Cylindrical Capillaries Research Articles

Capillary dynamics driven by molecular self-layering

Capillary dynamics is a ubiquitous everyday phenomenon. It has practical applications in diverse fields, including ink-jet printing, lab-on-a-chip, biotechnology, and coating. Understanding capillary dynamics requires essential knowledge on the molecular level of how fluid molecules interact with a solid substrate (the wall). Recent studies conducted with the surface force apparatus (SFA), atomic force microscope (AFM), and statistical mechanics simulation revealed that molecules/nanoparticles confined into the film/wall surfaces tend to self-layer into 2D layer/s and even 2D in-layer with increased confinement and fluid volume fraction. Here, the capillary rise dynamics of simple molecular fluids in cylindrical capillary is explained by the molecular self-layering model. The proposed model considers the role of the molecular shape on self-layering and its effect on the molecularly thin film viscosity in regards to the advancing (dynamic) contact angle. The model was tested to explain the capillary rise dynamics of fluids of spherical, cylindrical, and disk shape molecules in borosilicate glass capillaries. The good agreement between the capillary rise data and SFA data from the literature for simple fluid self-layering shows the validity of the present model. The present model provides new insights into the design of many applications where dynamic wetting is important because it reveals the significant impact of molecular self-layering close to the wall on dynamic wetting.

Prediction of the moments in advection-diffusion lattice Boltzmann method. I. Truncation dispersion, skewness, and kurtosis.

The effect of the heterogeneity in the soil structure or the nonuniformity of the velocity field on the modeled resident time distribution (RTD) and breakthrough curves is quantified by their moments. While the first moment provides the effective velocity, the second moment is related to the longitudinal dispersion coefficient (k_{T}) in the developed Taylor regime; the third and fourth moments are characterized by their normalized values skewness (Sk) and kurtosis (Ku), respectively. The purpose of this investigation is to examine the role of the truncation corrections of the numerical scheme in k_{T}, Sk, and Ku because of their interference with the second moment, in the form of the numerical dispersion, and in the higher-order moments, by their definition. Our symbolic procedure is based on the recently proposed extended method of moments (EMM). Originally, the EMM restores any-order physical moments of the RTD or averaged distributions assuming that the solute concentration obeys the advection-diffusion equation in multidimensional steady-state velocity field, in streamwise-periodic heterogeneous structure. In our work, the EMM is generalized to the fourth-order-accurate apparent mass-conservation equation in two- and three-dimensional duct flows. The method looks for the solution of the transport equation as the product of a long harmonic wave and a spatially periodic oscillating component; the moments of the given numerical scheme are derived from a chain of the steady-state fourth-order equations at a single cell. This mathematical technique is exemplified for the truncation terms of the two-relaxation-time lattice Boltzmann scheme, using plug and parabolic flow in straight channel and cylindrical capillary with the d2Q9 and d3Q15 discrete velocity sets as simple but illustrative examples. The derived symbolic dependencies can be readily extended for advection by another, Newtonian or non-Newtonian, flow profile in any-shape open-tabular conduits. It is established that the truncation errors in the three transport coefficients k_{T}, Sk, and Ku decay with the second-order accuracy. While the physical values of the three transport coefficients are set by Péclet number, their truncation corrections additionally depend on the two adjustable relaxation rates and the two adjustable equilibrium weight families which independently determine the convective and diffusion discretization stencils. We identify flow- and dimension-independent optimal strategies for adjustable parameters and confront them to stability requirements. Through specific choices of two relaxation rates and weights, we expect our results be directly applicable to forward-time central differences and leap-frog central-convective Du Fort-Frankel-diffusion schemes. In straight channel, a quasi-exact validation of the truncation predictions through the numerical moments becomes possible thanks to the specular-forward no-flux boundary rule. In the staircase description of a cylindrical capillary, we account for the spurious boundary-layer diffusion and dispersion because of the tangential constraint of the bounce-back no-flux boundary rule.

Prediction of the moments in advection-diffusion lattice Boltzmann method. II. Attenuation of the boundary layers via double-Λ bounce-back flux scheme.

Impact of the unphysical tangential advective-diffusion constraint of the bounce-back (BB) reflection on the impermeable solid surface is examined for the first four moments of concentration. Despite the number of recent improvements for the Neumann condition in the lattice Boltzmann method-advection-diffusion equation, the BB rule remains the only known local mass-conserving no-flux condition suitable for staircase porous geometry. We examine the closure relation of the BB rule in straight channel and cylindrical capillary analytically, and show that it excites the Knudsen-type boundary layers in the nonequilibrium solution for full-weight equilibrium stencil. Although the d2Q5 and d3Q7 coordinate schemes are sufficient for the modeling of isotropic diffusion, the full-weight stencils are appealing for their advanced stability, isotropy, anisotropy and anti-numerical-diffusion ability. The boundary layers are not covered by the Chapman-Enskog expansion around the expected equilibrium, but they accommodate the Chapman-Enskog expansion in the bulk with the closure relation of the bounce-back rule. We show that the induced boundary layers introduce first-order errors in two primary transport properties, namely, mean velocity (first moment) and molecular diffusion coefficient (second moment). As a side effect, the Taylor-dispersion coefficient (second moment), skewness (third moment), and kurtosis (fourth moment) deviate from their physical values and predictions of the fourth-order Chapman-Enskog analysis, even though the kurtosis error in pure diffusion does not depend on grid resolution. In two- and three-dimensional grid-aligned channels and open-tubular conduits, the errors of velocity and diffusion are proportional to the diagonal weight values of the corresponding equilibrium terms. The d2Q5 and d3Q7 schemes do not suffer from this deficiency in grid-aligned geometries but they cannot avoid it if the boundaries are not parallel to the coordinate lines. In order to vanish or attenuate the disparity of the modeled transport coefficients with the equilibrium weights without any modification of the BB rule, we propose to use the two-relaxation-times collision operator with free-tunable product of two eigenfunctions Λ. Two different values Λ_{v} and Λ_{b} are assigned for bulk and boundary nodes, respectively. The rationale behind this is that Λ_{v} is adjustable for stability, accuracy, or other purposes, while the corresponding Λ_{b}(Λ_{v}) controls the primary accommodation effects. Two distinguished but similar functional relations Λ_{b}(Λ_{v}) are constructed analytically: they preserve advection velocity in parabolic profile, exactly in the two-dimensional channel and very accurately in a three-dimensional cylindrical capillary. For any velocity-weight stencil, the (local) double-Λ BB scheme produces quasi-identical solutions with the (nonlocal) specular-forward reflection for first four moments in a channel. In a capillary, this strategy allows for the accurate modeling of the Taylor-dispersion and non-Gaussian effects. As illustrative example, it is shown that in the flow around a circular obstacle, the double-Λ scheme may also vanish the dependency of mean velocity on the velocity weight; the required value for Λ_{b}(Λ_{v}) can be identified in a few bisection iterations in given geometry. A positive solution for Λ_{b}(Λ_{v}) may not exist in pure diffusion, but a sufficiently small value of Λ_{b} significantly reduces the disparity in diffusion coefficient with the mass weight in ducts and in the presence of rectangular obstacles. Although Λ_{b} also controls the effective position of straight or curved boundaries, the double-Λ scheme deals with the lower-order effects. Its idea and construction may help understanding and amelioration of the anomalous, zero- and first-order behavior of the macroscopic solution in the presence of the bulk and boundary or interface discontinuities, commonly found in multiphase flow and heterogeneous transport.

Microgravity spreading of water spheres on hydrophobic capillary plates

We create nearly perfect centimetric spheres of water by splitting a cavity consisting of two metal hemispheres coated with a hydrophobic paint and under-filled with liquid, while releasing the apparatus in free-fall. A high-speed camera captures how water spread on hydrophobic aluminum and polycarbonate plates perforated with cylindrical capillaries. We compare observations at the ZARM drop tower in Bremen with Lattice-Boltzmann numerical simulations of Frank, Perre and Li for the inertial phase of imbibition.

Экспериментальное исследование двухфазного течения жидкостей в цилиндрическом капилляре

Экспериментальное исследование двухфазного течения жидкостей в цилиндрическом капилляре

Capillary pressure across a pore throat in the presence of surfactants

AbstractCapillarity controls the distribution and transport of multiphase and immiscible fluids in soils and fractured rocks; therefore, capillarity affects the migration of nonaqueous contaminants and remediation strategies for both LNAPLs and DNAPLs, constrains gas and oil recovery, and regulates CO2 injection and geological storage. Surfactants alter interfacial tension and modify the invasion of pores by immiscible fluids. Experiments are conducted to explore the propagation of fluid interfaces along cylindrical capillary tubes and across pore constrictions in the presence of surfactants. Measured pressure signatures reflect the interaction between surface tension, contact angle, and the pore geometry. Various instabilities occur as the interface traverses the pore constriction, consequently, measured pressure signatures differ from theoretical trends predicted from geometry, lower capillary pressures are generated in advancing wetting fronts, and jumps are prone to under‐sampling. Contact angle and instabilities are responsible for pronounced differences between pressure signatures recorded during advancing and receding tests. Pressure signatures gathered with surfactant solutions suggest changes in interfacial tension at the constriction; the transient surface tension is significantly lower than the value measured in quasi‐static conditions. Interface stiffening is observed during receding fronts for solutions near the critical micelle concentration. Wetting liquids tend to form plugs at pore constrictions after the invasion of a nonwetting fluid; plugs split the nonwetting fluid into isolated globules and add resistance against fluid flow.

Modeling and simulation of the motion of nanoparticles in cylindrical capillaries allowing particle‐to‐wall interactions

The process of transporting nanoparticles at the blood vessels level stumbles upon various physical and physiological obstacles; therefore, a Mathematical modeling will provide a valuable means through which to understand better this complexity. In this paper, we consider the motion of nanoparticles in capillaries having cylindrical shapes (i.e., tubes of finite size). Under the assumption that these particles have spherical shapes, the motion of these particles reduces to the motion of their centers. Under these conditions, we derive the mathematical model, to describe the motion of these centers, from the equilibrium of the gravitational force, the hemodynamic force and the van der Waals interaction forces. We distinguish between the interaction between the particles and the interaction between each particle and the walls of the tube. Assuming that the minimum distance between the particles is large compared with the maximum radius R of the particles and hence neglecting the interactions between the particles, we derive simpler models for each particle taking into account the particles‐to‐wall interactions. At an error of order O(R) or O(R3)(depending if the particles are 'near' or 'very near' to the walls), we show that the horizontal component of each particle's displacement is solution of a nonlinear integral equation that we can solve via the fixed point theory. The vertical components of the displacement are computable in a straightforward manner as soon as the horizontal components are estimated. Finally, we support this theory with several numerical tests. Copyright © 2016 John Wiley & Sons, Ltd.

Ferrofluid Capillary Rise in Porous Medium Under the Action of Nonuniform Magnetic Field

The capillary flow of a ferrofluid in a single cylindrical capillary tube and through a sandy porous medium under the action of a nonuniform magnetic field is studied experimentally. The dynamics of the capillary rise and the static case have been considered. It has been shown that the nonuniform magnetic field with upward directed gradient accelerates the capillary rise; contrary, the nonuniform magnetic field with downward directed gradient decelerates the capillary rise. Time dependences of the ferrofluid height and maximum reachable height of ferrofluid have been analyzed. The method of the study of ferrofluid capillary rise based on the use of magnetic measurements has been proposed. It has been demonstrated that porous material parameters can be extracted from the results of measurements of the inductances of the solenoid with porous medium inside and the small sensing coil within a single experiment.

The angular distribution at the outlet of a capillary in a wide range of rarefaction

The angular distribution at the outlet of a capillary is an important topic in rarefied gas dynamics. Here the procedure to calculate the near field angular distribution based on velocity distribution function or DSMC (Direct Simulation Monte Carlo) method was proposed. Then, the angular distribution at the outlet of cylindrical capillary was evaluated with different rarefaction parameter δ using DSMC method with open source solver dsmcFoam. The results showed that the normalized flux intensity at small polar angle decreased with δ when δ was smaller than 10, and the distribution did not approximate the cosine distribution when δ at the inlet was large enough. Besides, capillary with conical end was also evaluated. The results showed that the conical end could decrease the divergence of the beam even δ at the inlet increased to 50 when the outlet was set as vacuum. Last, the influence of CL (Cercignani Lampis) accommodation coefficients and VSS (Variable Soft Sphere) parameters on the angular distribution was studied.

Thermal diode made by nematic liquid crystal

This work investigates how a thermal diode can be designed from a nematic liquid crystal confined inside a cylindrical capillary. In the case of homeotropic anchoring, a defect structure called escaped radial disclination arises. The asymmetry of such structure causes thermal rectification rates up to 3.5% at room temperature, comparable to thermal diodes made from carbon nanotubes. Sensitivity of the system with respect to the heat power supply, the geometry of the capillary tube and the molecular anchoring angle is also discussed.

Propagation of femtosecond pulses in a hollow-core revolver fibre

We have studied for the first time the propagation of femtosecond pulses through an optical fibre with an air-filled hollow core and a cladding in the form of one ring of noncontacting cylindrical capillaries for high-power radiation transmission in the telecom range. Numerical analysis results demonstrate that the parameters of the fibre enable radiation transmission in the form of megawatt-power Raman solitons through up to a length of the fibre and tuning of the emission wavelength over . We have experimentally demonstrated femtosecond pulse transmission through fibres up to in length in the linear propagation regime, without distortions of the pulse spectrum, with a dispersion-induced temporal pulse broadening within 20 %.

A neuron-in-capillary platform for facile collection and mass spectrometric characterization of a secreted neuropeptide.

The integration of microfluidic devices—which efficiently handle small liquid volumes—with separations/mass spectrometry (MS) is an effective approach for profiling the neurochemistry occurring in selected neurons. Interfacing the microfluidic cell culture to the mass spectrometer is challenging because of geometric and scaling issues. Here we demonstrate the hyphenation of a neuron-in-capillary platform to a solid phase extraction device and off-line MS. A primary neuronal culture of Aplysia californica neurons was established directly inside a cylindrical polyimide capillary. The approach also uses a particle-embedded monolith to condition neuropeptide releasates collected from several Aplysia neurons cultured in the capillary, with the subsequent characterization of released peptides via MS. This system presents a number of advances compared to more traditional microfluidic devices fabricated with polydimethylsiloxane. These include low cost, easy access to cell culture, rigidity, ease of transport, and minimal fluid handling. The cylindrical geometry of the platform allows convenient interface with a wide range of analytical tools that utilize capillary columns.

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.

The influence of a diverging conical end on the beam's angular distribution at the outlet of the capillary

A cylindrical capillary with a diverging conical end was proposed to decrease the divergence of the beam at the capillary outlet in the free molecular regime. To evaluate the effect of the conical end on the angular distribution, test particle Monte Carlo simulations based on Cercignani-Lampis (CL) reflection were conducted. Firstly, the influence of the capillary's structural parameters on the azimuth integrated flux intensity was evaluated. The peak point of the azimuth integrated flux intensity shifted to small polar angle when decreasing the half angle of the conical end, and the magnitude of the peak decreased with the half angle when it was less than 20°, but the magnitude was still larger than that of cylindrical capillary. Meanwhile, the influence range of the conical end on the distribution increased with its height, and the structural parameters of the cylindrical part had little effect on the shape of angular distribution. Then, the effect of the conical end was studied with different CL accommodation coefficients, and the results showed that the shape of the distribution barely changed except for the transmission probability. Finally, capillary with two conical structures and the effect of conical end on an atomic hydrogen beam were discussed.

Viscoelectric effect on electroosmotic flow in a cylindrical microcapillary

Electroosmotic flow, under the Debye–Hückel approximation, has been widely analyzed in the specialized literature. This is a severe restriction in practice, where zeta potentials as high as 100–200 mV are encountered frequently. Under this condition, the variation of the viscosity with the electric field in the electric double layer (EDL), known as the viscoelectric effect, can lead to a considerable variation in comparison to the Helmholtz–Smoluchowsky equation for the electroosmotic velocity. The objective of this work is to analyze the electroosmotic flow in a cylindrical capillary at high zeta potentials in the thin EDL approximation, taking into account the viscoelectric effect. In order to obtain the potential distribution, the Poisson–Boltzmann equation was solved by using the matched asymptotic expansions method, and then, by applying the same technique, the flow field was determined from the momentum equation by considering that the viscosity of the electrolyte changes according to the relationship , where is the viscosity evaluated in the absence of an electric field, f is the viscoelectric constant and E is the intrinsic electric field in direction transversal to the EDL. For asserting the correctness of the asymptotic solution, this result was compared against a numerical solution, and a very good agreement between them was found. The results show that the viscoelectric effect has a noticeable influence by reducing the electroosmotic flow velocity in about 10% in comparison to the standard Helmholtz–Smoluchowski velocity.

Pore-size distribution in loamy soils: A comparison between microtomographic and capillarimetric determination methods

Pore-size distribution in a soddy-podzolic silt loamy soil developing from mantle loesslike loam (Eutric Albic Retisol (Loamic, Cutanic)) was calculated from the water retention curve according to Jurin’s equation and directly determined in microtomographic experiments. Rounded macropores with the diameter of their sections from 75 to 1000 μm predominate in horizontal sections if the studied soil samples. A larger part of the soil pores (>30–35%) belongs to micro- and nanopores, and they cannot be quantitatively determined by the tomographic method, because their sizes are smaller than the detection limit of the applied X-ray microtomography (8.75 μm per pixel). This leads to a significantly larger pore volume determined from the water retention curve in comparison with the “tomographic” pore volume. A comparative analysis of pore-size distribution curves obtained by these methods shows that the major regularities of the pore-size distribution in the range from 30 to 5000 μm are similar in both cases. Fine macropores and, partly, mesopores predominate. Common characteristics of the pore-size distribution curves obtained by these methods, including the coincidence of the peaks, attest to the validity of classical approaches, according to which the hydrology of soil pore space can be perceived as a physical model of cylindrical capillaries of different sizes with capillary-sorbed water.

The dynamics of the annular liquid layer inside a cylindrical capillary

When one fluid displaces another in a cylindrical capillary, a layer of the original fluid is often left behind on the capillary wall. We studied the dynamics of a cylindrical hexadecane layer deposited inside glass capillaries after the oil/air displacement experimentally and by a theoretical model prediction. Our experiments have shown that an annular oil layer is formed on the capillary wall after hexadecane is displaced by air. The oil layer subject to surface perturbation becomes unstable over time (Rayleigh instability), forming uniform, regularly spaced double concave meniscuses across the capillary that are bridged with dimples (collars). With time, the film between the meniscus and the dimple thins, but does not break, during the thinning process. The dynamics of the oil layer and the formation of the double concave meniscus with the dimple are more pronounced in a large capillary compared to those phenomena found in a small capillary. In order to reveal the phenomena of the film thinning and stability between the double concave meniscus and the dimple, we monitored an air bubble approaching a flat glass surface in hexadecane. We found that the oil film thinning in a cylindrical glass capillary and on a flat glass substrate was similar; the film did not break during the thinning process. The analysis also showed that the macroscopic contact angle (based on the Laplace solution-extrapolation to a solid substrate) was different from the microscopic contact angle (between the film and meniscus). We adapted the model proposed by Gauglitz and Radke [“An extended evolution equation for liquid film breakup in cylindrical capillaries,” Chem. Eng. Sci. 43, 1457 (1988)] for our system (oil-air displacement) and solved it numerically. The numerical result shows a stable film between the liquid bridge and the dimple, which is consistent with our experimental observations. We also estimated the meniscus-film-dimple thickness profile and found it was in fair agreement with the model prediction.

Advances of capillary filling of Newtonian fluids in micro- and nanochannels

Capillary filling is extensively involved in natural science and engineering technology, such as oil recovery, building conservation, ink printing, etc. Due to large surface to volume ratio, capillary action is very prominent at micro- and nonoscale regime, and recent years it has triggered a tremendous acceleration of research related to the capillary filling process in micro- and nanochannels. For instance, the capillary action is used to eliminate some additional accessories such as electric drive devices or syringe pumps, which can greatly simplify the design of microfluidic and nanofluidic devices. All these facts show that a thorough understanding of the kinetics of capillary-driven filling in micro- and nanochannels is of great significance. Almost a century ago, Lucas and Washburn reported an analytical solution for capillary filling of Newtonian fluids in a small cylindrical capillary tube: the filling distance is proportional to the square root of time, which is also known as the classical LW equation. Although the LW equation can well describe macroscopic capillary filling process, it’s availability at micro- and nanoscale regime is still an open question, which has attracted a lot of attention. This paper summarizes the progress of capillary filling kinetics in micro- and nanochannels in views of theoretical models, numerical simulations and experimental studies. All the three perspectives indicate that the capillary filling process should be discussed by dividing into four stages as follows: (1) purely inertial time stage, where the filling distance is proportional to the time t ; (2) visco-inertial time stage, where the inertia force, capillary force and viscous force have comparable effect on the filling kinetics; (3) purely viscous time stage, where the capillary force is balanced by viscous force and the filling distance is linearly related to the t 1/2; (4) the gravity should be considered when the pipe is vertical and there is a viscous and gravitational time stage. In purely viscous time stage, the LW equation can qualitatively describe the capillary filling process in micro- and nanochannels. Quantitatively, however, significant deviations between the experiment or simulation results and theoretical expectations have been observed in capillary filling process. Although several factors are considered to explain the deviation, such as the dynamic contact angle, bubble formation, electro-viscous effect and other factors, there is no unified understanding on the capillary filling kinetics. Finally, possible pending problems are summarized based on the results in previous work. In addition, brief introduction and prospect have been made on capillary filling of non-Newtonian fluids.

Dynamics of liquid plugs in prewetted capillary tubes: from acceleration and rupture to deceleration and airway obstruction.

The dynamics of individual liquid plugs pushed at a constant pressure head inside prewetted cylindrical capillary tubes is investigated experimentally and theoretically. It is shown that, depending on the thickness of the prewetting film and the magnitude of the pressure head, the plugs can either experience a continuous acceleration leading to a dramatic decrease of their size and eventually their rupture or conversely, a progressive deceleration associated with their growth and an exacerbation of the airway obstruction. These behaviors are quantitatively reproduced using a simple nonlinear model [Baudoin et al., Proc. Natl. Acad. Sci. U. S. A., 2013, 110, 859] adapted here for cylindrical channels. Furthermore, an analytical criterion for the transition between these two regimes is derived and successfully compared with extensive experimental data. The potential implications of this work for pulmonary obstructive diseases are discussed.

Oscillatory regimes of capillary imbibition of viscoelastic fluids through concentric annulus

Here we report the capillary filling dynamics of a viscoelastic fluid through a concentric annulus, which offers a distinct disparity in the dynamical characteristics as compared to the classical cylindrical capillary based paradigm.