Capillary Boundary Research Articles

Rigidity theorems for minimal Lagrangian surfaces with Legendrian capillary boundary

In this note, we study minimal Lagrangian surfaces in B4 with Legendrian capillary boundary on S3. On the one hand, we prove that any minimal Lagrangian surface in B4 with Legendrian free boundary on S3 must be an equatorial plane disk. On the other hand, we show that any annulus type minimal Lagrangian surface in B4 with Legendrian capillary boundary on S3 must be congruent to one of the Lagrangian catenoids. These results confirm the conjecture proposed by Li, Wang and Weng [12].

Heat Driven Flows in Microsized Nematic Volumes: Computational Studies and Analysis

The nematic fluid pumping mechanism responsible for the heat driven flow in microfluidic nematic channels and capillaries is described in a number of applications. This heat driven flow can be generated either by a laser beam focused inside the nematic microvolume and at the nematic channel boundary, or by inhomogeneous heating of the nematic channel or capillary boundaries. As an example, the scenario of the vortex flow excitation in microsized nematic volume, under the influence of a temperature gradient caused by the heat flux through the bounding surface of the channel, is described. In order to clarify the role of heat flux in the formation of the vortex flow in microsized nematic volume, a number of hydrodynamic regimes based on a nonlinear extension of the Ericksen–Leslie theory, supplemented by thermomechanical correction of the shear stress and Rayleigh dissipation function, as well as taking into account the entropy balance equation, are analyzed. It is shown that the features of the vortex flow are affected not only by the power of the laser radiation, but also by the duration of the energy injection into the microsized nematic channel.

Dynamic Pore-Scale Network Modeling of Spontaneous Water Imbibition in Shale and Tight Reservoirs

Spontaneous water imbibition plays an imperative role in the development of shale or tight oil reservoirs. Spontaneous water imbibition is helpful in the extraction of crude oil from the matrix, although it decreases the relative permeability of the hydrocarbon phase dramatically. The dynamic pore-scale network modeling of water imbibition in shale and tight reservoirs is presented in this work; pore network generation, local capillary pressure function, conductance calculation and boundary conditions for imbibition are all presented in detail in this paper. The pore network is generated based on the characteristics of Barnett shale formations, and the corresponding laboratory imbibition experiments are matched using this established dynamic pore network model. The effects of the wettability, throat aspect ratio, viscosity, shape factor, micro-fractures, etc. are all investigated in this work. Attempts are made to investigate the water imbibition mechanisms from a micro-scale perspective. According to the simulated results, wettability dominates the imbibition characteristics. Besides this, the viscous effects including viscosity, initial capillary pressure and micro-fractures increase the imbibition rate, while the final recovery factor is more controlled by the capillarity effect including the cross-area shape factor, contact angle and the average pore-throat aspect ratio.

A mean curvature type flow with capillary boundary in a unit ball

In this paper, we study a mean curvature type flow with capillary boundary in the unit ball. Our flow preserves the volume of the bounded domain enclosed by the hypersurface, and monotonically decreases an energy functional E. We show that it has the longtime existence and subconverges to spherical caps. As an application, we solve an isoperimetric problem for hypersurfaces with capillary boundary.

Gradient estimates for capillary-type problems via the maximum principle, a second look

We prove gradient bounds for solutions of a class of boundary value problems related to the capillary problem, using the maximum principle. Our results extend those of the author and those of Ma and Xu. In addition to the capillary boundary condition, we can prove results for the general boundary condition for any choice of the parameter (The range is not handled by any previous results.)

Method for Calculating Non-Darcy Flow Permeability in Tight Oil Reservoir

Capillary force and boundary layer effect are the main causes of non-Darcy flow in tight oil reservoir. This paper proposes a non-Darcy flow dynamics characterization method for low-speed water flooding in tight oil reservoirs. It applies constant-speed mercury injection and casting thin section experiments to quantitatively characterize the micro-pore throat structure parameters, and uses the visual experimental device to measure the boundary layer thickness and fit the expression of the relationship between boundary layer thickness and displacement pressure gradient and fluid viscosity. The results show that the ratio of boundary layer thickness to microtubule radius changes exponentially with the pressure gradient and fluid viscosity and that the boundary layer thickness decreases gradually with the increase of pressure gradient. Given the capillary force and boundary layer thickness, the flow rate of single capillary is calculated. On this basis, the equation of nonlinear seepage dynamic characteristics per unit area of core is derived by taking into account the throat distribution frequency and throat size characteristics. The new seepage flow model can reflect the nonlinear seepage flow law of tight oil reservoir and provide reference for parameter formulation during water flooding development of tight oil reservoir.

Pore Network Model Predictions of Darcy‐Scale Multiphase Flow Heterogeneity Validated by Experiments

AbstractSmall‐scale heterogeneities in multiphase flow properties fundamentally control the flow of fluids from very small to very large scales in geologic systems. Inability to characterize these heterogeneities often limits numerical model descriptions and predictions of multiphase flow across scales. In this study, we evaluate the ability of pore network models (PNMs) to characterize multiphase flow heterogeneity at the millimeter scale using X‐ray micro‐computed tomography images of centimeter‐scale rock cores. Specifically, PNM capillary pressure and relative permeability output are used to populate a Darcy‐scale numerical model of the rock cores. These pore‐network‐derived Darcy‐scale simulations lead to accurate predictions of core‐average relative permeability, and water saturation, as validated by independent experimental data sets from the same cores and robust uncertainty analysis. Results highlight that heterogeneity in capillary pressure characteristics is more important for predicting local and upscaled flow behavior than heterogeneity in permeability or relative permeability. The leading uncertainty in core‐average relative permeability is driven not by the image processing or PNM extraction but rather by ambiguity in capillary pressure boundary condition definition in the Darcy‐scale simulator. This workflow enables characterization of local capillary heterogeneity and core‐averaged multiphase flow properties while circumventing the need for the most complex experimental observations conventionally required to obtain these properties.

Optimal placement of droplets for UV nanoimprint lithography

Optimizing the locations and sizes of droplets are key to reduce defects and increase throughput of ultraviolet nanoimprint lithography (UVNIL). Previously, simulation models describing the flow and coalescence of multiple fluid drops were developed and used to predict the fluid flow during spreading and feature filling. However, the effect of small channels on the resulting capillary pressure is neglected even though the flow along small channels or grooves is encountered in UVNIL. In this study, an accurate method to estimate capillary pressure boundary conditions at the fluid-air interface is developed along with fluid simulation. A method to estimate and compute the anisotropic capillary pressure for templates with line and space patterns is presented. It is found that the droplets flow faster in the direction of the pattern not only because of anisotropic permeability but also the nanostructure of the template, which further propels anisotropic spreading of the droplets by exerting larger capillary pressure. Using the new capillary pressure boundary condition, the simulation of multidrop spreading in UVNIL is performed to study the effects of anisotropic capillary pressures caused by the template structure. A simulation approach to determine optimal droplet placement was developed. From the simulation, a general rule of thumb is developed: delaying droplet merging as much as possible and reducing the number of merging events.

Geophysical response to simulated methane migration in groundwater based on a controlled injection experiment in a sandy unconfined aquifer

Geophysical methods have the capacity to detect and characterize gas-phase dynamics in groundwater. Suitable methods can be deployed at surface or within boreholes depending on the required depth of investigation, spatial/temporal resolution, and geologic conditions. While the application of geophysical methods to monitor immiscible phase contaminants in the subsurface has been extensively documented, the effects of hydraulic properties and flow system conditions on the nature of the geophysical responses used to elucidate multi-phase fluid flow remains underdeveloped. A series of numerical 2-dimensional multi-phase flow and geophysical model simulations based on a controlled methane release experiment in the Borden unconfined sand aquifer was carried out to assess the influence of porous media hydraulic properties and flow system conditions on geophysical signatures associated with transient gas-phase saturation and gas migration behaviour. Specifically, the utility of electrical resistivity tomography (ERT) and ground-penetrating radar (GPR) to monitor gas-phase plume dynamics in shallow groundwater flow systems is examined. ERT and GPR responses to gas-phase distribution and migration during a 72-day methane gas injection and subsequent recovery period was calculated using a numerical multi-phase flow model (CFbio) simulating four distinct parameterizations of the sandy aquifer system. Geophysical models showed that ERT was effective at imaging the central position of the plume but was less effective at detecting thinner lateral migration pathways extending beyond the primary high gas saturation bulb. Conversely, GPR was able to detect thin gas pools emanating from the primary gas bulb and small-scale vertical preferential pathways arising from capillary boundaries with contrasting saturations; however, gradational boundaries proved to be more difficult to resolve using GPR. This study demonstrates that ERT and GPR can be very useful tools in combination for longer-term monitoring of stray gas leakage from decommissioned hydrocarbon wells in shallow granular media freshwater aquifers, especially given the likelihood of strong lateral migration.

Estimating local capillary trap volume capacities using a geologic criterion

Capillary pressure heterogeneity causes local capillary trapping of CO2 in saline aquifers. However, quantifying local capillary trapping using conventional reservoir simulation is computationally intensive. This work employs a geologic criterion (GC) to rapidly estimate the volume capacity of local capillary traps in static geologic models. The criterion refers to the ‘critical capillary entry pressure’ that is used to indicate flow barriers and flow paths during buoyant flow. A previous study (Saadatpoor, 2012) found that issues exist in the criterion method: unknown physical critical capillary entry pressures and boundary barriers. This work addresses the two issues. It is shown that the criterion method gives a close upper bound estimation of local capillary trap volume capacities. Several fine-scale geostatistical realizations of capillary entry pressure fields are considered, and the effects of reservoir heterogeneity, system sizes, aspect ratios, and boundary types are examined. The results from the GC are also strictly interpreted through invoking a simple counting argument. The overall work enhances our mechanistic understanding of the geological controls of local capillary traps.

On numerical modeling of capillary flow dynamics in a microchannel model by using the finite element method

A simple microchannel model with submillimeter-scale geometries is proposed for studying capillary flows and investigating the dynamics in the channel. The finite element method incorporating surface tension and two-phase flow characteristic is applied. Velocity and pressure fields in the microchannel are presented. It is shown that the capillary-phase front in the microchannel is stirred, suffering small oscillations and retreating from the previous position before traveling again. Such a phenomenon is caused by nonlinear interaction of the capillary flow, surface tension, and boundary conditions.

Electro-hydrodynamic concentration of genomic length DNA.

We report a method of concentrating genomic length DNA within a microfluidic device, using a novel mechanism that combines polyelectrolyte migration with electrophoretic recirculation. Suitable combinations of geometry, pressure and voltage will trap long DNA molecules (>10 kbp) within a small volume (approximately 1 nL), amplifying the local concentration at rates in excess of 1000 fold per minute. The rate at which DNA accumulates is length dependent, while charged particles of similar size pass freely through the device. Experimental observations confirm that the rapid accumulation of DNA at the inlet is caused by an outward migration of the polyelectrolyte towards the capillary boundaries, followed by electrophoresis of DNA within the stagnant fluid layer next to the wall.

Global Hydrocarbon Energy Potential of Euro-Asia or Solution of Navier-Stokes Equation for Deformed Micro-Structure of the Earth’s Porous Space

The authors present the hydro-geological basin-type model of global energetics with hydro-dynamic potential showing the interaction of inland platforms of the Earth. The authors propose the new cluster-type approach towards the asymmetric multi-scaled modeling at the basis of integral solution within the quadrature of Navier-Stokes equation for deformed micro-structure of Earth’s porous space. We have studied the effect of poor local tectonic faults upon the arrangement of hydrocarbon traps in lithosphere, shale tight fields, that is based upon the interconnected methods in geophysics, hydro-geology and geo-mechanics, tectono-physics and structural geology. The authors also present the scientific concept of new principles to increase the level of geo-informatics while searching exploring and developing the hydro-carbon reserves, geo-physical studies of seismic emissions, micro-seismic and seismology of mega-scales in geological ages of stresses with transition to predictable man-induced time for geological/technological events. Basing upon the conjugation of Navier-Stokes equation and due consideration of deforming relaxation we have built the energy self-arranged model of Earth’s lithosphere de-fluidization, have found inherent energy delayed spectra for the dynamic contacts of stratified structure. We have obtained the energy conjugated solution of micro-structure porous media interaction for hydro-geological decompression of subduction channel in seabed and saturation of generalized Middle Oceanic Ridge with self-organization of classic sedimentological hydro-carbon traps and complexly organized shale reservoirs with compacted depositions of Allochthon structures in Domanik and Bazhenov formations. The authors present the energy stable mean filtration profile as per Darcy, conjugated with stress-deformed status of porous geo-media micro-structure at various boundary conditions: closed-type or capillary jammed boundaries of filtration blocks and free-type – with phase filtration front and diffusive displacement of fluids by saturated porous media and smart technologies of multi-stage hydro-fracture in dense shale reservoirs. Analytically, in quadrature, there is the dissipation velocity, potential and kinetic energy potentials of mean outflow and shear layer of filtration dissipative structure, like a generalized model of viscous elasticity that depends upon the wave number, phase velocity, thickness of the layer and geo-mechanical parameters that reflect the geo-media heterogeneity.

Characterization of Liquid Water Invasion in Gdls Using X-Ray Tomographic Microscopy

The accumulation of liquid water in the gas diffusion layer (GDL) of low temperature polymer electrolyte fuel cells (PEFC) results in increased mass transport limitations [1] and eventually in a significant potential and efficiency penalty. To achieve efficient water removal and maintain high performance, it is necessary to understand the morphological (porosity, pore and throat sizes) and chemical (surface tension) properties of the GDL, which control the water transport [2]. An ex-situ capillary pressure (pc) – saturation setup was developed in the framework of the IMPALA project [3] for imaging experiments using X-ray tomographic microscopy (XTM) at the Swiss Light Source synchrotron facility as it offers the advantage of well defined capillary pressure boundary conditions. This approach allows a quantitative analysis of the water transport through the GDL by linking the local saturation at the achieved pc levels with the microstructure of the invaded pores and throats.Within the setup, a hydrophilic membrane implements a homogeneous boundary condition at the bottom of the GDL. At the top of the GDL either a hydrophobic membrane or a flow field was placed. While the hydrophobic membrane setup allows to study complete liquid wetting of the pore space, the flow field structure allows to implement an anisotropic compression simulating PEFC conditions and to study its consequences on water transport. GDL samples of different suppliers have been tested. The breakthrough pressure, which corresponds to the capillary pressure when water reaches the opposite side of the injection surface, is a function of the materials. Correlation with the dry GDL microstructure shows that pore (and throat) size is the major controlling parameter. SGL 24BA shows a lower breakthrough pressure than Toray TGP-H060 due to larger throats and exhibits a stronger channel rib deviation of pore and throat sizes as well as of saturation.

Axisymmetric Boundary Element Method for vesicles in a capillary

The problem of a vesicle transported by a fluid flow can present a large range of length scales. One example is the case of a vesicle producing a tether, and eventually pearls, in an elongational flow. Another case occurs when a lubrication film is formed, such as during the short range interaction between two vesicles. Such problems are still challenging for 3D simulations. On the other hand, a good understanding could be obtained by first considering the axisymmetric regime when such a regime exists. An axisymmetric model could then be used, without the criticisms that can be made of a 2D approach. We propose such a model, primarily interested in flows through narrow cylindrical capillaries. Two options are compared, with and without explicit representation of the capillary boundaries by a mesh. The numerical effort is characterized as a function of the vesicle's initial shape, the flow magnitude and the confinement. The model is able to treat typical configurations of red blood cells flowing through very narrow pores with extremely thin lubrication films.

J0560102 OpenFOAMによる燃料電池内の水輸送現象の解析

Capillary pressure boundary condition model was introduced into the numerical solver for polymer electrolyte fuel cell based on the OpenFOAM. The boundary condition module can predict water saturation jump so that the thermodynamic equation of state is satisfied on the interface between the catalyst layer and gas diffusion layer. In this paper, liquid water transport in the cathode electrode of PEM fuel cell was calculated by using the OpenFOAM solver. The result shows that the numerical model can describe typical behavior of water removal through porous materials.

Confined Active Nematic Flow in Cylindrical Capillaries

We use numerical modeling to study the flow patterns of an active nematic confined in a cylindrical capillary, considering both planar and homeotropic boundary conditions. We find that active flow emerges not only along the capillary axis but also within the plane of the capillary, where radial vortices are formed. If topological defects are imposed by the boundary conditions, they act as local pumps driving the flow. At higher activity, we demonstrate escape of the active defects and flow into the third dimension, indicating the importance of dimensionality in active materials. We argue that measuring the magnitude of the active flow as a function of the capillary radius allows determination of a value for the activity coefficient.

Compound capillary rise

AbstractIrregular conduits, complex surfaces, and porous media often manifest more than one geometric wetting condition for spontaneous capillary flows. As a result, different regions of the flow exhibit different rates of flow, all the while sharing common dynamical capillary pressure boundary conditions. The classic problem of sudden capillary rise in tubes with interior corners is revisited from this perspective and solved numerically in the self-similar ${\ensuremath{\sim} }{t}^{1/ 2} $ visco-capillary limit à la Lucas–Washburn. Useful closed-form analytical solutions are obtained in asymptotic limits appropriate for many practical flows in conduits containing one or more interior corner. The critically wetted corners imbibe fluid away from the bulk capillary rise, shortening the viscous column length and slightly increasing the overall flow rate. The extent of the corner flow is small for many closed conduits, but becomes significant for flows along open channels and the method is extended to approximate hemiwicking flows across triangular grooved surfaces. It is shown that an accurate application of the method depends on an accurate a priori assessment of the competing viscous cross-section length scales, and the expedient Laplacian scaling method is applied herein toward this effect.

An ALE finite element method for a coupled Stefan problem and Navier–Stokes equations with free capillary surface

SUMMARYIn this article, an ALE finite element method to simulate the partial melting of a workpiece of metal is presented. The model includes the heat transport in both the solid and liquid part, fluid flow in the liquid phase by the Navier–Stokes equations, tracking of the melt interface solid/liquid by the Stefan condition, treatment of the capillary boundary accounting for surface tension effects and a radiative boundary condition.We show that an accurate treatment of the moving boundaries is crucial to resolve their respective influences on the flow field and thus on the overall energy transport correctly. This is achieved by a mesh‐moving method, which explicitly tracks the phase boundary and makes it possible to use a sharp interface model without singularities in the boundary conditions at the triple junction.A numerical example describing the welding of a thin‐steel wire end by a laser, where all aforementioned effects have to be taken into account, proves the effectiveness of the approach.Copyright © 2012 John Wiley & Sons, Ltd.

Bifurcation of Cylinders for Wetting and Dewetting Models with Striped Geometry

We show that some pieces of cylinders bounded by two parallel straight lines bifurcate in a family of periodic nonrotational surfaces with constant mean curvature and with the same boundary conditions. These cylinders are initial interfaces in a problem of microscale range modeling the morphologies that adopt a liquid deposited in a chemically structured substrate with striped geometry or a liquid contained in a right wedge with Dirichlet and capillary boundary condition on the edges of the wedge. Experiments show that starting from these cylinders and once a certain stage is reached, the shape of the liquid changes drastically in an abrupt manner. Studying the stability of such cylinders, the paper provides a mathematical proof of the existence of these new interfaces obtained in experiments. The analysis is based on the theory of bifurcation by simple eigenvalues of Crandall and Rabinowitz.