoir and the condensate saturation versus the distance from the production well has been investigated. It was found that NCa can increase the relative permeability of the gas followed by the reduction in condensate formation and pressure drop in the vicinity of wellbore. Furthermore, the results stated that NCa exists in about 10 ft away from the well and affects mainly the well productivity parameters such as bottom-hole pressure and gas flow rate. However, it does not affect the average reservoir pressure and condensate throughout the reservoir as much as the near wellbore parameters.

The effect of weak-inertia on droplet formation phenomena in T-junction microchannel

We present droplet formation in a T-junction microfluidic device in five different regimes of squeezing, dripping, transition, jetting and parallel. Droplet is created as a result of interaction of two immiscible liquids. Effects of Capillary number (Ca) and Reynolds number (Re) are investigated which changes the regime of droplet formation and creates rotational flow inside droplet, respectively. Simulations were done with the open source code Gerris using volume of fluid method and adaptive mesh refinement techniques in order to track interface properly. Two kinds of jetting regimes, i.e., stable and unstable, were simulated in this work. For higher Re number the parallel regime is observed so Re number is limited to 25. This study shows that the results of Re > 1 have some differences compared with those of Re 1 and Re < 1 which are due to wall shear stresses. Droplets with rotational flow can increase diffusivity, which is motivation of this work.

Dynamics of isolated confined air bubbles in liquid flows through circular microchannels: an experimental and numerical study

Experimental and numerical studies are performed to characterise the dynamics of isolated confined air bubbles in laminar fully developed liquid flows within channels of diameters d = 0.5 mm and d = 1 mm. Water and glycerol are used as the continuous liquid phase, and therefore, a large range of flow capillary numbers 10−4 < Ca < 10−1 and Reynolds numbers 10−3 < Re < 103 are covered. An extensive investigation is performed on the effect of bubble size and flow capillary number on different flow parameters, such as the shape and velocity of bubbles, thickness of the liquid film formed between the bubbles and the channel wall, and the development lengths in front and at the back of the bubbles. The micro-particle shadow velocimetry technique (μPSV) is employed in the experimental measurements allowing simultaneous quantification of important flow parameters using a single sequence of high-speed greyscale images recorded at each test condition. Bubble volume and flow rate of the continuous liquid phase are precisely determined in the post-processing stage using the μPSV images. These parameters are then used as initial and boundary conditions to set up CFD simulations reproducing the corresponding two-phase flow. Simulations based on the volume of fluid technique with the aim of capturing the interface dynamics are performed with both ANSYS Fluent v. 14.5, here augmented by implementing self-defined functions to improve the accuracy of the surface tension force estimation, and ESI OpenFOAM v. 2.1.1. The present approach not only results in valuable findings on the underlying physics involved in the problem of interest but also allows us to directly compare and validate results that are currently obtained by the experimental and computational methods. It is believed that similar methodology can be employed to rigorously investigate more complex two-phase flow regimes in micro-geometries.

Direct pore-to-core up-scaling of displacement processes: Dynamic pore network modeling and experimentation

Summary We present a new dynamic pore network model that is capable of up-scaling two-phase flow processes from pore to core. This dynamic model provides a platform to study various flow processes in porous media at the core scale using the pore-scale physics. The most critical features of this platform include (1) the incorporation of viscous, capillary, and gravity pressure drops in pore-scale displacement thresholds, (2) wetting-phase corner flow in capillary elements with angular cross-sections, (3) adjustments of corner interfaces between wetting and non-wetting phases based on changes in local capillary pressure, (4) simultaneous injection of wetting and non-wetting phases from the inlet of the medium at constant flow rates that makes the study of steady-state processes possible, (5) heavy parallelization using a three-dimensional domain decomposition scheme that enables the study of two-phase flow at the core scale, and (6) constant pressure boundary condition at the outlet. For the validation of the dynamic model, three two-phase miniature core-flooding experiments were performed in a state-of-the-art micro core-flooding system integrated with a high-resolution X-ray micro-CT scanner. The dynamic model was rigorously validated by comparing the predicted local saturation profiles, fractional flow curves, relative permeabilities, and residual oil saturations against their experimental counterparts. The validated dynamic model was then used to study low-IFT and high-viscosity two-phase flow processes and investigate the effect of high capillary number on relative permeabilities and residual oil saturation.

Deformation of an elastic capsule in a uniform electric field

The deformation of a thin elastic capsule subjected to a uniform electric field is investigated in the Stokes flow regime. The electrohydrodynamic flow is analyzed using a perfect conductor and a perfect dielectric model for the capsule and the fluid phase, respectively. A theoretical analysis is carried out using an asymptotic expansion in the electric capillary number (Ca) (a ratio of the electric stress to the elastic tension) in the small deformation limit using the finite deformation Hooke’s law. The analysis is used to determine the elasticity of polysiloxane capsules suspended in oil, the deformation of which is obtained using videography. The boundary element method is implemented to seek numerical solutions to the hydrodynamic, elastic, and electrostatics equations. The finite deformation Hooke’s law, the Mooney-Rivlin, and Skalak’s model for elasticity are employed. The effect of electric capillary number, unstressed geometry, and the type of membrane material on the deformation of a capsule is presented in the high Ca number limit using numerical simulation. Capsules synthesized with higher monomer concentration displayed electric stress induced wrinkling process at high electric field strengths. Burst of a capsule is characterized by poration of the polymer membrane, which could be symmetric or asymmetric at the two poles, depending upon the value of the capillary number. The results should be useful in understanding the response of elastic capsules such as red blood cells and polymerized membranes, to an electric field, in applications such as electrodeformation and electroporation. It also provides a theoretical framework for a possible way of determining the elastic parameters of a capsule.

Simulation of Newtonian and non-Newtonian rheology behavior of viscous fingering in channels by the lattice Boltzmann method

Viscous fingering phenomenon in channels is numerically investigated using the lattice Boltzmann method. The effects of capillary number, viscosity ratio, wettability, gravitational acceleration, three dimensional (3D) geometry and non-Newtonian rheology property on finger generation are examined. The results show that high capillary number and high viscosity ratio lead to narrow finger. The finger growth is enhanced when the displacing fluid is non-wetting to the channel walls and otherwise suppressed. The gravitational acceleration induces the finger pattern asymmetric and shortens the breakthrough time. The finger pattern generated in 3D geometry is quite different from the pattern generated in two dimensional (2D) geometry, and the finger width is influenced both by the 3D geometry and the wettability of channel walls. Due to the changing apparent viscosity of the power-law fluid, the viscous fingering is enhanced in shear thickening fluid while suppressed in shear thinning fluids. The results provide an understanding of the viscous fingering phenomenon from a mesoscopic view and confirm that the lattice Boltzmann method is an effective tool to investigate the immiscible displacement in complex geometry as well as non-Newtonian multiphase fluid flow behavior problems.

Direct simulations of two-phase flow on micro-CT images of porous media and upscaling of pore-scale forces

Pore-scale forces have a significant effect on the macroscopic behaviour of multiphase flow through porous media. This paper studies the effect of these forces using a new volume-of-fluid based finite volume method developed for simulating two-phase flow directly on micro-CT images of porous media. An analytical analysis of the relationship between the pore-scale forces and the Darcy-scale pressure drops is presented. We use this analysis to propose unambiguous definitions of Darcy-scale viscous pressure drops as the rate of energy dissipation per unit flow rate of each phase, and then use them to obtain the relative permeability curves. We show that this definition is consistent with conventional laboratory/field measurements by comparing our predictions with experimental relative permeability. We present single and two-phase flow simulations for primary oil injection followed by water injection on a sandpack and a Berea sandstone. The two-phase flow simulations are presented at different capillary numbers which cover the transition from capillary fingering at low capillary numbers to a more viscous fingering displacement pattern at higher capillary numbers, and the effect of capillary number on the relative permeability curves is investigated. Overall, this paper presents a new finite volume-based methodology for the detailed analysis of two-phase flow directly on micro-CT images of porous media and upscaling of the results to the Darcy scale.

All-printed flexible organic transistors enabled by surface tension-guided blade coating.

A combination of surface energy-guided blade coating and inkjet printing is used to fabricate an all-printed high performance, high yield, and low variability organic thin film transistor (OTFT) array on a plastic substrate. Functional inks and printing processes were optimized to yield self-assembled homogenous thin films in every layer of the OTFT stack. Specifically, we investigated the effect of capillary number, semiconductor ink composition (small molecule-polymer ratio), and additive high boiling point solvent concentrations on film fidelity, pattern design, device performance and yields.

Self-triggering regime for synchronized formation of two droplets

This letter reports experimental results of the synchronized formation of two liquid droplets in a microfluidic device. A pair of droplets is formed periodically in a T-junction configuration with a single channel for the continuous phase and two inlets for the dispersed phase. The pair-wise droplet formation process is self-triggering, as the first droplet formed upstream triggers the breakup of the second droplet downstream. The triggered breakup happens across the different formation regimes. The effects of capillary number and flow rate ratio on the size and order of the droplets are investigated. The configuration reported here may serve as a parallel to serial sampling device for droplet-based lab-on-a-chip platforms.

The Effect of Hydraulic Fracturing on the Performance of Gas Condensate Systems

Gas condensate reservoirs usually exhibit complex flow behaviors due to the buildup of condensate bank around the wellbore when the bottom-hole pressure falls below the dew point. Hydraulic fracturing improves well productivity by delaying the onset of dew point pressure and also reducing the condensate saturation near the wellbore area. The authors present the results of a study that compared the near wellbore behaviors and productivities of a vertical nonfractured well and a vertical hydraulically fractured well in a low permeability lean gas condensate reservoir. Results show that there is no indication of capillary number effects in this low permeability reservoir because of low production rates.

CO2/Water Displacement in Porous Medium Under Pressure and Temperature Conditions for Geological Storage

This paper presented CO2 injected into water saturated porous media for immiscible displacement using high-resolution MRI. The porous medium was formed from the packed bed of glass beads 0.2mm. CO2/water displacement processes were implemented by a spin echo sequence with MRI technique. CO2/water displacement process was investigated for different flow rates. Then CO2 and water distribution were distinguished from MRI images. Then residual water saturation were obtained at steady state. The effects of capillary number were investigated. The study provides useful data for transport process in CO2 storage.

Microfluidic flow-focusing in ac electric fields

We demonstrate the control of droplet sizes by an ac voltage applied across microelectrodes patterned around a flow-focusing junction. The electrodes do not come in contact with the fluids to avoid electrochemical effects. We found several regimes of droplet production in electric fields, controlled by the connection of the chip, the conductivity of the dispersed phase and the frequency of the applied field. A simple electrical modelling of the chip reveals that the effective voltage at the tip of the liquid to be dispersed controls the production mechanism. At low voltages (≲ 600 V), droplets are produced in dripping regime; the droplet size is a function of the ac electric field. The introduction of an effective capillary number that takes into account the Maxwell stress can explain the dependance of droplet size with the applied voltage. At higher voltages (≳ 600 V), jets are observed. The stability of droplet production is a function of the fluid conductivity and applied field frequency reported in a set of flow diagrams.

The Effect of Relative Permeability on the Well Testing Behavior of Naturally Fractured Lean Gas Condensate Reservoirs

Gas condensate reservoirs show complicated thermodynamic behavior when their pressure reduces to under dew point pressure. Condensate blockage around the producing well cause significant reduction of production rate as well bottom-hole pressure drops below saturation pressure. The main objective of this work was to examine the well test analysis of naturally fractured lean gas condensate reservoir and investigate the effect of condensate formed around the well bore on behavior of single phase pseudopressure and its derivative curves. In this work a naturally fractured lean gas condensate reservoir is simulated with compositional simulator. Different sensitivity analysis done on Corey parameters and result of simulator is fed to analytical well testing software. For consideration of these phenomena 18 compositional models with capillary number effect are constructed. Matrix relative permeability obeys Corey's relative permeability and relative permeability in fracture is linear. Well testing behavior of these models are studied and interpreted. Results show different sensitivity analysis on relative permeability of matrix does not have strong effect on well testing behavior even though most part of the matrix around the well is occupied with condensate.