Vertical Capillary Research Articles

Enhanced mass transfer in micro‐capillary two‐phase flow

AbstractProcess design of multi‐phase unit operations on the micro‐scale relies on the detailed knowledge of the hydrodynamics and mass transfer of discrete disperse fluid particles. The present work examines gas bubbles in micro‐capillaries. For the case of bubbles rising in vertical capillary, the hydrodynamics and concentration fields are determined over a wide field of parameters (Re, Sc, dbubble/dcapillary) using a combination of level‐set and body‐fitted mesh methods. Drag coefficients and Sherwood numbers are computed from the results and can be used to derive empirical correlations for each parameter and mode of operation. These correlations allow for the individual optimization of the mass transfer process in micro‐capillaries. The results are compared to experimental data and available correlations in literature with generally good agreement. It can be shown that mass transfer can be enhanced by using small geometries like micro‐capillaries. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Intrusion of a Liquid Droplet into a Powder under Gravity.

Intrusion of a liquid droplet into a hexagonal close-packed array of spheres under gravity is investigated using analytical methods and volume-of-fluid simulations. Four regimes of ultimate fluid behavior are identified: (A) no liquid imbibition into the bed, (B) trapping of liquid high in the bed, (C) liquid descending to the bottom of the bed, and (D) liquid spreading around the surface of all particles. These regimes are mapped based on the contact angle and Bond number of the system. Many aspects of the dynamics and ultimate liquid behavior are captured using a simplified model of a mass of liquid moving under gravity in a vertical capillary of undulating cross-sectional area. This simplified model is used to form momentum transport equations with four forms of nondimensional time, which are shown to collapse the simulation data with different fluid parameters in different regimes.

Modeling of water rising in systems of cylindrical capillaries of different radii

The promotion of water in the systems of cylindrical capillaries is studied in detail. A mathematical model of the water movement in both symmetric and asymmetric capillaries connected to a vertical capillary is built. In this case, the radii of both vertical and angled capillaries are considered identical. General properties of the water movement in branching capillaries are determined on the basis of the mathematical model. In particular, the greatest promotion of water occurs in the lower level of the capillaries. It is found that the shape of plants depends on the presence of capillary systems in them. However, the capillary systems of various parts of the plants differ in radii. For example, the diameter of the central capillary of a leaf is larger than that of the capillaries in the lamina. The patterns of water movement in the branching capillary systems with capillaries of different radii are considered. An expression for calculating the critical vertical capillary height at which water does not come from the vertical capillary to the inclined capillaries is obtained. It is shown that under certain conditions, the height of water in a vertical capillary can twofold exceed the height of water in a single vertical capillary of the same radius.

Investigation of hydrodynamic and heat transfer characteristics of gas–liquid Taylor flow in vertical capillaries

Heat transfer and flow characteristics of Taylor flow in vertical capillaries with diameters of 0.5, 1, and 2mm have been investigated numerically with the volume of fluid method. 30 different cases have been conducted with inlet Reynolds number ranging from 100 to 500 and initial void fraction ranging from 0.2 to 0.4. Simulation results of the normalized bubble rising velocity, frictional pressure drops, and average Nusselt number fit well with the experimental data and empirical correlations. The results indicate that the normalized bubble rising velocity is related to the capillary number. The flow-pattern dependent and modified Lockhart–Martinelli correlations can predict the numerical frictional pressure drops well. A low temperature region is formed in the liquid slug, where a recirculation zone is formed. The average Nusselt number increases with increasing Re, tube diameters, and with decreasing ξG, and is about 1.2~3 times of that of a fully developed laminar single phase flow in circular tubes with constant wall heat flux boundary conditions.

К вопросу о механизме крупномасштабного переноса компонентов металлических расплавов в неоднородно нагретых тонких капиллярах

The results of numerical simulation for concentration-induced convection have been presented in this paper. Two-component melt of both liquid metals filling vertical thin capillary with non-uniform temperature distribution on the boundaries is considered. It is assumed that the condition of absolute nonwetting takes place on the sidewalls. Because of this effect there is a free surface on vertical boundaries, where thermocapillary force is appeared due to the external longitudinal temperature gradient which makes to move liquid elements at a big distance, compared with axial size of capillary. Processes of adsorption-desorption on a surface, thermocapillary force, motion in a volume and diffusion are characterized by essentially different times. These mechanisms generate a large-scale process of circulation as carrying-out of admixture on the surface in the hot higher part of capillary, its following transfer down along the boundary due to thermocapillary force and its return in the volume over the desorption in the lower part of capillary. The numerical calculations by the method of finite differences show that the lifting speed of returning motion in the volume is less, than on the surface, that’s why admixture in the stage of saturation can be accumulated nearby the lower part of capillary. After establishing the flow is stationary and determined as in the volume as on the surface by the Marangony number. Intensity of motion and processes of adsorption-desorption on the free boundary have the decisive influence upon the formation of surface and volume concentration fields and speed of redistribution of components in a mixture. Thus, one of the possible mechanisms of longitudinal division on components of liquid binary mixtures in thin channels has been demonstrated. This can explain the results of certain experiments with fusible metals on segregation of molten metal mixes.Received 17.10.2016; accepted 03.12.2016

Investigation of mass transfer in milli-channels using high-resolution microfocus X-ray imaging

In this work, the absorption rate of a single Taylor bubble of carbon dioxide in water was investigated within vertical capillaries using high resolution X-ray imaging. The liquid side mass transfer coefficient was calculated from the changes in the size of the bubble at constant pressure obtained from the high-resolution X-ray images by image processing. The bubbles were continuously monitored by holding the bubble stationary in a downward flow of liquid. The processed images, which give the volume of the bubble with high accuracy as a function of time, were processed to evaluate the liquid side mass transfer coefficient between bubble and liquid using the mass conservation equation.The experiments covered a large range of initial Taylor bubble length varying from 5 to 22mm. The results show that the measured Sherwood numbers depend strongly on the bubble length and also equivalent diameter, which is the same trend as in previously reported results for larger pipe sizes. However the values of measured Sherwood numbers could not be predicted by available correlations. As a result a new mass transfer coefficient in the form of Sherwood number and as a function of Peclet number as well as the ratio of bubble equivalent diameter to capillary diameter (deq/D) is presented. The proposed correlation is applicable for a large range of the ratio deq/D that varies from 0.8 to 1.6. The average relative error between measured Sherwood number and the one calculated with the new correlation is less than 9.6%.

Gas bubbles in micro capillaries – hydrodynamics and mass transfer

AbstractProcess design of multi‐phase unit operations on the micro‐scale relies on the detailed knowledge of the hydrodynamics and mass transfer behavior of discrete disperse fluid particles. The present work examines the hydrodynamics and mass transfer of gas bubbles in vertical capillaries. The hydrodynamic behavior of a single bubble in a capillary including is examined numerically using a modified level‐set method [1]. Additionally, the influence of surface‐active contaminations (‘surfactants’) and the resulting Marangoni effects are taken into account [2]. This enables the differentiation between bubbles with a mobile, i.e. clean, interface and those with a immobile, i.e. contaminated, interface. Based on the hydrodynamics, the mass transfer is examined. In the present work, mass transfer is from the bubble into the bulk fluid. By using a very high mesh resolution, the local concentration field in and around the gas bubble can be resolved, which gives access to the local mass transfer. Results are in good agreement available correlations from literature. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Influence of the Marangoni–Gibbs effect on the separation of binary metallic melts in capillaries

The separation of the tin and lead melts at an artificially maintained temperature gradient along the capillary length is studied. Direct experiments demonstrate that the separation rate and the component concentration difference along the capillary length remain unchanged at any gradient direction for vertical, inclined, and horizontal capillaries. These results show that the Marangoni–Gibbs effect weakly affects the melt separation.

Effect of vapor flow on the wetting behavior of unstable evaporating menisci in heated capillary tubes

The wicking height of a heated, evaporating meniscus formed by surface-wetting liquid in a vertical capillary tube with dynamic flow has been investigated. Previous experimental results and analytical models for measuring/predicting wicking heights in capillaries are also reviewed. An analytical model is presented that accounts for both major and minor vapor pressure losses along the vertical capillary tube. It is shown that during thermo-mechanical instability, vapor/meniscus interaction can become more prevalent due to increased vapor generation/pressure near the meniscus free surface. A relatively simple procedure for estimating onset of meniscus instability is presented and, when used with the vapor Reynolds number, can estimate whether vapor pressure loss is significant. By comparing the current model with the available experimental data, it is shown that the wicking height of an unstable, evaporating meniscus of n-pentane in a vertical, glass capillary tube is better estimated by considering vapor flow pressure losses – providing a 40% improvement over previous models that neglect vapor flow. In addition to vapor flow pressure loss, the dynamic contact angle and thin film profile must also be calculated to ensure accurate prediction of wicking height. Although the proposed model shows improvement, it is prone to under-predicting the actual meniscus wicking height for stable, evaporating menisci at lower relative heat loads. The proposed model can be used for predicting wicking behavior of heated, vertically-aligned liquid columns in capillary structures – which is relevant to the design of miniature heat transfer equipment/media such as wicked heat pipes, micro-channels and sintered/porous surfaces.

Bubble coalescence: Effect of bubble approach velocity and liquid viscosity

The goal of this study is to present new experimental data on the effect of the bubble approach velocity and liquid viscosity on pairwise bubble coalescence. Measurements were performed to investigate the dynamics of bubble coalescence under well-defined laboratory conditions. Air and pure aqueous solutions of alginate (no surfactants) were the phases. The bubbles were formed from two vertical capillaries, under constant flow conditions. The coalescence process was recorded with a fast video and then image analysed, to evaluate the bubble growth, bubble expansion rate, the first bubble touch, bubble contact time T, bubble coalescence efficiency E. Three control parameters were tested. The bubble size D on contact was set by the spacing between the capillaries (D=1 and 1.5mm). The bubble approach velocity V was controlled by the gas input (V=0.031–39mm/s). The liquid viscosity μ was adjusted by the alginate content (μ=1.2–10.3mPas). It was found that the bubble contact time T monotonously increases with the liquid viscosity, passing through three stages: initial rise (low μ, coalescence), then jump (intermediate μ, transient region), and finally forming a plateau (high μ, non-coalescence). In the coalescent regime, the bubble contact time monotonously decreases with the bubble approach velocity obeying a power law, which for a typical 1mm bubble reads: T∼V−0.85. The difference in the bubble size did not change the coalescence pattern qualitatively, but only quantitatively in a modest manner.

MRI investigation of water–oil two phase flow in straight capillary, bifurcate channel and monolayered glass bead pack

The study of immiscible fluid displacement between aqueous-phase liquids and non-aqueous-phase liquids in porous media is of great importance to oil recovery, groundwater contamination, and underground pollutant migration. Moreover, the attendant viscous, capillary, and gravitational forces are essential to describing the two-phase flows. In this study, magnetic resonance imaging was used to experimentally examine the detailed effects of the viscous, capillary, and gravitational forces on water–oil flows through a vertical straight capillary, bifurcate channel, and monolayered glass-bead pack. Water flooding experiments were performed at atmospheric pressure and 37.8°C, and the evolution of the distribution and saturation of the oil as well as the characteristics of the two-phase flow were investigated and analyzed. The results showed that the flow paths, i.e., the fingers of the displacing phase, during the immiscible displacement in the porous medium were determined by the viscous, capillary, and gravitational forces as well as the sizes of the pores and throats. The experimental results afford a fundamental understanding of immiscible fluid displacement in a porous medium.

Surface tension of supercooled water determined by using a counterpressure capillary rise method.

Measurements of the surface tension of supercooled water down to -25 °C have been reported recently (Hrubý et al. J. Phys. Chem. Lett. 2014, 5, 425-428). These experiments did not show any anomalous temperature dependence of the surface tension of supercooled water reported by some earlier measurements and molecular simulations. In the present work, this finding is confirmed using a counterpressure capillary rise method (the counterpressure method) as well as through the use of the classical capillary rise method (the height method). In the counterpressure method, the liquid meniscus inside the vertical capillary tube was kept at a fixed position with an in-house developed helium distribution setup. A preset counterpressure was applied to the liquid meniscus when its temperature changed from a reference temperature (30 °C) to the temperature of interest. The magnitude of the counterpressure was adjusted such that the meniscus remained at the same height, thus compensating the change of the surface tension. One advantage of the counterpressure method over the height method consists of avoiding the uncertainty due to a possible variation of the capillary diameter along its length. A second advantage is that the equilibration time due to the capillary flow of the highly viscous supercooled water can be shortened. For both the counterpressure method and the height method, the actual results are relative values of surface tension with respect to the surface tension of water at the reference temperature. The combined relative standard uncertainty of the relative surface tensions is less than or equal to 0.18%. The new data between -26 and +30 °C lie close to the IAPWS correlation for the surface tension of ordinary water extrapolated below 0.01 °C and do not exhibit any anomalous features.

Транспіраційний механізм капілярного транспорту в ксилемі рослин

The capillary transport of the aqueous solution of mineral salts in the xylem of plants owing to the transpiration process has been considered. By analyzing the balance of driving forces (capillary forces, gravity forces, and viscous friction), a differential equation describing the liquid flow in the xylem consisting of capillaries with varying cross-sections is derived and integrated. The profile of a vertical capillary with varying cross-section for the maximum water flow is calculated. On the basis of the formula obtained for the minimum capillary cross-section and the Thomson law for the vapor pressure over the concave meniscus of leaf stoma, an expression is obtained for the dependence of the maximum capillary length on the humidity of the atmospheric air.

Dynamics of viscous slugs fall in dry capillaries

The dynamics of viscous slug fall in vertical dry capillaries is investigated by extending a published model (perfect wetting case) accounting for the film left behind the slug as it falls, and Laplace pressures at both ends of the slug in the momentum balance. The present investigation provides and uses an advancing contact-angle correlation determined based on a published theoretical work. The results are found in excellent agreement with published experimental values for falling slugs. The present model does not require any fitting parameter in the perfect wetting case, and is extended to include the non-perfect wetting case along with the unsteady-state dynamics using the quasi-steady-state approximation.

Capillary rise dynamics of aqueous glycerol solutions in glass capillaries: A critical examination of the Washburn equation

The classic description of capillary rise given by the Washburn equation was recently questioned in the light of experimental evidence for a velocity dependent dynamic contact angle at a moving contact line. We present a systematic investigation of the capillary rise dynamics of glycerol and aqueous glycerol solutions in vertical glass capillaries of various radii. For pure glycerol, the results of our experiments are in almost perfect agreement with the predictions of the Washburn equation using independently measured values for the liquid and capillary parameters. For aqueous glycerol solutions we observe discrepancies between the theoretical expectations and the experimental results, which are increasing with the water content of the solution. A thorough analysis, combined with scaling arguments, allows us to conclude that dynamic contact angle effects alone cannot provide a consistent explanation for these discrepancies. Rather, they can be perfectly accounted for if the mixture flowing in the capillary would have an effective, increased viscosity (in respect to the nominal value). We suggest and briefly discuss various mechanisms that could contribute to this observed behavior.

Design of an experimental apparatus for measurement of the surface tension of metastable fluids

A unique experimental apparatus for measurement of the surface tension of aqueous mixtures has been designed, manufactured, and tested in our laboratory. The novelty of the setup is that it allows measurement of surface tension by two different methods: a modified capillary elevation method in a long vertical capillary tube and a method inspired by the approach of Hacker ( National Advisory Committee for Aeronautics, Technical Note 2510, 1-20, 1951 ), i.e. in a short horizontal capillary tube. Functionality of all main components of the apparatus, e.g., glass chamber with the capillary tube, temperature control unit consisting of two thermostatic baths with special valves for rapid temperature jumps, helium distribution setup allowing pressure variation above the liquid meniscus inside the capillary tube, has been successfully tested. Preliminary results for the surface tension of the stable and metastable supercooled water measured by the capillary elevation method at atmospheric pressure are provided. The surface tension of water measured at temperatures between +26 °C and –11 °C is in good agreement with the extrapolated IAPWS correlation ( IAPWS Release on Surface Tension of Ordinary Water Substance, September 1994 ); however it disagrees with data by Hacker.

Double porous screen element for gas–liquid phase separation

We consider an assembly of two parallel porous screens suspended in a tube at a distance L. The screens are connected by wicking aids. If one screen is brought into contact with a wetting liquid, the other screen will be wetted as well enclosing gas in between. Due to surface tension in the screen pores, the gas can only be removed from the chamber when the pressure difference across one screen exceeds the bubble point. With such a double porous screen element it is therefore possible to block liquid flow using trapped gas as plug. We present a model approach, experiments and numerical calculations on the performance of such a screen element. The model is based on capillary transport in vertical and radial capillaries and allows to predict how fast the element will trap the gas to become operational. For the experiments, we have built such an element using Dutch Twilled weaves made of stainless steel. Placed in a vertical tube and initially dry, it is wetted from below or above and submitted to an increasing pressure difference until breakthrough occurs where the element fails. Corresponding numerical calculations elucidate what happens within the element when it fails. Our results confirm the concept of the double porous screen element and encourage its application as liquid management device.

Cooperative suction by vertical capillary array pump for controlling flow profiles of microfluidic sensor chips.

A passive pump consisting of integrated vertical capillaries has been developed for a microfluidic chip as an useful component with an excellent flow volume and flow rate. A fluidic chip built into a passive pump was used by connecting the bottoms of all the capillaries to a top surface consisting of a thin layer channel in the microfluidic chip where the thin layer channel depth was smaller than the capillary radius. As a result the vertical capillaries drew fluid cooperatively rather than independently, thus exerting the maximum suction efficiency at every instance. This meant that a flow rate was realized that exhibited little variation and without any external power or operation. A microfluidic chip built into this passive pump had the ability to achieve a quasi-steady rather than a rapidly decreasing flow rate, which is a universal flow characteristic in an ordinary capillary.

Dynamics of liquid rise in a vertical capillary tube

The governing equation for capillary rise in a vertical tube is derived using energy balance. The derived governing equation includes kinetic, gravity, and viscous effects. Through normalizing different terms in the governing equation, a form of nonlinear ordinary differential equation (ODE) with a positive dimensionless parameter was obtained. The ODE equation was solved numerically and the numerical results were compared with some published experimental data. The derived governing equation was found to be quite accurate for predicting the liquid rise and oscillation in a capillary tube. The effect of a dimensionless parameter on the behavior of the liquid rise was explored numerically. A simple critical condition, which leads to the oscillation of the liquid column in the capillary tube, was found in the form of a dimensionless parameter in the governing equation.

Passive fluidic chip composed of integrated vertical capillary tubes developed for on-site SPR immunoassay analysis targeting real samples.

We have successfully developed a surface plasmon resonance (SPR) measurement system for the on-site immunoassay of real samples. The system is composed of a portable SPR instrument (290 mm(W) × 160 mm(D) × 120 mm(H)) and a microfluidic immunoassay chip (16 mm(W) × 16 mm(D) × 4 mm(H)) that needs no external pump system. An integrated vertical capillary tube functions as a large volume (150 μL) passive pump and a waste reservoir that has sufficient capacity for several refill operations. An immunoassay was carried out that employed the direct injection of a buffer and a test sample in sequence into a microfluidic chip that included 9 antibody bands and 10 reference reagent bands immobilized in the flow channel. By subtracting a reliable averaged reference sensorgram from the antibody, we effectively reduced the influence of the non-specific binding, and then our chip successfully detected the specific binding of spiked IgG in non-homogeneous milk. IgG is a model antigen that is certain not to be present in non-homogeneous milk, and non-homogeneous milk is a model of real sample that includes many interfering foreign substances that induce non-specific binding. The direct injection of a real sample with no pretreatment enabled us to complete the entire immunoassay in several minutes. This ease of operation and short measuring time are acceptable for on-site agricultural, environmental and medical testing.