Vertical Capillary Research Articles

Measurements and characterization of bubble dynamics in capillary two-phase flows by a micro double-tip conductivity probe

With a particular focus on the characterization of gas–liquid Taylor flow in individual channels of monolithic beds, a micro double-tip conductivity probe was developed for the measurements and characterization of bubble dynamics in capillary two-phase flows. The Taylor flow hydrodynamics in vertical capillaries with a circular cross section of 2.98 mm in hydraulic diameter was investigated including flow regime, bubble rise velocity, and liquid slug length in a wide range of gas and liquid superficial velocities. It is demonstrated that the micro double-tip conductivity probe method is suitable for identifying flow regimes in small-scale capillaries and measuring bubble dynamic parameters of the Taylor flow. Furthermore, variation trends of bubble rise velocity and frequency, and liquid slug length with varying gas and liquid superficial velocities in the Taylor flow regime are demonstrated. Based on the experimental data, correlations for prediction of the above parameters were obtained.

Vertically-Oriented-Capillary Video-Microscopy: Drops Levitated by a (Reacting) Fluid

Microscopy in a vertical capillary provided the ability to continuously observe the dynamic particle phenomena on microscopic objects levitated by an imposed flow. Such a technique was developed and used to monitor flow-levitated droplets, by manually regulating the imposed flow so as to keep the droplets suspended in the area of view. Local sudden increases and decreases in temperature were achieved with an external heating filament, which produced rapid changes in the fluids’ properties (viscosity and density). Even in such cases it was possible to control the levitated drop’s position in the microscope’s field of vision by adjusting the levitating fluid’s vertical flow. The shrinkage and alteration of levitated acid drops that react with the basic nanoparticles of levitating oil, verified that, when compared to static conditions, fluid flow significantly accelerated the neutralization of the acid drop by the oil’s basic nanoparticles. Allowing droplets to levitate and rotate due to the flow of another fluid in high-temperature regions, this technique may be used as an improved way to mix contents in suspended microscopic droplets.

Numerical Simulation of Thermocapillary Flow Induced by Non-Uniform Evaporation on the Meniscus in Capillary Tubes

Three-dimensional numerical simulation was developed to investigate thermocapillary flow induced by non-uniform evaporation on the meniscus in capillary tubes. Capillary tube radiuses ranging from 0.1 to 1 mm were considered and the working liquid was methanol. The effects of tube size, evaporation heat flux and buoyancy on thermocapillary flow were investigated. The results show that the non-uniform evaporation on the meniscus leads to two opposite temperature gradients along the radial direction, which generate two thermocapillary flow vortexes under the meniscus. For horizontal capillary tubes with r0 ≥ 0.32 mm, the path-lines in the vertical center plane are asymmetrical, which is attributed to the combined buoyancy and thermocapillary effects. For the vertical capillary tube, with increasing average evaporation heat flux, the steady axisymmetrical flow will gradually transit to a steady asymmetrical flow and eventually becomes a three-dimensional oscillatory flow.

Superfluid ultra-dense deuterium [formula omitted] at room temperature

Ultra-dense deuterium D(−1) is expected to be both superfluid and superconductive. It is deposited on surfaces below a novel source producing a stream of D(−1) clusters. It is studied by laser probing and Coulomb explosions giving cluster fragments which are observed by time-of-flight measurements. It is observed on surfaces at a few cm height above the container below the source, and on the outside of the container. D(−1) is detected above a 1 cm long vertical capillary in vacuum (fountain effect). This suggests the existence of superfluid D(−1) which is the only material that may be superfluid at room temperature.

Gas−Liquid Mass Transfer in Taylor Flow through Circular Capillaries

Based on computational fluid dynamics (CFD), gas−liquid mass transfer in upward Taylor flow through vertical circular capillaries was studied. To save computational resources and time, the numerical simulations were carried out in a moving frame of reference attached to Taylor bubbles. Three consecutive Taylor bubbles were used to mimic the behavior of Taylor flow in an infinitely long capillary. Steady-state solutions of concentration fields were obtained to describe gas transfer from Taylor bubbles to the liquid phase. The liquid-phase volumetric mass-transfer coefficient, KLa, was investigated as a function of various parameters, including the liquid-film length, liquid-slug length, liquid-film thickness, bubble rise velocity, liquid-phase diffusivity, capillary diameter, and gravity. One fitted equation, expressed with three dimensionless numbers, was developed to quantify the relationship between KLa and the above parameters. The examples show that the equation could predict KLa well. The contributions of the cylindrical bodies and hemispherical caps of Taylor bubbles on the overall mass transfer were studied separately.

Forced impregnation of a capillary tube with drop impact

We experimentally investigate how the impregnation of porous media can be forced using the initial kinetic energy of an impacting drop. We focus on the scale of a single pore – either hydrophilic or hydrophobic – and thus study the impact of a single drop falling on vertical cylindrical capillary tubes. This experimental configuration therefore differs from the impregnation of a porous media because of the finite volume of the drop and its initial kinetic energy. We observe different limit regimes: at low impact velocity, we recover the classical results for impregnation. The liquid does not impregnate the hydrophobic pore while it is totally sucked into the hydrophilic one. At high impact velocities, the drop is broken in two parts: one part spreads at the top of the surface while an isolated slug is trapped within the pore. We determine the critical speeds for these regimes and obtain a full phase-diagram for our observations. We also stress the characteristics of impregnating slugs namely their volume and their motion within the pores.

Oscillating bubbles in ultrasonic acoustic field

Behavior of oscillating bubbles is of fundamental study for acoustic cavitations, and is of great importance for medical field. For example, angiographic and diagnosis of cancer of liver. We focused on behavior of multiple air bubbles exposed to ultrasonic wave. The bubbles were injected into the static water from a vertical capillary tube, and then the ultrasonic wave of 20 kHz was applied from above toward the bubbles. Vibrating motion of the bubbles was captured by a high-speed camera at frame rates up to 45000 fps. Excitations of surface wave and shape oscillation with distinct mode number were realized. Correlation between the accelerated bubble behavior and the bubble-bubble distance.

Microfeeding with different ultrasonic nozzle designs

Microfeeding of dry powder excited by ultrasonic vibration makes use of relatively simple equipment and can be applied to solid freeforming and pharmaceutical dosing. The nozzle was a vertical glass capillary and four configurations for ultrasonic actuation were investigated: Type I had a piezoelectric transducer ring bonded to the base of a cylindrical water-containing vessel containing an axial nozzle; Type II had a piezoelectric transducer ring attached to the sidewall of the vessel; Type III used direct mechanical connection to the glass wall of the capillary to give nominally longitudinal vibration; and Type IV also used direct connection to the glass tube but arranged to give progressive wave vibration. The experimental results show that all four configurations realized powder microfeeding and dosing but the characteristics, in terms of minimum flow rate, dependence on voltage amplitude and uniformity of dose varied considerably. The discharge of particles was observed by a high-speed camera.

Confined drop motion in viscoelastic two-phase systems

In this study, we numerically examine the buoyancy-driven, axisymmetric motion of drops through vertical cylindrical capillaries. Combinations of Newtonian and viscoelastic drop and suspending fluid phases are considered. The effects of confinement, material properties, and rheological properties of the two phases on drop mobility and deformation are examined. Four dimensionless parameters (Reynolds number, capillary number, Deborah number, and the drop-to-tube size ratio) play critical roles in determining the drop motion. In general, a Newtonian drop immersed in a viscoelastic fluid experiences an extending trailing edge, while a viscoelastic drop in a Newtonian fluid develops an indentation around the rear stagnation point. Under certain conditions, a cusped drop appears due to fluid viscoelasticity that triggers shape instability.

Motion of Miscible Magnetic Fluids in a Vertical Capillary Tube

AbstractAn experimental study of miscible magnetic fluid motion in a vertical capillary tube is presented. Transporting ferrofluids is dominated by a dimensionless magnetic number Ma, which characterizes the ratio of upward magnetic force to the downward gravity. Two distinct stages of motion, referred to as the sub-critical mode of finite lift and the effective transportation, are identified. These two modes are determined by the values of the sub-critical magnetic number Masub and critical magnetic number Macr respectively. For the cases of sub-critical mode (Masub < Ma < Macr), the ferrofluids are lifted to quasiequilibrium heights, which are nearly proportional to the magnetic number Ma. As for the situations of effective transportation (Ma > Macr), a penetrating finger of ferrofluids is formed similar to the conventional miscible displacements. A dimensionless proportionality of fingertip velocity ν, magnetic number Ma and field distribution profile fz is obtained as ν ∼ Ma1/2fz by scaling arguments. This proportional correlation shows a good agreement with the experiments.

Capillary Rise of a Non-Newtonian Power Law Liquid: Impact of the Fluid Rheology and Dynamic Contact Angle

The impact of non-Newtonian behavior and the dynamic contact angle on the rise dynamics of a power law liquid in a vertical capillary is studied theoretically and experimentally for quasi-steady-state flow. An analytical solution for the time evolution of the meniscus height is obtained in terms of a Gaussian hypergeometric function, which in the case of a Newtonian liquid reduces to the Lucas-Washburn equation modified by the dynamic contact angle correction. The validity of the solution is checked against experimental data on the rise dynamics of a shear-thinning cmc solution in a glass microcapillary, and excellent agreement is found.

Flow and transport in brush-coated capillaries: A molecular dynamics simulation

We apply an efficient method of forced imbibition to (nano-)capillaries, coated internally with a polymer brush, to derive the change in permeability and suction force, corresponding to different grafting densities and lengths of the polymer chains. While the fluid is modeled by simple point particles interacting with Lennard-Jones forces, the (end-grafted, fully flexible) polymers, which form the brush coating, are described by a standard bead-spring model. Our computer experiments reveal a significant increase in the suction force (by a factor of 4, as compared to the case of a capillary with bare walls) when the brush width approaches the tube radius. A similar growth in the suction force is found when the grafting density of the brush is systematically increased. Even though the permeability of the tube is found to decline with both growing brush width and grafting density, the combined effect on the overall fluid influx into the capillary turns out to be weak, i.e., the total fluid uptake under spontaneous imbibition decreases only moderately. Thus we demonstrate that one may transport the fluid in vertical brush-coated capillaries to a much larger height than in an equivalent capillary with bare walls. Eventually, we also study the spreading of tracer particles transported by the uptaking fluid in brush-coated capillaries with regard to the grafting density of the brush and the length of the polymers. The observed characteristic asymmetric concentration profiles of the tracers and their evolution with elapsed time are interpreted in terms of a drift-diffusion equation with a reflecting boundary that moves with the fluid front. The resulting theoretical density profiles of the tracer particles are found to be in good agreement with those observed in the computer experiment.

The margination propensity of spherical particles for vascular targeting in the microcirculation

The propensity of circulating particles to drift laterally towards the vessel walls (margination) in the microcirculation has been experimentally studied using a parallel plate flow chamber. Fluorescent polystyrene particles, with a relative density to water of just 50 g/cm3comparable with that of liposomal or polymeric nanoparticles used in drug delivery and bio-imaging, have been used with a diameter spanning over three order of magnitudes from 50 nm up to 10 μm. The number of particles marginating per unit surface have been measured through confocal fluorescent microscopy for a horizontal chamber, and the corresponding total volume of particles has been calculated. Scaling laws have been derived as a function of the particle diameter d. In horizontal capillaries, margination is mainly due to the gravitational force for particles with d > 200 nm and increases with d4; whereas for smaller particles increases with d3. In vertical capillaries, since the particles are heavier than the fluid they would tend to marginate towards the walls in downward flows and towards the center in upward flows, with increasing with d9/2. However, the margination in vertical capillaries is predicted to be much smaller than in horizontal capillaries. These results suggest that, for particles circulating in an external field of volume forces (gravitation or magnetic), the strategy of using larger particles designed to marginate and adhere firmly to the vascular walls under flow could be more effective than that of using particles sufficiently small (d < 200 nm) to hopefully cross a discontinuous endothelium.

Static and Dynamic Aspects of Liquid Capillary Flow in Thermally Bonded Polyester Nonwoven Fabrics

The weight gain method is employed to study the vertical capillary flow of wetting liquids in polyester nonwoven fabrics with different basis weights. The quantity of liquid absorbed by capillarity in the nonwoven is recorded as a function of time, until saturation. The liquid retention capacity of the nonwovens has been studied from their “saturation level”, i.e. the fraction of pore volume effectively filled with liquid. It is found that this saturation level varies greatly with the type of nonwoven, and generally decreases with nonwoven thickness. Moreover, the expected 100% value is rarely attained even when the sample height is smaller than the Jurin equilibrium height. These observations are attributed to the more heterogeneous pore sizes in very thin nonwovens, where the interconnection of large and small pores inhibits the continued capillary rise of liquid front. The other part of the study concerns the kinetics of liquid capillary flow which has been analyzed by taking into account the contribution of the meniscus in filling the pores. By subtracting this contribution from the mass of liquid absorbed, the new absorption mass is found to vary linearly with the square root of time, in agreement with the Washburn theory. For the thinnest nonwovens, the very small and unrealistic values of Washburn radii deduced from the experimental results do not correspond to the real physical pore sizes, but reflect slow capillary kinetics. This phenomenon is, however, less important when the thickness of the sample increases.

Flow Pattern and Pressure Drop of Upward Two-Phase Flow in Vertical Capillaries

Gas-liquid two-phase flow patterns were investigated visually with a digital camera for upward air-water flow in capillaries with diameters of 1.47, 2.37, and 3.04 mm. several distinctive flow patterns were observed and described. the flow pattern maps developed in this work were compared with the conventional flow-pattern transition criteria for larger-diameter tubes and the experimental data that have been published. the total pressure drop in capillaries was measured with a differential pressure transducer for taylor flow, which existed broadly in multiphase monolith reactors and microchannel reactors. a new correlation was presented to calculate the total pressure gradient (tpg) of taylor flow. in addition, the other three models, which were proposed previously by other researchers, were also used to predict the tpg. the four theoretical results all were in overall agreement with the experimental data. finally, the effects of method used to calculate the void fraction on the tpg were checked. it was observed that the void fraction influenced the tpg remarkably, and the drift flux model was not suitable to evaluate the void fraction under the present experimental conditions.

Estimation of size from capillary pressure—A correction factor for a two menisci capillary

Extrusion of a liquid from a single vertical glass capillary, forming two menisci, by the application of air pressure is studied, to obtain a correct estimate of the capillary radius from the measured capillary pressure. Experimental measurements of critical extrusion pressure demonstrate the conditions under which the same capillary system can exhibit significantly different extrusion pressures. The absolute value of capillary radius is obtained by optical microscopy. Comparison of the estimated radius from capillary pressure measurements and optical microscopy show that the single meniscus-based capillary pressure equation results in a radius estimate that is smaller than the optically measured radius by 35%. This may be expected since the single meniscus-based capillary pressure equation is not applicable for the two menisci capillary. A theoretical analysis of the two menisci system, is presented, which leads to a new factor, β, in the single meniscus capillary pressure equation. This correction factor is estimated by solving the coupled Young–Laplace equations for the two menisci shapes. This “coupled menisci shape factor” is first estimated for a known capillary radius, and is subsequently used to predict capillary radius in capillaries of unknown radii of the same material. The use of the above correction factor leads to an estimate of the capillary radius, which differs from the optically estimated radius by less than 7%. Hence the two menisci-based capillary pressure equation developed in this paper results in a significant improvement, when the above liquid extrusion, from a capillary containing two menisci, is used for capillary pressure measurement.

On the nonuniformity of a capillary flow

It is established that the capillary rise of a liquid has an oscillatory character, in contrast to the commonly accepted opinion that a vertical capillary is filled at a monotonically varying velocity. The value of the tangential shear stress arising in an ascending liquid is evaluated for ethyl alcohol and distilled water.

Effect of surfactant on two-phase flow patterns of water–gas in capillary tubes

Flow patterns of liquid–gas two-phase flow were experimentally investigated. The experiments were carried out in both vertical and horizontal capillary tubes having inner diameters of 1.60 mm. The working liquid was the mixture of water and Sodium Dodecyl Benzoyl Sulfate (SDBS). The working gas was Nitrogen. For the water/SDBS mixture–gas flow in the vertical capillary tube, flow-pattern transitions occurred at lower flow velocities than those for the water–gas flow in the same tube. For the water/SDBS mixture–gas flow in the horizontal capillary tube, surface tension had little effect on the bubbly–intermittent transition and had only slight effect on the plug–slug and slug–annular transitions. However, surface tension had significant effect on the wavy stratified flow regime. The wavy stratified flow regime of water/SDBS mixture–gas flow expanded compared with that of water–gas.

Prediction of coupled menisci shapes by Young–Laplace equation and the resultant variability in capillary retention

This paper shows how 2 coupled Young–Laplace equations can be solved to predict the shapes of two coupled menisci formed in a capillary system. Experiments are performed, which demonstrate that the equilibrium volume of liquid retained in a vertical capillary, can be variable, even when all the properties of the system are invariant. This variability in liquid retention also leads to different equilibrium shapes of the top and bottom menisci. A coupled form of the Young–Laplace equation is solved to predict the two coupled menisci shapes. The curvature of the top meniscus is fitted to the experimentally recorded meniscus shape. The coupled Young–Laplace equation solution is used to predict the shape of the bottom meniscus. The shape of the bottom meniscus thus obtained, is shown to match the experimentally recorded bottom meniscus shape reasonably well. This observed coupling of the menisci has a significant impact on some porosimetric techniques which are based on liquid extrusion and explains why the volume of liquid that can be retained in a capillary can vary, under invariant conditions. Retention of liquids in capillaries is of interest in several applications like fabric wash.

Excitation of a vertical liquid capillary jet waveguide by modulated ultrasonic radiation pressure

The excitation of a liquid capillary jet issuing from a nozzle is investigated using internally applied modulated ultrasonic radiation pressure. The transducer used here is more efficient than one used in prior studies [J. B. Lonzaga et. al., J. Acoust. Soc. Am. 116, 2598 (2004)] and is suitable for nozzle velocities as low as 25 cm/s. At low velocities, the liquid jet is significantly tapered. As a consequence of the taper, the acoustic cutoff frequency increases with increasing distance from the nozzle. For ultrasound propagation down the jet from the nozzle, finite‐element calculations of the radiation pressure show that the radial stress at the cutoff location is significantly larger than at any other region of the jet. Two distinct capillary modes exist and are conjectured to be excited near the cutoff location by modulated radiation pressure: one traveling upward and the other traveling downward. In a certain range of modulation frequencies, the latter is an exponentially growing mode and leads to the forced disintegration of the jet into liquid drops. Excitation of the growing mode at the nozzle is achieved for low‐speed jets by using carrier frequencies close to or below the nozzle cutoff frequency. [Work supported by NASA.]