Vertical Capillary Research Articles

Dynamics of capillary rise in yarns: Influence of fiber and liquid characteristics

AbstractLiquid transport and movement in yarns were studied using an experimental system based on the analysis of charge couple device images taken during the capillary rise of a colored liquid in the yarn. The generalized dynamic model of the liquid penetration into vertical cylindrical capillary used was based on the Lucas–Washburn equation. It had the advantage of independently characterizing the equivalent pore radius and the contact angle by determining the coefficient of diffusion of the liquid noted D and the height attained at equilibrium noted he. We studied cotton and viscose yarns and found that the diffusion of liquid and the height attained at equilibrium depending on the fiber type. These results were discussed on the basis of the wettability of the fibers. We used water and a chemical agent added to water to investigate the effect of the characteristics of liquid on the capillary rise in yarns. The capillary parameters values (D and he) depended on the concentration of the chemistry agent added to water. These results were discussed by studying the evolution of the characteristic of the porous media and the liquid properties by calculating the equivalent pore radius and the contact angle andmeasuring the surface tension and the viscosity of the fluid. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007

Using Solid Mechanics to Evaluate the Capillary and Viscous Behavior of Noncircular Tube Shapes

The similarity between torsion-solid mechanics and incompressible-viscous tube flow is investigated by finite element solutions of the governing partial differential equations. After the numerical solutions are validated against several well-known analytical functions for noncircular shapes, a method is presented to illustrate how hydraulic resistance factors may be computed from the polar moment of inertia. Since the results are scaleable, the macroscopic solid mechanics information can be used to predict the viscous pressure loss term for micro-machined flow features. The numerical technique is then further developed to estimate the Laplace pressure jump across the main terminal meniscus in noncircular capillaries. The solid mechanics based numerical technique is demonstrated on several special cases involving horizontal and vertical capillary flow in noncircular regimes. The numerical technique compares well to published experimental results. Then a nozzle shape figure of merit is derived, and applied to a variety of noncircular shapes. Finally, the numerical methods are merged into the LXK droplet simulation model where their effectiveness is demonstrated against lab data from a wide experimental space for thermal inkjet.

On the Capillary Problem for Compressible Fluids

Classical capillarity theory is based on a hypothesis that virtual motions of fluid particles distinct from those on a surface interface have no effect on the form of the interface. That hypothesis cannot be supported for a compressible fluid. A heuristic reasoning suggests that even small amounts of compressibility could have significant effect on surface behavior. In an earlier work, Finn took a partial account of compressibility, and formulated a variant of the classical capillarity equation for fluid surface height in a vertical capillary tube; he was led to a necessary condition for existence of a solution with prescribed mass in a tube closed at the bottom. For a circular tube, he proved that the condition also suffices, and that solutions are uniquely determined for any contact angle γ.

Density-driven instabilities in capillary tubes: Influence of a variable diffusion coefficient

The influence of a variable diffusion coefficient on the gravitational instability at the interface between two variable viscosity fluids in a vertical capillary tube is investigated, based on the three-dimensional Stokes equations. As the viscosity contrast between the fluids grows, the maximum density gradient of the self-similar base concentration profile increases while its location is shifted into the more viscous fluid. Thus the perturbations are forced to grow in a more viscous environment, which can reduce their growth rate by up to 30%. For large viscosity contrasts, intermediate interface thicknesses are seen to give rise to the highest growth rates. For most parameter combinations, the first azimuthal mode is found to be most unstable. However, for large viscosity ratios and small interface thicknesses the axisymmetric mode dominates.

Preparation of carbon materials by modeling of impregnating coal-tar pitch into carbon preform

Using coal-tar pitch as a matrix precursor to prepare carbon materials is widely used by impregnation/carbonization processing technology. The primary QI, hard particles in liquid pitch at impregnation temperature, generally can deposit on the surface of the carbon preform and partly form a filter cake. The process can cause complex flow behaviors for liquid coal-tar pitch leading to impregnation models of metal or resin unsuitable to it. The flow of liquid coal-tar pitch in the carbon preform remains laminar as estimated by the Reynolds number. The open and closed pores in preform are regarded as vertical and transverse capillaries. Considering the size distributions of QI particles and open pores, two different kinetics models based on Darcy's law are proposed to describe impregnation mechanism of liquid coal-tar pitch into open pores. The kinetics formula for pitch infiltrating in closed pore is obtained also. The total impregnation efficiency model is obtained. The predicted results are in reasonable agreement with experiment data. Several effects of impregnation efficiency, including effective pressure, impregnation temperature, porosity of preform, dimension of pore and QI particles, are analyzed by the model to increase the technical understanding of such process. It is expected to optimize the operation parameters of impregnation.

D232 毛細管内の粘性の異なる二液体の混和性置換に関する反応性流れ(反応性流れの基礎と応用3)

It is known that the spike is formed in the miscible displacement in capillary tubes under a certain condition. In the present study, miscible displacement with chemical reaction in vertical capillary tubes is investigated experimentally in the condition where the spike is formed. The effect of reactant concentration on the reaction characteristics is focused on. We have found that the initial reactant concentration ratio included in the more-and less-viscous liquids normalized by the stoichiometric ratio of the chemical reaction, ψv, significantly influences the distribution of the products. We propose that the difference in the product distribution is caused by both two factors ; the idiosyncratic shape (spike) of boundary region and the difference between the diffusion coefficient of interdiffusion of miscible two liquids and that of reactants in less viscous liquid.

Estudio de un oscilador de densidad mediante medidas de potencial eléctrico

Un oscilador de densidad u oscilador salino, es un sistema no lineal que presenta cambios alternantes del sentido de flujo en el tiempo, como efecto de las restricciones espaciales entre dos fluidos de diferente densidad. Los fluidos están en recipientes separados, los cuales están interconectados por medio de un tubo capilar vertical. En este trabajo se construye un oscilador de densidad para estudiar la influencia de la variación de algunos de sus parámetros sobre las oscilaciones en el sentido de flujo. Sean dichos parámetros, la concentración de la sal (NaCl) del electrólito y la longitud del capilar. Para medir el efecto de la variación de los parámetros, se coloca un electrodo de aluminio en cada una de las soluciones y la señal de potencial eléctrico es registrada mediante un multímetro digital, lo que permite observar como evoluciona temporalmente la inversión en el sentido de flujo del oscilador de densidad. El análisis se efectuó mediante la interpretación gráfica de las series de potencial eléctrico en función del tiempo, encontrando relaciones fenomenológicas entre el período de oscilación y la diferencia de potencial pico a pico respecto a los parámetros experimentales: concentración de la sal y longitud del capilar.

Weight-controlled capillary viscometer

The draining of a water column through a vertical discharge capillary tube is examined with the aid of a force sensor. The change of the mass of the liquid in the column with time is found to be not purely exponential as implied by Poiseuille’s law. Using observed residuals associated with a kinetic energy correction, an approximate formula for the mass as a function of time is derived and excellent agreement with experimental data is attained. These results are verified by a viscosity test of distilled water at room temperature. A simple and inexpensive weight-controlled capillary viscometer is proposed that is especially suitable for undergraduate physics and chemistry laboratories.

Hydrodynamics of Taylor Flow in Vertical Capillaries: Flow Regimes, Bubble Rise Velocity, Liquid Slug Length, and Pressure Drop

Two-phase flow hydrodynamics in vertical capillaries of circular and square cross sections were experimentally studied, using air as the gas phase and water, ethanol, or an oil mixture as the liquid phase. The capillary hydraulic diameters ranged from 0.9 mm to 3 mm, with the superficial gas and liquid velocities covering a span of 0.008−1 m/s, which is typical of that obtained in monolith reactors. Using a high-speed video camera, four distinct flow regimes were observed within the range at which experiments were conducted: bubbly, slug-bubbly, Taylor, and churn flows. Annular flow was observed at excessively high gas and low liquid flow rates, well beyond those of interest to this study. Based on the definition of a two-class flow regime, the combination of two parametersthe slip ratio (S) and the ratio of the superficial gas velocity to two-phase superficial velocity (UG/UTP)was observed to be suitable for determining the transition from homogeneous flow to nonhomogeneous flow. The influence of capillary geometry, capillary hydraulic diameter, and fluid properties on bubble rise velocity (Vb) were investigated and determined to be of little significance. Furthermore, a new and simplified correlation for predicting Vb and, by implication, the gas holdup (εG) was proposed. Liquid slug lengths were also experimentally studied, using a correlation that was developed to estimate them. Pressure drop experiments were also performed, and the peculiar phenomenon of negative frictional pressure drops was observed at very low liquid velocities. By defining a new dimensionless quantitythe pressure factor, FEa flow-regime-dependent method for estimating the total pressure drop in two-phase vertical capillary flows was developed.

Magnetic field effect on capillary rise of magnetic fluids

The objective of this work is to study the effect of the external uniform magnetic field on the height and dynamics of magnetic fluid ascension into a vertical cylindrical capillary. Due to demagnetization effects in the magnetic fluid, the height of ascension increases in the magnetic field longitudinal to the capillary and decreases in the transverse field, proportionally to the square of the magnetic fluid magnetization. Magnetic fluid ascension decelerates strongly in the transverse field.

Acoustic initiation of powder flow in capillaries

Second generation solid freeforming devices will have the capability to render both shape and the spatial arrangement of composition directly from a computer file. In order to build three-dimensional functional gradients in selective laser sintering it is necessary to have a computer-controlled mixing and dispensing system. We report such a system based on the horizontal acoustic vibration of vertical capillary tubes that provides both switching and flow rate control. An orchestra of such tubes can be constructed to deposit a multi-component system onto a building platform. Our concern is the initiation of flow. It requires an “attack” waveform to break the domes that provide flow arrest and release the potential energy of powder above the dome. The intensity of attack also influences the mass that flows out before a new dome forms, i.e., the response time of the valve. Neither the extension to vibration caused by ringing nor the wave amplitude account for the over-run of the valve. Much better correlation is obtained with acceleration and with calculated kinetic energy of horizontally vibrating particles.

Spontaneous rise of surfactant solutions into vertical hydrophobic capillaries

It has been found earlier (N.V. Churaev, G.A. Martynov, V.M. Starov, Z.M. Zorin, Colloid Polym. Sci. 259 (1981) 747) that aqueous surfactant solutions spontaneously rise in vertical hydrophobized quartz capillaries. A theory of this phenomenon is presented, which connects the experimental observations with the adsorption of surfactant molecules in front of the moving meniscus on the bare hydrophobic interface.

Binary Fluid Mixture and Thermocapillary Effects on the Wetting Characteristics of a Heated Curved Meniscus

An investigation has been conducted into the interactions of binary fluid mixtures (pentane [C5H12] coolant and decane [C10H22] additive) and thermocapillary effects on a heated, evaporating meniscus formed in a vertical capillary pore system. The experimental results show that adding decane, the secondary fluid that creates the concentration gradient, actually decreases the meniscus height to a certain level, but did increase the sustainable temperature gradient for the liquid-vapor interface, so did the heat transfer rate, delaying the onset of meniscus instability. The results have demonstrated that interfacial thermocapillary stresses arising from liquid-vapor interfacial temperature gradients, which is known to degrade the ability of the liquid to wet the pore, can be counteracted by introducing naturally occurring concentration gradients associated with distillation in binary fluid mixtures. Also theoretical predictions are presented to determine the magnitudes of both the thermocapillary stresses and the distillation-driven capillary stresses, and to estimate the concentration gradients established as a result of the distillation in the heated pore.

Periodicity and bifurcations in capillary tube boiling with a concentric heating wire

Nucleate boiling from a vertical glass capillary in a pool of water is investigated here. Electrical heating is provided with a wire passing concentrically through the center of the capillary, and a fast-response thermocouple at the lip of the capillary records the instants of bubble departure. Different lengths and diameters of capillaries are used in the experiments. The average frequency of bubbling is seen to increase with applied heat flux, the relation being linear in the initial stages. With the heat flux used as a bifurcation parameter, one-dimensional return maps of the time interval between successive bubble emission events are used to study the transitions from the periodic state. The first bifurcation from the periodic to a two-period state is observed to be due to lateral instability of the liquid film adhering to the capillary wall. Further bifurcations to period two and then to period three bubbling are also observed. Simplified analysis of the different phases of the boiling process yields solutions which show close agreement with the experimental data.

Self‐sealing in sedimentary basins

Over the last decade, the picture that has emerged from several geologic disciplines is that the Earth's crust is permeable to great depths and that fluids are more or less constantly moving, transporting both heat and mass and affecting virtually every geologic process. In contrast, workers in the petroleum industry have maintained that sections of the crust contain impermeable pressure seals and hydraulically sealed compartments. We show that these starkly different conceptions can be reconciled by a theory of self‐sealing through gas generation in sedimentary basins. The model especially applies to older sedimentary basins where overpressuring cannot be readily explained as the result of ongoing sedimentation and compaction disequilibrium. In our conceptual model, overpressuring is created by catagenic gas generation and maintained by a combination of vertical and horizontal gas capillary seals. Data from the Anadarko Basin in Oklahoma provide support for the self‐sealing hypothesis. Well logs reveal the presence of 9 or 10 gas‐water interfaces over a 30‐m overpressured interval. Capillary pressure measurements show that the force necessary for gas to displace water from a shale is ∼3 × 106 Pa, a pressure equivalent to that exerted by a column of water 300 m high. A theory of self‐sealing explains the anomalous overpressuring observed in some older sedimentary basins by invoking known mechanisms and forces; it is both parsimonious and falsifiable.

Mechanism for Helical Gel Formation from Evaporation of Colloidal Solutions

We use MRI imaging to decipher the physical mechanism behind helical gel formation when a colloidal solution is evaporated from a small vertical or inclined capillary. A gel column, surrounded by the solvent, is observed to appear in the middle of a capillary. For nearly vertical capillaries, the denser gel column buckles under gravity to form a loose spiral. Further heating leads to the formation of a helical vapor pocket, surrounded by asymmetric liquid menisci. As the heating continues, this vapor pocket propagates downward and traces the buckled column. If gravity buckling occurs and if the maximum thickness of the annular solvent film is less than the solvent capillary length, significant nonuniform vapor pressure builds up within the vapor bubble because the vapor's escape is obstructed and because the evaporation is nonuniform. This upward air pressure spiral is amplified by asymmetric menisci of the vapor pocket to produce a high liquid pressure gradient along the liquid spiral next to the helical vapor pocket. Both pressures are inversely proportional to the internal capillary diameter d, and together, they twist the buckled column to a much higher pitch. The balance of this force to the elastic force of the buckled column, which opposes coiling, leads to a minimum distance between pitches L that scales as d. When all the fluid outside the column has evaporated, the slow vapor release by the drying gel cannot provide sufficient pressure for coiling. Hence, the “compressed spring” starts to rewind and lengthen. The dominant force balance with the opposing dry friction force leads to a lower final pitch with an L ∼ d2 scaling. Both these scalings are consistent with our experimental data.

Use of the geotechnical centrifuge as a tool to model dense nonaqueous phase liquid migration in fractures

We describe a study undertaken to investigate the potential of the geotechnical centrifuge as an experimental tool to study dense nonaqueous phase liquid (DNAPL) behavior in fracture systems. Scaling laws are developed that link observations made in a centrifuge model of a fracture system to the full‐scale problem (prototype). Centrifuge experiments carried out in synthetic fractures, described by smooth‐walled vertical capillary tubes, demonstrate for the first time that the geotechnical centrifuge can be used to model DNAPL transport in a simplified system provided that inertial forces are negligible in both the model and the prototype. Experiments also confirm, as predicted by Kueper and McWhorter [1991], that DNAPL invades a smooth‐walled, vertical fracture when the DNAPL pool height at its entrance reaches its entry pressure. A simple mathematical model describing the displacement of the DNAPL‐water interface is also presented. The predictions of this model and the experimental data are in good agreement with each other in the lower half of an invaded fracture. However, at the early stages of DNAPL invasion into the fracture, our observed DNAPL‐water interface velocities are slower than predicted by the model. We attribute this to an apparent dependence of the local capillary pressure on the interface displacement velocity.

An innovative extensional viscometer for low-viscosity and low-elasticity liquids

A spinline-type extensional viscometer is described in which an innovative method of tensile stress measurement is employed. A limited amount of liquid flows through a vertical capillary at a constant flow rate under the influence of a constant pressure head. The drainage time decreases when the liquid stream leaving the capillary is stretched by the application of vacuum. These drainage times are measured in a manner similar to that used for intrinsic viscosity measurements. The measured difference in drainage times, with and without stretching, is trivially related to the extensional stress at the capillary exit, and this provides a very simple method of accurately determining fluid stretching forces having a magnitude as low as 10–4 N; stresses at other axial locations in the stretched liquid jet are obtained by means of a force balance in the usual manner. The validity of the proposed technique is demonstrated by obtaining the expected results for a Newtonian oil having a shear viscosity of 56.2 mPa-s. Also presented are preliminary data on polyethylene oxide-in-water solutions having an even lower shear viscosity.

Drop formation from a capillary tube: Comparison of one-dimensional and two-dimensional analyses and occurrence of satellite drops

The axisymmetric formation of drops of Newtonian liquids from a vertical capillary into air is governed by the three-dimensional but axisymmetric Navier–Stokes system and appropriate boundary and initial conditions. Algorithms for obtaining accurate solutions of the resulting two-dimensional (2D) system of equations have recently been developed by Wilkes et al. [Phys. Fluids 11, 3577 (1999)], but are computationally intensive. A one-dimensional (1D) model based on simplification of the governing 2D system through the use of the slender-jet approximation has gained popularity in recent years [Eggers, Rev. Mod. Phys. 69, 865 (1997)]. Such 1D algorithms not only result in great computational savings but appear to capture well the physics of drop formation as has been learned through a somewhat limited number of studies [Eggers and Dupont, J. Fluid Mech. 262, 205 (1994); Brenner et al., Phys. Fluids 9, 1573 (1997)]. Indeed, existing 1D analyses [Eggers and Dupont, J. Fluid Mech. 262, 205 (1994); Brenner et al., Phys. Fluids 9, 1573 (1997)] have considered solely those situations in which the drops are grown quasi-statically prior to the onset of the instability and hence have ignored the effect of a finite flow rate or nonzero Weber number We, which measures the relative importance of inertial to capillary force, on the dynamics. In this paper, the accuracy of 1D algorithms is critically evaluated by comparing predictions made with them to those obtained with a recently developed 2D algorithm [Wilkes et al., Phys. Fluids 11, 3577 (1999)] based on the finite element method (FEM) over large ranges of the governing parameter space spanned by the Weber and Ohnesorge numbers, where the latter group, Oh, measures the relative importance of viscous to capillary force. When capillarity dominates, the predictions of the 1D algorithm are demonstrated to deviate no more than a couple of percent from those of the 2D algorithm. When inertial or viscous force is large compared to surface tension force, the 1D model can be in error by up to 15%. The limitations of and errors incurred by the 1D model due to its inability to predict interface overturning for low Oh fluids are also discussed. Because the 2D algorithm [Wilkes et al., Phys. Fluids 11, 3577 (1999)] may take hours to a day to simulate the dynamics of a single drop up to the instant in time t=td at which the drop first breaks, and the 1D algorithm can perform the same task in a few minutes, the 2D FEM algorithm has not been used to date beyond the instant of first breakup. In this paper, calculations are continued beyond t=td with the 1D algorithm as in some previous works [Brenner et al., Phys. Fluids 9, 1573 (1997)], but with the following distinctions. First, for the first time regions in parameter space are identified over which satellite droplets are formed and ones over which formation of satellites are suppressed. The computed limit delineating the formation of satellites from suppression of satellites is compared when Oh≪1 to that determined by Zhang [J. Coll. Int. Sci. 212, 107 (1999)] for water-like liquids. Second, formation of several drops in a sequence is studied to determine the number of drops required to reach a state of steady dripping.

Analytical Approach for the Lucas–Washburn Equation

Porous media can be characterized by studying the kinetics of liquid rise within the pore spaces. Although porous media generally have a complex structure, they can be modeled as a single, vertical capillary or as an assembly of such capillaries. The main difficulties lie in separately estimating the effective mean radius of the capillaries and the contact angle between the liquid and the pore. In this paper we circumvent these obstacles by exploring another approach and suggest an analytical approach of the classical Lucas–Washburn equation (LWE). Specifically, we consider that the contact angle between the liquid meniscus and the inner surface of the capillary becomes a dynamic contact angle when the liquid front is in movement. It has previously been demonstrated that the resulting time dependence is due to frictional dissipation at the moving wetting front.