Circular Capillaries Research Articles

Multistability of a long droplet in a capillary tube under transverse body force

Bistable states for a sufficiently large amount of liquid can appear in an eccentric capillary due to the eccentricity effect under zero gravity (J. Fluid Mech, vol. 863, 2019, pp. 364–385). A transverse body force, which can lead to rich physical phenomena of a droplet, may lead to multistable states (bistability, tristability and the likes) of a sufficiently large amount of liquid in a capillary. We theoretically investigate this situation in a circular or annular capillary tube under a transverse body force. The results show that there can be tristable (bistable) states in an annular (circular) capillary tube: an occluding configuration and two (one) non-occluding configurations. In the annular tube, for one of the non-occluding configurations, the gas–liquid interface in the middle cross-section of the droplet meets both the inner and outer walls of the tube (bridging configuration); for the other non-occluding configuration, the gas–liquid interface in the middle cross-section of the droplet does not meet the inner wall (non-bridging configuration). The multistability is dependent on the Bond number, the contact angle and the cross-sectional shape. The multistability cannot occur for a zero or very large Bond number. A hydrophilic condition (the contact angle smaller than 90°) contributes to the non-occluding non-bridging configuration, while the hydrophobic condition (the contact angle larger than 90°) contributes to the non-occluding bridging configuration (only for the annular capillary). For the annular capillary with a not-so-large contact angle, increasing the inner-to-outer radius ratio can lead to a larger range of Bond numbers, in which the multistability occurs.

Deposition of shear‐thinning viscoelastic fluids by an elongated bubble in a circular channel regarding the weakly elastic regime

AbstractThin‐film deposition of fluids is ubiquitous in a wide range of engineering and biological applications, such as surface coating, polymer processing, and biomedical device fabrication. While the thin viscous film deposition in Newtonian fluids has been extensively investigated, the deposition dynamics in frequently encountered non‐Newtonian complex fluids remain elusive, with respect to predictive scaling laws for the film thickness. Here, we investigate the deposition of thin films of shear‐thinning viscoelastic fluids by the motion of a long bubble translating in a circular capillary tube. Considering the weakly elastic regime with a shear‐thinning viscosity, we provide a quantitative measurement of the film thickness with systematic experiments. We further harness the recently developed hydrodynamic lubrication theory to quantitatively rationalize our experimental observations considering the effective capillary number and the effective Weissenberg number , which describe the shear‐thinning and the viscoelastic effects on the film formation, respectively. The obtained scaling law agrees reasonably well with the experimentally measured film thickness for all test fluids. Our work may potentially advance the fundamental understanding of the thin‐film deposition in a confined geometry and provide valuable engineering guidance for processes that incorporate thin‐film flows and non‐Newtonian fluids.

Non-linear electro-rheological model of a membrane immersed in Tanner-Power law fluids applied to outer hair cells: Shear-thinning mechanisms

Flexoelectric actuation employs an applied electric field to induce membrane curvature, which is the mechanism utilized by the outer hair cells (OHC) present in the inner ear. The model developed for this study, representing the OHC, integrates two key components: (i) an approximation of the flexoelectric membrane shape equation for circular membranes attached to the inner surface of a circular capillary, and (ii) the coupled capillary flow of contacting liquid viscoelastic phases characterized by the Tanner-Power law rheological equation of state. A second-order non-linear differential equation for average curvature has been derived, and a robust numerical method has been programmed. This model simplifies to a linear model used previously. The main challenge involves identifying and describing the enhancement in curvature change rate. It was observed that low symmetry, low viscosity, and soft membrane and shear-thickening behavior of the phases enhance the curvature change rate. Additionally, there exists a critical electric field frequency value that maximizes the curvature change rate (resonance effect). The current theory, model, and computational simulations add to the ongoing development comprehension of how biological membrane shape actuation through electromechanical couplings.

Acoustofluidic patterning in glass capillaries using travelling acoustic waves based on thin film flexible platform

Surface acoustic wave (SAW) technology has been widely used to manipulate microparticles and biological species, based on acoustic radiation force (ARF) and drag force induced by acoustic streaming, either by standing SAWs (SSAWs) or travelling SAWs (TSAWs). These acoustofluidic patterning functions can be achieved within a polymer chamber or a glass capillary with various cross-sections positioned along the wave propagating paths. In this paper, we demonstrated that microparticles can be aligned, patterned, and concentrated within both circular and rectangular glass capillaries using TSAWs based on a piezoelectric thin film acoustic wave platform. The glass capillary was placed at different angles along with the interdigital transducer directions. We systematically investigated effects of tilting angles and wave characteristics using numerical simulations in both circular and square shaped capillaries, and the patterning mechanisms were discussed and compared with those agitated under the SSAWs. We then experimentally verified the particle patterns within different glass capillaries using thin film ZnO SAW devices on aluminum (Al) sheets. Results show that the propagating SAWs can generate acoustic pressures and patterns in the fluid due to the diffractive effects, drag forces and ARF, as functions of the SAW device’s resonant frequency and tilting angle. We demonstrated potential applications using this multiplexing, integrated, and flexible thin film-based platform, including patterning particles (1) inside multiple and successively positioned circular tubes; (2) inside a solidified hydrogel in the glass capillary; and (3) by wrapping a flexible ZnO/Al SAW device around the glass capillary.

Directed alignment of graphene-oxide liquid crystals in confined spaces: Effects of flow, pickering stabilization, and phase transition

Because of its versatility for processing, graphene oxide (GO) serves as a superior substance for two-dimensional carbon-based materials. Controlling GO alignment is crucial to augment its inherent anisotropic nature. Here, we report the controlled alignment of GO confined in the rectangular and circular capillary tubes. GO aligns in contrasting orientations according to the phase of GO dispersion during loading into a capillary. Upon GO liquid crystal (LC) loading, GO-layers are oriented tangential to the inner surface of capillary, resulting in a concentric organization of the GO-layers. In the LC phase, the GO orientation is mainly influenced by the flow so that the GOs are aligned tangential to the hydraulic shear plane. However, GO self-assembles parallel to the capillary cross-section when loaded in the isotropic phase and then concentrated into the LC phase. Surprisingly, by excluding flow-induced effects, the GO layer is aligned perpendicular to the inner surface throughout the capillary. This unexpected alignment of the GO-layers is initiated in the meniscus region by the “Pickering effect” (i.e., tangential adsorption of GO along the Air-Liquid interface). Upon solvent evaporation, GO dispersions experience a sequential isotropic to nematic phase transition from the meniscus to the central region. During the phase transition, the orientation of the GO layer is determined by the long-range ordering of the LC phase. As a result, the alignment effect caused by the Air-Liquid interface determines the GO alignment throughout the capillary. Our results provide useful insight into the delicate control of GO alignment in a confined space. Precise control of GO alignment in a confined space can be achieved based on the appropriate directional design of the Air-Liquid interface and the corresponding sequential phase transition.

Analytic solutions of heat and mass transfer in flat heat pipes with porous wicks

Flat heat pipes have been used in cooling computer chips. However, previous models impose heat rate through the pipe as an input parameter, preventing optimization of heat transfer. We consider a horizontal flat heat pipe with an idealized porous wick on either one or both walls. A constant temperature difference is imposed across the two ends of the pipe, and we seek a steady-state solution. The pores in the wick are straight circular capillaries running along and across the wick, and are filled with a partially-wetting liquid. Its vapor fills the center region of the pipe and is connected to the liquid through circular pore openings on the wick surface. At the hot end, the liquid evaporates from the pore openings into vapor, which moves to the cold end where it condenses and the condensate flows in the wick to the hot end to complete a cycle. The mass evaporation rate at each pore opening on the wick surface is found from evaporation kinetics. This pore-level result is incorporated into pipe-level mass, momentum, and energy balances. The mass evaporation rate is found to depend only on the pipe temperature and is essentially independent of the vapor pressure. Consequently, the pipe behaves like a fin with evaporative cooling instead of convective cooling. Thus, the analytic fin solution holds for the pipe temperature and contains only one dimensionless number S (S2 is the ratio of evaporative to conductive heat rate through the pipe). It is observed that in heat pipes, S≫1 and thermal energy is chiefly transferred by vapor flow. Analytic solutions are subsequently found for the evaporation rate, the heat rate through the pipe, and the liquid and vapor flows along the pipe. Our idealized-wick parameters are converted to the porosity and permeability of a porous medium, so that we can compare directly with two published flat heat-pipe experiments. We analyze the effects of pipe length and wick thickness on the heat rate through the pipe, and provide guides for future design of flat heat pipes.

An experimental study on the mobility of droplets in liquid-liquid Taylor flows within circular capillaries

Further development of microfluidics devices that reply on liquid-liquid droplet flows, requires a thorough understanding of the parameters influencing droplet velocity. This study provides greater insights into this subject through an analysis of parameters effecting droplet mobility in such flows. A novel, fully automated experimental setup was designed to accurately measure droplet velocity and length. Measurements were performed over a wide range of Capillary number (2×10−4 to 3.7×10−2), Bond number (0.05 to 3.2) and carrier to dispersed viscosity ratio (0.059 to 23.2) while also varying droplet length. Five different fluid combinations were examined within circular capillaries with inlet diameters ranging from 555μm to 1.70mm. Results reveal a complex relationship between droplet velocity and droplet length, viscosity ratio and Bond number. In all cases, as droplet length exceeds a threshold value, droplet velocity becomes independent of length and is shown to scale with ∼ Ca0.5. As the droplet length falls below the threshold, the droplet velocity faces a changeover zone in which the velocity initially declines and then rises by further increase in the length. For shorter droplets, higher Bond numbers cause the droplet phase to travel asymmetrically with respect to the channel centre line which substantially impacts the mobility of these droplets. Finally, a new expression has been developed to estimate the velocity of elongated droplets.

Abnormal Phenomena and Mathematical Model of Fluid Imbibition in a Capillary Tube

At present, the imbibition behavior in tight rocks has been attracted increasing attention since spontaneous imbibition plays an important role in unconventional oil and gas development, such as increasing swept area and enhancing recovery rate. However, it is difficult to describe the imbibition behavior through imbibition experiment using tight rock core. To characterize the imbibition behavior, imbibition and drainage experiments were conducted among water, oil, and gas phases in a visible circular capillary tube. The whole imbibition process is monitored using a microfluidic platform equipped with a high frame rate camera. This study conducts two main imbibition experiments, namely liquid-displacing-air and water-displacing-oil experiments. The latter is a spontaneous imbibition that the lower-viscosity liquid displaces the higher-viscosity liquid. For the latter, the tendency of imbibition rate with time does not match with previous model. The experimental results indicate that it is unreasonable to take no account of the effect of accumulated liquid flowing out of the capillary tube on imbibition, especially in the imbibition experiments where the lower-viscosity liquid displaces the higher-viscosity liquid. A mathematical model is established by introducing an additional force to describe the imbibition behavior in capillary tube, and the model shows a good prediction effect on the tendency of imbibition rate with time. This study discovers and analyzes the effect of additional force on imbibition, and the analysis has significances to understand the imbibition behavior in tight rocks.

Solvability of a moving contact-line problem with interface formation for an incompressible viscous fluid

We investigate the free-boundary problem of a steadily advancing meniscus in a circular capillary tube. The problem is described using the “interface formation model,” which was originally introduced with the aim of avoiding the singularities that arise when classical hydrodynamics is applied to problems with a moving contact line. We prove the existence of an axially symmetric solution in weighted Hölder spaces for low meniscus speeds.

Velocity measurements of individual droplets in liquid-liquid Taylor flows in circular capillaries

This study is focused on the effect of droplet length on droplet velocity in liquid-liquid Taylor flows for microfluidic applications. An experimental set up was designed to measure droplet velocity over a wide range of droplet lengths and flow velocities while also varying viscosity ratio. Five different fluid combinations were examined by employing AR20, FC40, HFE7500 and water. Results indicate the complexity of predicting droplet velocity in such flow regimes and also show a strong influence of viscosity ratio and Bond number.

Acoustofluidic Patterning inside Capillary Tubes Using Standing Surface Acoustic Waves

Acoustofluidic platforms have great potentials to integrate capillary tubes for controlling and manipulating microparticles and biological cells in both non-flowing and continuous-flow settings. In order to effectively manipulate microparticles/cells inside capillary tubes, it is essential to fully understand and control the patterns generated inside the capillary tubes with different cross-sections, and to investigate the influences of configuration and position arrangement of electrodes along with the capillary tubes. This paper aims to systematically investigate the patterning and alignment of microparticles inside glass capillary tubes using thin film surface acoustic wave (SAW) devices. Through both experimental studies and numerical modelling, effects of various cross-section geometries of the capillary tubes and their positioning with respect to the direction of interdigital transducers (IDTs) of the SAW device in both a stationary fluid and a continuous flow fluid were studied. Results showed that for the rectangular glass capillary tubes, the patterned lines of particles are parallel to the tube's side walls, irrelevant to the tube positions along with the IDTs, which is mainly caused by the standing wave field generated inside the rectangular glass tube. Whereas for the circular glass capillary tubes, alignment patterns of particles are quite different along the tube's height. At the bottom of the circular tube, particles are patterned into lines parallel to the tube direction, because the acoustic waves propagate into the water and form a standing wave along the direction of the circular tube. Whereas at the middle height of the tube, the particles are patterned into lines perpendicular to the tube direction, because the formed standing waves also propagate around the circular cross-section of the tube and are perpendicular to the tube direction. For the cases with a continuous liquid flow, under the agitation of acoustic waves, particles are patterned in lines parallel to the flow directions for both the rectangular and circular glass tubes, and the fluid flow enhances and smoothens the patterned lines of the particles.

Single-mode eccentric-core D-shaped photonic crystal fiber surface plasmon resonance sensor

A single-mode eccentric-core D-shaped photonic crystal fiber (PCF) surface plasmon resonance (SPR) sensor is proposed and comprehensively investigated based on Finite Element Method (FEM). The critical properties of the sensor such as single mode regimes, beam spot size, and confinement losses are all tailored for more practical network-integrable PCF SPR sensor with high coupling efficiency using commonly used single-mode optical fibers. The sensor has analyte Refractive-Index (RI) detection range between 1.330 and 1.420 with maximum sensitivity of 21200 nm/Refractive-Index-Unit (RIU), maximum Figure-of-Merit (FOM) of 294 RIU−1, maximum resolution of 4.72 × 10-6 RIU for analyte refractive index change of 0.005 with the finest Full-Width at Half-Maximum (FWHM) of 29 nm, and a maximum confinement loss of 14 dB/cm. The sensor exhibits high linear response at low analyte RI regime between analyte index 1.330 and 1.370. The proposed sensor design can be fabricated using comparatively simpler stack-and-draw method which is based solely on standard circular glass capillaries and solid rods.

Synthesis of Cerium Dioxide Nanoparticles by Gas/Liquid Pulsed Discharge Plasma in a Slug Flow Reactor

Cerium dioxide (CeO2) nanoparticles have gained immense attention owing to their use in various applications. Current synthesis methods for CeO2 nanoparticles including hydrothermal and chemical precipitation are time-consuming and require chemical reagents. In order to shorten the reaction time and avoid the use of organic reagents, a new method for CeO2 nanoparticles synthesis in a slug flow system by atmospheric-pressure pulsed discharge plasma was proposed, which provided an easy, efficient, and continuous reaction at room temperature. Cerium nitrate was used as a feed solution, and starch was added as a stabilizer to separate the nucleation and growth processes of the nanoparticles to prevent their aggregation. The system was powered by a high voltage of 10.0 kV (peak-to-peak) from an ac power supply. The products were characterized by transmission electron microscopy (TEM), high-resolution TEM, energy-dispersive X-ray spectroscopy, and UV–vis spectroscopy. The results showed that when a circular capillary glass tube coil was used as the slug flow reactor, the amount of the CeO2 nanoparticles increased compared to the case when a straight glass tube was used. The size also increased from 3.4 to 6.3 nm. The synthesis mechanism of the CeO2 nanoparticles by gas/liquid plasma was finally elucidated.

Confinement loss of anti-resonant capillaries with curved boundaries.

A systematic analysis of the dependence of the confinement loss of an anti-resonant capillary on the curvature of the core surround is presented. The core boundary is described by circular arcs and the construction allows for a wide range of core shapes to be considered. It is found that both negative and positive curvatures substantially reduce the confinement loss relative to that of a circular anti-resonant capillary and that this effect is insensitive to the size of the core relative to the wavelength and to the properties of the glass capillary wall. In contrast, for a solid core surround there is a small increase in the confinement loss with curvature. Results of scalar and vector calculations are shown to be similar. A qualitative explanation of the results is proposed based on azimuthal confinement of the wave fields generated by the curved boundaries.

Computational modeling and simulation of gas focused liquid micro-sheets

The purpose of this work is to numerically evaluate the behavior of microscopic gas-focused liquid sheets in terms of material properties, nozzle structure and operating conditions used for experiments in spectroscopy and scattering where a short optical path is required. The numerical simulations are presented of a gas flow focusing nozzle, capable of producing a stream consisting of a sequence of perpendicular micrometre thin liquid sheets. The nozzle structure consists of a central circular capillary for delivery of the liquid and two circular capillaries that provide the focusing gas flow in a converging direction from opposite directions. High velocity impinging gas jets accelerate and form a thin elliptically shaped liquid sheet which contracts downstream and eventually forms a similar shaped sheet in the plane perpendicular to the primary sheet. The process repeats further downstream with another contraction, forming the tertiary sheet, existing now in the same plane as the primary sheet. This produces a liquid jet in form of a series of perpendicular micrometre thin liquid sheets. Three dimensional conservation equations of mass, energy and momentum for a compressible two-phase system are solved with a finite volume approach and an algebraic volume of fluid method. The influence of liquid viscosity, density, surface tension, nozzle layout variation as well as gas and liquid operating parameters on the evolution of the primary liquid sheet is elaborated. The parameter space of six flow characterizing dimensionless numbers is explored in the following ranges: Reynolds gas number 64–130, Reynolds liquid number 122–620, Weber number 23–803, ratio of liquid to gas mass flow rate 16–58, viscosity ratio 26–79, and density ratio 4807–7221. The layout of the primary sheet is given in terms of sheet thickness, width and length. The results show minor effect of dynamic viscosity, a moderate effect of density and a dominant role of the surface tension. The liquid sheet shape is sensitive to the variation of gas and liquid flow rates as well as the nozzle's structure width and the angle between the liquid delivery and the focusing gas capillaries.

Correction to: Effect of the internal degrees of freedom of the gas molecules on the heat and mass transfer in long circular capillaries

Correction to: Effect of the internal degrees of freedom of the gas molecules on the heat and mass transfer in long circular capillaries

Pore-scale compositional modeling of gas-condensate flow: Effects of interfacial tension and flow velocity on relative permeability

Liquid dropout and retention in gas-condensate reservoirs, specially in the near wellbore region, obstruct gas flowing paths and impact negatively the produced fluid volume and composition. Yet, condensate banking forecasting is commonly inaccurate, as experiments seldom reproduce reservoir extreme conditions and complex fluid composition, while most pore-scale models oversimplify the physics of phase transitions between gas and condensate. To address this gap, a fully implicit isothermal compositional pore-network model for gas and condensate flow is presented. The proposed pore-networks consist of 3D structures of pores connected by constricted circular capillaries. Hydraulic conductances are calculated for the capillaries, which can exhibit single-phase flow or two-phase annular flow, according to local gas and liquid saturations, or be blocked by a liquid bridge, when capillary forces overcome viscous forces. A PT-flash based on the Peng-Robinson EoS is performed at control volumes defined for the pores at each time step, updating the phases properties. Flow analyses were carried based on coreflooding experiments reported in the literature, with matching fluid composition and flow conditions, and approximated pore-space geometry. Predicted and measured relative permeability curves showed good quantitative agreement, for two values of interfacial tension and three values of gas flow velocity.

A colorimetric technique to characterize mass transfer during liquid-liquid slug flow in circular capillaries

Continuous slug flow in microreactors are featured by alternative presence of regulate segments of immiscible phases in microchannel or capillaries with lateral dimensions below 1 mm. Due to the high interfacial area and short diffusive distance therein, such microreactors have been widely applied in chemical engineering processes that are sensitive to mass transfer. Therefore, mass transfer rates in microreactors have long been broadly investigated via either typical offline or online methods. Compared to these conventional methods, the colorimetric technique based on the oxidation of resazurin with oxygen enables direct determination of physical mass transfer rates. However, this technique was currently applied only to the gas-liquid system in microreactors, and mostly in rectangular channels due to the simplicity in image processing. Based on this, the current paper showed a demo where the colorimetric technique using resazurin was adapted to a liquid-liquid system for the mass transfer study of flowing droplets within a slug flow capillary. Experimental tips and tricks were summarized, and a sliced color-concentration calibration strategy was proposed to balance analyzing efficiency and accuracy.

Comparing flow characteristics of viscoelastic liquids in long and short capillaries (entrance effects)

This study is devoted to the analysis of the physical meaning of the difference in the results of the viscosity measurements obtained by using the two-capillary method—carrying on the same flow rate through two circular parallel capillaries of different lengths but the same diameter. Furthermore, there is the other approach for using short capillaries for determination of a value, known as “elongational viscosity,” based on the concept of domination extension at the convergent flow along the inlet of a capillary. The theory of this method dates back to the publication of Cogswell. However, it was shown that this approach is inadequate for polymeric liquids that demonstrate time-dependence effects. In this study, we present experimental data for melts of two polyethylenes of different molecular weights and their mixtures. The data of capillary viscometry are accompanied by measuring their viscoelastic properties. The obtained data showed that the two-capillary method cannot give a chance to estimate “elongational viscosity” for elastic liquids. The difference between the losses in flow through long and short capillaries is treated in the terms of “end correction,” which is determined by the Weissenberg number. Hence, elasticity is the main physical parameter responsible for additional losses in the flow through a short capillary.

Attenuation of waveguide modes in narrow metal capillaries.

The channeling of laser pulses in waveguides filled with a rare plasma is one of the promising techniques of laser wakefield acceleration. A solid-state capillary can precisely guide tightly focused pulses. Regardless of the material of the capillary, its walls behave like a plasma under the influence of a high-intensity laser pulse. Therefore, the waveguide modes in the capillaries have a universal structure, which depends only on the shape of the cross-section. Due to the large ratio of the capillary radius to the laser wavelength, the modes in circular capillaries differ from classical TE and TM modes. We consider the structure of capillary modes in a circular capillary, calculate the attenuation rates, discuss the mode expansion of the incident pulse using minimal simplifications, and analyze the accuracy of commonly used approximations. The attenuation length for such modes is two orders of magnitude longer than that obtained from the classical formula, and the incident pulse of the proper radius can transfer up to 98% of its initial energy to the fundamental mode. However, finding eigenmodes in capillaries of arbitrary cross-sections is a complex mathematical problem that remains to be solved.