Effect Of Capillary Number Research Articles

Motion of a confined bubble in a shear-thinning liquid

Abstract

Regime mapping of multiple breakup of droplets in shear flow by phase-field lattice Boltzmann simulation

Multiple breakup refers to a sequence of events through which a single droplet eventually produces multiple daughter droplets in a shear flow. It is a more common phenomenon than binary breakup. Using a phase-field lattice Boltzmann method, this work investigates the effects of Reynolds number, capillary number and soluble surfactant on multiple breakup in shear flow. We find that the regime map for a droplet in a surfactant-free shear flow can be segmented into the non-breakup, elementary breakup, multiple breakup, filament and coalescence regimes. By contrast, the multiple-breakup regime widens and the coalescence regime narrows in the system of surfactant. This difference on macroscale regimes originates from the mesoscale behaviour caused by the interaction of surfactant and shear flow. While surfactant hinders droplet breakup at lower Re, it promotes breakup at higher Re. The interfaces around the breaking points are stretched by the opposite reaction of Marangoni stress. While the regime map gives the number of daughter droplets in a given shear flow, a correlation is proposed to calculate the composition of breakup events, viz. the number of binary breakup and of ternary breakup events.

Breakup a droplet passing through an obstacle in an orthogonal cross-section microchannel

In this work, the breakup of a droplet passing through an obstacle in an orthogonal cross section is numerically investigated. The relevant boundary data of the velocity field is numerically computed by solving the depth-averaged Brinkman equation via a self-consistent integral equation using the boundary element method. To study the dependence of the droplet breakup on the obstacle shape, two different shapes of obstacle, circular and elliptical, are considered in the present work. We investigate the effect of obstacle size, obstacle position, and capillary number on the breakup treatment of the droplet. Numerical results indicate that the critical capillary number depends on the obstacle shape, obstacle position and droplet size. In the elliptical obstacle, in addition, the results also show that the area ratio of daughter droplets depends on the capillary number. Results show that the area ratio of daughter droplets depends on the capillary number, obstacle shape, and obstacle position. Our results is in a good agreement with the previous studies.

Structure and rheology of suspensions of spherical strain-hardening capsules

Abstract

Effect of Capillary Number on the Residual Saturation of Colloidal Dispersions Stabilized by a Zwitterionic Surfactant

We investigated oil recovery from porous rock using nanoscale colloidal dispersions, formed by adsorption of an anionic polymer [poly-(4styrenesulfonic acid-co-maleic acid); PSS-co-MA] and a zwitterionic surfactant [N-tetradecyl-N, N-dimethyl-3-ammonio-1-propanesulfonate, TPS] onto silica nanoparticles. In an emulsion, colloidal dispersion enhanced the stability of the oil-water interface in the absence of particle aggregation; the hydrophobic alkyl chains of TPS shifted into the oil drop, not only physiochemically, stabilizing the oil-water interface, but also promoting repulsive particle-to-particle interaction. Core flooding experiments on residual oil saturation as a function of capillary number, at various injection rates and oil viscosities, showed that the residual oil level was reduced by almost half when the zwitterionic surfactant was present in the colloidal dispersion. Consequently, the result revealed that this colloidal dispersion at the interface provides a mechanically robust layer at the oil-water interface without particle aggregation. Thus, the dispersion readily entered the pore throat and adhered to the oil-water interface, lowering the interfacial tension and improving oil recovery.

Effect of capillary number on morphological characterizations of trapped gas bubbles: Study by using micro-tomography

A series of capillary trapping experiments were conducted in unconsolidated porous media using high-resolution micro-tomography. Morphological characterizations of trapped gas bubbles, including residual gas saturation, bubble size distribution and interfacial area, were determined from reconstructed three-dimensional images. Different flooding flow rates, corresponding to capillary number ranges from 1.0 × 10−7 to 3.8 × 10−4, were performed to investigate the impact of flow rate on these characterizations during imbibition processes. At low capillary number, where capillary forces are dominant, the residual gas saturation is independent of capillary number and the bubble size distribution shows a universal power-law behavior predicted from percolation theory. When the capillary number increases above a critical value, the residual saturation decreases sharply, and the bubble size distribution no longer exhibits power-law behavior. As capillary number increases, the volume fraction of single-pore bubbles increases from about 16% to more than 80%. Furthermore, we explored the interfacial area of trapped bubbles, including gas–solid and gas–water (meniscus) interfacial areas, which directly affect the mass transfer process inside porous media. The specific interfacial area exhibits a linear relation with residual saturation, and the effect of particle size can be normalized by multiplying the median particle diameter. Moreover, we observed that the meniscus/total interfacial area ratio increases from 0.61 to 0.78 with an increase in capillary number, because the smaller singlet has a higher interfacial contact with the wetting phase.

Thin liquid films formation and evaporation mechanisms around elongated bubbles in rectangular cross-section microchannels

Thin film evaporation is the dominant mechanism of heat transfer in the microchannel flow boiling process. Hence, its understanding is paramount to development of predictive models and more efficient microchannel heat exchangers. Although microchannels mostly have a rectangular cross-section, the existing models are developed for circular cross-section microchannels. The non-uniformity of the liquid film thickness in microchannels with a rectangular cross-section has made prediction of the onset of dryout and heat transfer coefficient greatly challenging. Here, a test device capable of measuring the wall heat flux is utilized to fully characterize the thin film formation and evaporation process. The effects of flow capillary number (Ca) and channel aspect ratio on the liquid film thickness are determined in microchannels with 300 μm width and 300, 150, and 75 μm heights, representing aspect ratios of 1, 2, and 4, respectively. It is shown that the only existing mechanistic model for the elongated bubble regime in microchannels fails to predict the experimental heat transfer coefficient (HTC) both quantitively, by a 50–120% margin, and qualitatively, due to a fundamental difference in evaporation and dryout of a variable versus a uniform film assumed in the model. The results presented here pave the way for development of a more accurate mechanistic model for the thin film evaporation heat transfer mechanism in microchannels with a rectangular cross-section.

Experimental investigation on stable displacement mechanism and oil recovery enhancement of oxygen-reduced air assisted gravity drainage

The effects of gravity, capillary force, and viscous force on the migration characteristics of oil and gas interface in oxygen-reduced air-assisted gravity drainage (OAGD) were studied through a two-dimensional visualization model. The effects of bond number, capillary number and low-temperature oxidation on OAGD recovery were studied by long core displacement experiments. On this basis, the low-temperature oxidation number was introduced and its relationship with the OAGD recovery was established. The results show that the shape and changing law of oil and gas front are mainly influenced by gravity, capillary force and viscous force. When the bond number is constant (4.52×10 −4 ), the shape of oil-gas front is controlled by capillary number. When the capillary number is less than 1.68×10 −3 , the oil and gas interface is stable. When the capillary number is greater than 2.69×10 −2 , the oil and gas interface shows viscous fingering. When the capillary number is between 1.68×10 −3 and 2.69×10 −2 , the oil and gas interface becomes capillary fingering. The core flooding experiments results show that for OAGD stable flooding, before the gas breakthrough, higher recovery is obtained in higher gravity number and lower capillary number. In this stage, gravity is predominant in controlling OAGD recovery and the oil recovery could be improved by reducing injection velocity. After gas breakthrough, higher recovery was obtained in lower gravity and higher capillary numbers, which means that the viscous force had a significant influence on the recovery. Increasing gas injection velocity in this stage is an effective measure to improve oil recovery. The low-temperature oxidation number has a good correlation with the recovery and can be used to predict the OAGD recovery.

Wettability control on deformation: Coupled multiphase fluid and granular systems.

Understanding of multiphase flow in porous media is important for a wide range of applications such as soil science, environmental remediation, energy resources, and CO_{2} sequestration. This phenomenon depends on the complex interplay between the fluid and solid forces such as gravitational, capillary, and viscous forces, as well as wettability of the solid phase. Such interactions along with the geometry of the medium give rise to a variety of complex flow regimes. Although much research has been done in the area of wettability, its mechanical effect is not well understood, and it continues to challenge our understanding of the phenomena on macroscopic and microscopic scales. In this paper, therefore, the effect of wettability on the deformation of porous media and fluid-fluid patterns is studied through a series of three-dimensional (3D) simulations. To this end, the discrete element method (DEM) and volume of fluid (VOF) are coupled to accurately model free-surface flow interaction in a cylindrical pack of spheres. The fluid-particle interactions are modeled by exchanging information between DEM and VOF, while the effect of wettability is considered to study how it controls fluid displacement. The results indicate that the drag force and deformation in the pack vary with the change in wettability and capillary number. To demonstrate the effect of both wettability and capillary number, a series of numerical experiments were conducted with two capillary numbers and three wettability conditions. Our results show that the drag force was greatest for near extreme wettability conditions, which resulted in a larger deformation.

Modelling a surfactant-covered droplet on a solid surface in three-dimensional shear flow

A surfactant-covered droplet on a solid surface subject to a three-dimensional shear flow is studied using a lattice-Boltzmann and finite-difference hybrid method, which allows for the surfactant concentration beyond the critical micelle concentration. We first focus on low values of the effective capillary number ( ) and study the effect of , viscosity ratio ( ) and surfactant coverage on the droplet behaviour. Results show that at low the droplet eventually reaches steady deformation and a constant moving velocity . The presence of surfactants not only increases droplet deformation but also promotes droplet motion. For each , a linear relationship is found between contact-line capillary number and , but not between wall stress and due to Marangoni effects. As increases, decreases monotonically, but the deformation first increases and then decreases for each . Moreover, increasing surfactant coverage enhances droplet deformation and motion, although the surfactant distribution becomes less non-uniform. We then increase and study droplet breakup for varying , where the role of surfactants on the critical ( ) of droplet breakup is identified by comparing with the clean case. As in the clean case, first decreases and then increases with increasing , but its minima occurs at instead of in the clean case. The presence of surfactants always decreases , and its effect is more pronounced at low . Moreover, a decreasing viscosity ratio is found to favour ternary breakup in both clean and surfactant-covered cases, and tip streaming is observed at the lowest in the surfactant-covered case.

Experimental Evaluation of the Effects of Capillary Number on Permeability in Glass Cloth

Experimental Evaluation of the Effects of Capillary Number on Permeability in Glass Cloth

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.

Numerical simulation and three-phase pressure transient analysis considering capillary number effect - case study of a gas condensate reservoir

When the wellbore pressure drops below the dew point pressure of gas in a gas condensate reservoir, there is the possibility of condensate bank build-up and wellbore blockage. These adverse processes result in development of different mobility zones around the wellbore which complicates the pressure transient test analysis. The focus of this study is on the analytical and numerical analysis of pressure testing data obtained from a well in a target gas condensate reservoir. First, the well test data were analytically interpreted through which several well and reservoir parameters were identified such as condensate bank radius, gas effective permeability, mechanical skin and skin due to non-Darcy flow. A three-phase compositional reservoir model was then built using the analytical solution, for numerical analysis of the pressure transient data as well as validation of the analytical results. This numerical model was then used to estimate well deliverability and predict future reservoir performance. [Received: August 17, 2018; Accepted: March 15, 2019]

Numerical simulation and three-phase pressure transient analysis considering capillary number effect – case study of a gas condensate reservoir

Numerical simulation and three-phase pressure transient analysis considering capillary number effect – case study of a gas condensate reservoir

Influence of Capillary Number on the droplet Shape, Film Thickness, and Pressure Drop in a Liquid-Liquid Taylor Flow inside a Microcapillary

Numerical analysis of a two-dimensional, axisymmetric, incompressible, laminar liquid-liquid Taylor flow inside a vertical circular microchannel is carried out in the present study. The focus is laid on fluid flow characteristics in the slug flow regime. Although many researchers have performed numerical and experimental studies of two-phase flows in narrow channels, their efforts seem to have been fairly successful in explaining the underlying mechanisms of fluid flow phenomena, especially for slug flow regime. Here, an attempt has been made to explore the hydrodynamics of such flows. In the present study, dodecane and Pd5 have been used as the carrier phases and water is used as the discontinuous phase. The internal diameter of the circular microchannel is 1.5 mm with its wall being insulated. The flow and volume fraction equations are solved by the finite volume approach (FVM). The volume of fluid (VOF) method has been adopted for capturing the interface. The effect of Capillary number on film thickness and interfacial pressure drop is explained. The film thickness is found to increase with Capillary number and is also found to be in a close match with the models available in the literature. The pressure drop per unit length obtained from the CFD study is compared with a standard model available in the literature. The pressure drop across the unit cell is found to be following the phenomenological model. It is observed that the pressure drop at the interface has the highest contribution to the total pressure drop in contrast to the other pressure drops in the channel, with ~50-55% in dodecane-water and ~55-62% in Pd5-water systems. Besides, the distribution of the velocity, axial, and wall pressure fields inside the microcapillary are also discussed.

Pore-scale simulation of water/oil displacement in a water-wet channel

Water/oil flow characteristics in a water-wet capillary were simulated at the pore scale to increase our understanding on immiscible flow and enhanced oil recovery. Volume of fluid method was used to capture the interface between oil and water and a pore-throat connecting structure was established to investigate the effects of viscosity, interfacial tension (IFT) and capillary number (Ca). The results show that during a water displacement process, an initial continuous oil phase can be snapped off in the water-wet pore due to the capillary effect. By altering the viscosity of the displacing fluid and the IFT between the wetting and non-wetting phases, the snapped-off phenomenon can be eliminated or reduced during the displacement. A stable displacement can be obtained under high Ca number conditions. Different displacement effects can be obtained at the same Ca number due to its significant influence on the flow state, i.e., snapped-off flow, transient flow and stable flow, and ultralow IFT alone would not ensure a very high recovery rate due to the fingering flow occurrence. A flow chart relating flow states and the corresponding oil recovery factor is established.

Numerical simulation on dynamic behaviors of bubbles flowing through bifurcate T-junction in microfluidic device**Project supported by the National Natural Science Foundation of China (Grant Nos. 51706194 and 51876184).

Based on the volume of fluid (VOF) method, a numerical model of bubbles splitting in a microfluidic device with T-junction is developed and solved numerically. Various flow patterns are distinguished and the effects of bubble length, capillary number, and diameter ratio between the mother channel and branch are discussed. The break-up mechanism is explored in particular. The results indicate that the behaviors of the bubbles can be classified into two categories: break-up and non-break. Under the condition of slug flowing, the branches are obstructed by the bubbles that the pressure difference drives the bubbles into break-up state, while the bubbles that retain non-break state flow into an arbitrary branch under bubbling flow condition. The break-up of the short bubbles only occurs when the viscous force from the continuous phase overcomes the interfacial tension. The behavior of the bubbles transits from non-break to break-up with the increase of capillary number. In addition, the increasing of the diameter ratio is beneficial to the symmetrical break-up of the bubbles.

Effective interfacial tension in flow-focusing of colloidal dispersions: 3-D numerical simulations and experiments

An interface between two miscible fluids is transient, existing as a non-equilibrium state before complete molecular mixing is reached. However, during the existence of such an interface, which typically occurs at relatively short time scales, composition gradients at the boundary between the two liquids cause stresses effectively mimicking an interfacial tension. Here, we combine numerical modelling and experiments to study the influence of an effective interfacial tension between a colloidal fibre dispersion and its own solvent on the flow in a microfluidic system. In a flow-focusing channel, the dispersion is injected as core flow that is hydrodynamically focused by its solvent as sheath flows. This leads to the formation of a long fluid thread, which is characterized in three dimensions using optical coherence tomography and simulated using a volume of fluid method. The simulated flow and thread geometries very closely reproduce the experimental results in terms of thread topology and velocity flow fields. By varying the interfacial tension numerically, we show that it controls the thread development, which can be described by an effective capillary number. Furthermore, we demonstrate that the applied methodology provide the means to measure the ultra-low but dynamically highly significant effective interfacial tension.

Numerical Study of Droplet Dynamics on a Solid Surface with Insoluble Surfactants.

Surfactants are widely used in many industrial processes, where the presence of surfactants not only reduces the interfacial tension between fluids but also alters the wetting properties of solid surfaces. To understand how the surfactants influence the droplet motion on a solid surface, a hybrid method for interfacial flows with insoluble surfactants and contact-line dynamics is developed. This method solves immiscible two-phase flows through a lattice Boltzmann color-gradient model and simultaneously solves the convection-diffusion equation for surfactant concentration through a finite difference method. In addition, a dynamic contact angle formulation that describes the dependence of the local contact angle on the surfactant concentration is derived, and the resulting contact angle is enforced by a geometrical wetting condition. Our method is first used to simulate static contact angles for a droplet resting on a solid surface, and the results show that the presence of surfactants can significantly modify surface wettability, especially when the surface is more hydrophilic or more hydrophobic. This is then applied to simulate a surfactant-laden droplet moving on a substrate subject to a linear shear flow for varying effective capillary number ( Cae), Reynolds number ( Re), and surface wettability, where the results are often compared with those of a clean droplet. For varying Cae, the simulations are conducted by considering a neutral surface. At low values of Cae, the droplet eventually reaches a steady deformation and moves at a constant velocity. In either a clean or surfactant-laden case, the moving velocity of the droplet linearly increases with the moving wall velocity, but the slope is always higher (i.e., the droplet moves faster) in the surfactant-laden case where the droplet exhibits a bigger deformation. When Cae is increased beyond a critical value ( Cae,c), the droplet breakup would happen. The presence of surfactants is found to decrease the value of Cae,c, but it shows a non-monotonic effect on the droplet breakup. An increase in Re is able to increase not only droplet deformation but also surfactant dilution. The role of surfactants in the droplet behavior is found to greatly depend upon the surface wettability. For a hydrophilic surface, the presence of surfactants can decrease the wetting length and enables the droplet to reach a steady state faster; while for a hydrophobic surface, it increases the wetting length and delays the departure of the droplet from the solid surface.

Unsteady conjugate mass and heat transfer from/to a prolate spheroidal droplet in uniaxial extensional creeping flow

The unsteady conjugate mass/heat transfer from/to a prolate droplet suspended in uniaxial extensional creeping flow was numerically investigated. Based on the Stokes velocity field of a prolate droplet at small Reynolds numbers, a numerical algorithm combined with the finite difference method, the concentration transformation method and the level set approach was adopted to solve the convection-diffusion transport equations. The effects of Peclet number (1 ≤ Pe ≤ 1000), capillary number (0 ≤ Ca ≤ 0.1), viscosity ratio (0.01 ≤ λ ≤ 1), diffusivity ratio (0.1 ≤ K ≤ 10) and distribution coefficient (0.1 ≤ m ≤ 10) on interphase transport process were examined in terms of numerical simulation. The results show that the conjugate mass transfer from/to a single prolate droplet in the uniaxial extensional flow is significantly influenced by these five parameters, and the local and total mass transfer rates of a deformable droplet are slightly different from that of a spherical one. Given Pe, Ca, λ, K and m, an empirical correlation with an average relative deviation of 12.01% was proposed to predict Sh1,∞ of the prolate and spherical droplets suspended in uniaxial extensional creeping flow.