Capillary Pressure Gradient Research Articles

Three-dimensional transient two-phase study of the cathode side of a PEM fuel cell

A three-dimensional transient two-phase isothermal model has been developed for the cathode side of a proton exchange membrane fuel cell (PEMFC). This has been done in order to fully investigate the effects and the time variation of liquid water formation as well as the gas phase transport under the start up condition. It is considered that the generated water in the cathode catalyst layer (CL) is liquid water and that the gas diffusion layer (GDL) is hydrophobic. A non-equilibrium water condensation-evaporation is also assumed. The time variations of liquid water distribution in along-channel and through-plane directions are investigated. This is to determine the liquid water accumulation at the start up time (above the channel under the CL), then the movement of the liquid water in the domain and the final accumulation at the steady state condition (above the rib and near the CL). It has also been found that it takes less time for a high average current density to attain the steady state condition which is due to the capillary pressure gradient inside the porous media. Validation of the numerical results has been implemented via a polarization curve comparison with the experimental data. Both sets show good agreement.

Experimental Studies of Liquid Droplet Coalescence on the Gradient Surface

Visual experiments were conducted to study the behaviors of liquid droplet coalescence on the surface with gradient surface energy. The microscopic contour of the gradient energy surface, which was fabricated on the base of a silicon chip by diffusion-controlled silanization of alkyltrichlorosilanes, was characterized by atom force microscopy. The effects of droplets on the three-phase contact line and the contact angle were obtained. It was observed that the process of droplet coalescence accelerates the droplet speed on the gradient surface. On the high-energy surface, the triple-phase contact line of the coalescing droplet is prone to pinning. The interfacial energy released from coalescence is the main source for promoting the motion. Furthermore, the nonequilibrium capillary pressure gradient inside coalescence droplets is considered to aid in accelerating the coalescence.

Theory of breakup of core fluids surrounded by a wetting annulus in sinusoidally constricted capillary channels

Analysis of core-annular dynamics in the presence of base flow for arbitrary fluid viscosities leads to an equation describing the temporal evolution of the fluid/fluid interface. The equation follows from the conservation of mass in the “small-slope” approximation. Its useful applications occur, for example, in chemical engineering and petroleum recovery. The nonlinear equation allows inexpensive numerical analysis. For sinusoidally constricted pores, a purely geometric criterion exists that enables or prohibits the core-fluid breakup in the necks of the constrictions. The geometrically favoring condition sets up capillary-pressure gradients that ensure a continuous outflow of the core fluid from the necks into the “crests” of the profile. Such behavior is indeed observed in the numerical solutions of the evolution equation. For relatively large slopes of the initial configuration, setting up larger pressure gradients, the interface shape remains “smooth,” the evolution times are relatively fast, and the breakup is typically achieved by the growing film-fluid collar touching the axis of the channel at a single point. No satellite droplets are produced. Decreasing the slope lengthens the evolution times, allowing the formation and growth of “wavy” disturbances on the initial interface profile, which may touch the axis of the capillary in several places forming satellite drops. Thinner initial annuli also slow down the evolution process. Instability develops for the cases of the core both more and less viscous than the film. Finally, if the geometry prohibits the snap-off altogether, the initial interface configurations decay into steady-state solutions, and no breakup takes place. The solutions of the evolution equation validate well against two computational-fluid-dynamics codes.

A sharp surface tension modeling method for two‐phase incompressible interfacial flows

AbstractA surface tension implementation algorithm for two‐phase incompressible interfacial flows is presented in this study. The surface tension effect is treated as a jump condition at the interface and incorporated into the Navier–Stokes equation via a capillary pressure gradient. The interface is tracked by a coupled level set and volume‐of‐fluid (CLSVOF) method based on the finite‐volume formulation on a fixed Eulerian grid. It has been shown in a stationary benchmark test the spurious currents are greatly reduced and the sharp pressure jump across the interface is well preserved. Numerical instabilities caused by the sharp treatment on a fixed grid are avoided. Several dynamic tests are performed to further validate the accuracy and versatility of the present method, the results of which are in good agreement with data reported in the literature. Copyright © 2009 John Wiley & Sons, Ltd.

Self-regulating passive fuel supply for small direct methanol fuel cells operating in all orientations

A microfluidic fuel supply concept for passive and portable direct methanol fuel cells (DMFCs) that operates in all spatial orientations is presented. The concept has been proven by fabricating and testing a passive DMFC prototype. Methanol transport at the anode is propelled by the surface energy of deformed carbon dioxide bubbles, generated as a reaction product during DMFC operation. The experimental study reveals that in any orientation, the proposed pumping mechanism transports at least 3.5 times more methanol to the reactive area of the DMFC than the stoichiometry of the methanol oxidation would require to sustain DMFC operation. Additionally, the flow rates closely follow the applied electric load; hence the pumping mechanism is self-regulating. Oxygen is supplied to the cathode by diffusion and the reaction product water is transported out of the fuel cell along a continuous capillary pressure gradient. Results are presented that demonstrate the continuous passive operation for more than 40 h at ambient temperature with a power output of p = 4 mW cm−2 in the preferred vertical orientation and of p = 3.2 mW cm−2 in the least favorable horizontal orientation with the anode facing downwards.

Formation dry‐out from CO2 injection into saline aquifers: 1. Effects of solids precipitation and their mitigation

Injection of CO2 into saline aquifers may cause formation dry‐out and precipitation of salt near the injection well, which may reduce formation porosity, permeability, and injectivity. This paper uses numerical simulation to explore the role of different processes and parameters in the salt precipitation process and to examine injection strategies that could mitigate the effects. The main physical mechanisms affecting the dry‐out and salt precipitation process include (1) displacement of brine away from the injection well by injected CO2, (2) dissolution (evaporation) of brine into the flowing CO2 stream, (3) upflow of CO2 due to gravity effects (buoyancy), (4) backflow of brine toward the injection point due to capillary pressure gradients that oppose the pressure gradient in the CO2‐rich (“gas”) phase, and (5) molecular diffusion of dissolved salt. The different mechanisms operate on a range of spatial scales. CO2 injection at constant rate into a homogeneous reservoir with uniform initial conditions is simulated in 1‐D radial geometry, to resolve multiscale processes by taking advantage of the similarity property, i.e., the evolution of system conditions as a function of radial distance R and time t depends only on the similarity variable R2/t. Simulations in 2‐D vertical cross sections are used to examine the role of gravity effects. We find that counterflow of CO2 and brine can greatly increase aqueous phase salinity and can promote substantial salt precipitation even in formations with low dissolved solids. Salt precipitation can accentuate effects of gravity override. We find that injecting a slug of fresh water prior to commencement of CO2 injection can reduce salt precipitation and permeability loss near the injection well.

Capillary-driven pumping for passive degassing and fuel supply in direct methanol fuel cells

In this paper we present a new concept of creating and using capillary pressure gradients for passive degassing and passive methanol supply in direct methanol fuel cells (DMFCs). An anode flow field consisting of parallel tapered channels structures is applied to achieve the passive supply mechanism. The flow is propelled by the surface forces of deformed CO2 bubbles, generated as a reaction product during DMFC operation. This work focuses on studying the influence of channel geometry and surface properties on the capillary-induced liquid flow rates at various bubbly gas flow rates. Besides the aspect ratios and opening angles of the tapered channels, the static contact angle as well as the effect of contact angle hysteresis has been identified to significantly influence the liquid flow rates induced by capillary forces at the bubble menisci. Applying the novel concept, we show that the liquid flow rates are up to thirteen times higher than the methanol oxidation reaction on the anode requires. Experimental results are presented that demonstrate the continuous passive operation of a DMFC for more than 15 h.

Linear stability of a volatile liquid film flowing over a locally heated surface

The dynamics and linear stability of a volatile liquid film flowing over a locally heated surface are investigated. The temperature gradient at the leading edge of the heater induces a gradient in surface tension that leads to the formation of a pronounced capillary ridge. Lubrication theory is used to develop a model for the film evolution that contains three key dimensionless groups: a Marangoni parameter (M), an evaporation number (E), and a measure of the vapor pressure driving force for evaporation (K), which behaves as an inverse Biot number. The two-dimensional, steady solutions for the local film thickness are computed as functions of these parameters. A linear stability analysis of these steady profiles with respect to perturbations in the spanwise direction reveals that the operator of the linearized system can have both a discrete and a continuous spectrum. The continuous spectrum exists for all values of the spanwise wave number and is always stable. The discrete spectrum, which corresponds to eigenfunctions localized around the ridge, appears for values of M larger than a critical value for a finite band of wave numbers separated from zero. Above a second, larger critical value of M, a portion of the discrete spectrum becomes unstable, corresponding to rivulet formation at the forward portion of the capillary ridge. For sufficiently large heat transfer at the free surface, due either to phase change or to convection, a second band of unstable discrete modes appears, which is associated with an oscillatory, thermocapillary instability above the heater. The critical Marangoni parameter above which instability develops, Mcrit(K,E), has a nonmonotonic dependence on the steepness of the temperature increase at the heater, in contrast to the monotonic decrease for a nonvolatile film at vanishing Biot number. An energy analysis reveals that the dominant instability mechanism resulting from perturbations to the film thickness is either streamwise capillary flow or gravity for weakly volatile fluids and thermocapillary flow due to spanwise temperature gradients for more volatile fluids. The stability results are rather sensitive to the steepness of the temperature increase and heater width due to the nonlinear coupling of gravity, capillary pressure gradients, thermocapillary flow, and evaporation through the base states.

Simultaneous study of interfacial tension, surface tension, and viscosity of few surfactant solutions with survismeter

AbstractSurfaces and interfaces are receptive valuable significant property of chemical molecules due to their potential to develop several phenomena in a self‐controlled mechanism. Science of surfaces is vast and is being used industrially since time immemorial. Their accurate and simultaneous estimation is necessary; therefore, the survismeter was used for measuring them along with viscosity. Individually tensiometers, X‐ray reflective microscope, and viscometers are used for surface tension, interfacial tension, and viscosity, respectively. These devices are sophisticated, expensive, and individually consume much time and resources with poor reproducibility in measurements. Survismeter is an alternative device for similar measurements together with higher accuracies and reproducibility. It works on a principle of capillary flow and pressure gradient (PG) inside liquid‐holding and air‐filled bulbs. Several liquids have been used for study with ± 0.01 mN/m, ± 0.01 mN/m and ± 1 × 10−5 N s/m2 accuracies in respective data. Copyright © 2008 John Wiley & Sons, Ltd.

An Analytical Model for Capillary Pressure–Saturation Relation for Gas–Liquid System in a Packed-Bed of Spherical Particles

Capillary pressure is considered in packed-beds of spherical particles. In the case of gas-liquid flows in packed-bed reactors, capillary pressure gradients can have a significant influence on liquid distribution and, consequently, on the overall reactor performance. In particular, capillary pressure is important for non-uniform liquid distribution, causing liquid spreading as it flows down the packing. An analytical model for capillary pressure-saturation relation is developed for the pendular and funicular regions and the factors affecting capillary pressure in the capillary region are discussed. The present model is compared to the capillary pressure models of Grosser et al. (AIChE J., 34:1850-1860, 1988) and Attou and Ferschneider (Chem. Eng. Sci., 55:491-511, 2000) and to the experiments of Dodds and Srivastava (Part Part Syst. Charact., 23:29-39, 2006) and Dullien et al. (J. Colloid Interface Sci., 127:362-372, 1989). The non-homogeneity of real packings is considered through particle size and porosity distributions. The model is based on the assumption that the particles are covered with a liquid film, which provides hydrodynamic continuity. This makes the model more suitable for porous or rough particles than for non-porous smooth particles. The main improvements of the present model are found in the pendular region, where the liquid dispersion due to capillary pressure gradients is most significant. The model can be used to improve the hydrodynamic models (e.g., CFD and cellular automata models) for packed-bed reactors, such as trickle-bed reactors, where gas, liquid, and solid phases are present. Models for such reactors have become quite common lately (Saez and Carbonell, AIChE J., 31:52-62, 1985; Holub et al., Chem. Eng. Sci, 47, 2343-2348, 1992; Attou et al., Chem. Eng. Sci., 54:785-802, 1999; Iliuta and Larachi, Chem. Eng. Sci., 54:5039-5045, 1999, IJCRE 3:R4, 2005; Narasimhan et al., AIChE J., 48:2459-2474, 2002), but they still lack proper terms causing liquid dispersion.

Characteristic lengths affecting evaporative drying of porous media

Evaporation from porous media involves mass and energy transport including phase change, vapor diffusion, and liquid flow, resulting in complex displacement patterns affecting drying rates. Force balance considering media properties yields characteristic lengths affecting the transition in the evaporation rate from a liquid-flow-based first stage limited only by vapor exchange with air to a second stage controlled by vapor diffusion through the medium. The characteristic lengths determine the extent of the hydraulically connected region between the receding drying front and evaporating surface (film region) and the onset of flow rate limitations through this film region. Water is displaced from large pores at the receding drying front to supply evaporation from hydraulically connected finer pores at the surface. Liquid flow is driven by a capillary pressure gradient spanned by the width of the pore size distribution and is sustained as long as the capillary gradient remains larger than gravitational forces and viscous dissipation. The maximum extent of the film region sustaining liquid flow is determined by a characteristic length L_{C} combining the gravity characteristic length L_{G} and viscous dissipation characteristic length L_{V} . We used two sands with particle sizes 0.1-0.5 mm ("fine") and 0.3-0.9 mm ("coarse") to measure the evaporation from columns of different lengths under various atmospheric evaporative demands. The value of L_{G} determined from capillary pressure-saturation relationships was 90 mm for the coarse sand and 140 mm for the fine sand. A significant decrease in drying rate occurred when the drying front reached the predicted L_{G} value (viscous dissipation was negligibly small in sand and L_{C} approximately L_{G} ). The approach enables a prediction of the duration of first-stage evaporation with the highest water losses from soil to the atmosphere.

Asymptotic analysis of the selective dip coating of power-law fluids

The dip coating of a chemically micropatterned surface bearing alternating wetting and nonwetting vertical strips is analyzed for a non-Newtonian power-law fluid. Asymptotic matching is used to determine the thickness of liquid films deposited on the O(10μm) strips at small capillary and Bond numbers. The chemical patterning that confines the fluid laterally induces a significant transverse curvature of the free-surface. The streamwise variation in this transverse curvature along the strip provides an additional contribution to the capillary pressure gradient that is not present for uniform surfaces. Consequently, the difference in the thickness of the deposited liquid film relative to a Newtonian fluid is significantly less than for homogeneous plates or fibers.

Capillary instabilities of liquid films inside a wedge

We consider a liquid meniscus inside a wedge of included angle 2β that wets the solid walls with a contact angle θ. The meniscus has a convex interface that satisfies π∕2<θ+β<π. The capillary pressure gradient due to a small disturbance of the location of the contact line moves fluid from a neck region to a bulge region, causing instabilities. A dynamic contact-line condition is considered in which the contact angle varies linearly with the slipping speed of the contact line with a slope of G:G=0 representing perfect slip and a fixed contact angle. A nonlinear thin film equation is derived and numerically solved for the shape of the contact line as a function of parameters. The result for G=0 shows that the evolution process consists of a successive formation of bulges and necks in decreasing length and time scales, eventually resulting in a cascade structure of primary, secondary, and tertiary droplets. When G>0, there is a similar but slower nonlinear evolution process. The numerical results agree qualitatively with very recent experimental results.

2D modeling of salt precipitation during the injection of dry CO2 in a depleted gas reservoir

The precipitation of halite around a CO 2 injection well has been studied to investigate the possible effects on well injectivity for a pilot test of CO 2 injection in a depleted gas reservoir. The numerical simulations performed with the TMGAS simulator, using both 1D and 2D radial grids, show that the injection of dry supercritical CO 2 vaporizes the formation brine promoting NaCl concentration and the precipitation of halite. Different behaviors are observed depending on the initial liquid saturation: when the brine has a low mobility, the evaporation front advances with limited halite precipitation and only minor effects on well injectivity. On the other hand, when the brine has sufficient mobility, the precipitation front is recharged by the brine flowing towards the wellbore, due to the capillary pressure gradient driven by the evaporation. In this case the concentrated precipitation can strongly reduce the formation permeability. These effects depend on formation properties and on the porosity–permeability relationship which describes the effects of halite precipitation on permeability reduction. In the attempt to improve the prediction of halite precipitation effects, an extension of the so-called tube-in-series model of Verma and Pruess was developed, with pore-size distribution evaluated from the measured grain-size distribution of the sandy formation considered for the execution of the pilot CO 2 sequestration test.

Second law analysis for microscale flow and heat transfer

In phase change transport devices, capillary forces drive overall circulation of working fluid from an evaporator section to a condenser section, whereas the thin film flows at the evaporating meniscus are driven by capillary and disjoining pressure gradient. An analysis has been provided for the microscale fluid flow and heat transfer in an evaporating extended meniscus. Using the second law of thermodynamics, the entropy generated has been investigated. The geometric configuration that corresponds to the minimization of entropy generated and minimization of fluid flow resistance is identified.

Analytical Model for The Capillary Pressure Gradient in Oil–Water–Rock System

A simplified analytical expression for the capillary pressure gradient in homogeneous porous media is proposed. Basic assumptions are: (1) the three phase contact angle between two fluids and porous rock is finite, (2) the surface area of contact between two fluids is small in comparison with contact surface areas between each fluid and porous rock in the unit volume of the system under consideration, (3) the model corresponds to conditions when both phases are continuous.

Modelling the transmural transport of oxygen to the retina

Oxygen transport from retinal capillaries to retinal tissue is studied by use of a Krogh-type cylinder model. The retinal tissue is represented as an array of uniformly cylinders with capillaries along the axes. The model introduces the transmural transport of oxygen from the retinal capillaries to its surrounding (retinal) tissue in a hypoxia environment. Computational results for concentration distribution in the retinal tissue are presented through graphs and the effects of important model parameters: intraocular pressure, capillary wall permeability coefficient, capillary wall pressure gradient constant on the oxygen concentration distribution are depicted and discussed.

Steady flow and evaporation of a volatile liquid in a wedge

We develop a lubrication-type model of a liquid flow in a wedge in the limit of small capillary numbers and negligible gravity. Liquid flows under the action of capillary pressure gradients and thermocapillary stresses, and evaporates due to heating from the solid walls on which a constant axial temperature gradient is imposed. Steady vapor-liquid interface shapes are found for different wedge angles and material properties of the liquid. In the limit of weak evaporation (e.g., in the adiabatic region of a heat pipe) and negligible Marangoni number, the flow rate is the same in all cross sections and can be controlled by changing the wedge angle. We find the wedge angle that results in the maximum value of the flow rate for a given contact angle. For finite evaporation rates, both the flow rate and the amount of liquid in each cross section along the wedge decrease until the point of dry-out is reached. The location of the dry-out point is studied as a function of evaporation conditions. Somewhat counterintuitively, we find that the dry-out point shifts toward the region of higher temperature as evaporation intensity is increased. The effect of thermocapillary stresses on the vapor-liquid interface shape is also investigated in the limit of negligible evaporation. Since thermocapillarity generally opposes the capillary flow, it leads to shorter wetted lengths. The implications of the results for design and optimization of micro heat pipes are discussed.

Non-passive transport of volatile organic compounds in the unsaturated zone

A detailed model was formulated to describe the non-passive transport of water-soluble chemicals in the unsaturated zone and used to illustrate one-dimensional infiltration and redistribution of alcohol–water mixtures. The model includes the dependence of density, viscosity, surface tension, molecular diffusion coefficient in the liquid-phase, and gas–liquid partition coefficient on the aqueous mixture composition. It also takes into account the decrease in the gas–liquid partition coefficient at high capillary pressures, in accordance with Kelvin’s equation for multi-component mixtures. Simulation of butanol–water mixtures infiltration in sand was in agreement with the experimental data and simulations reported in the literature. Simulation of methanol infiltration and redistribution in two different soils showed that methanol concentration significantly affects volumetric liquid content and concentration profiles, as well as the normalized volatilization and evaporation fluxes. Dispersion in the liquid-phase was the predominant mechanism in the transport of methanol when dispersivity at saturation was set to 7.8 cm. Liquid flow was mainly due to capillary pressure gradients induced by changes in volumetric liquid content. However, for dispersivity at saturation set to 0.2 cm, changes in surface tension due to variation in composition induced important liquid flow and convection in the liquid-phase was the most active transport mechanism. When the Kelvin effect was ignored within the soil, the gas-phase diffusion was significantly lower, leading to lower evaporation flux of water and higher volumetric liquid contents near the soil surface.

Flow‐through drying of porous media

AbstractThe flow of a gas (saturated or dry) through a porous medium, which is partially occupied by a liquid phase, causes evaporation. The latter occurs, even if the inlet gas is fully saturated, as a result of volume expansion. This process, referred to as flow‐through drying, is important in a variety of natural and industrial applications, such as convective drying, fuel cells, and natural gas production, which is the context of this work. In this article, a mathematical model is developed to understand the process and to predict drying rates and the evolution of liquid saturation profiles. The model includes the effects of gas compressibility and capillarity. Compressibility effects account for the evaporation into the saturated gas phase, whereas the capillary pressure gradients cause the liquid flow that leads to spreading of the saturation profile. Two important parameters, a normalized viscous pressure drop across the medium and capillary “wicking” number, control the two respective regimes. Capillary‐driven flow from regions of high saturation to regions of low saturation leads to more uniform saturation profiles or spreading drying fronts. The results are compared against experimental data obtained by X‐ray imaging. © 2006 American Institute of Chemical Engineers AIChE J, 2006