Stability Of Liquid Bridges Research Articles

Solid bulk cargo liquefaction: Stability of liquid bridges

This work focuses on investigating the correlation between the evolution of liquid bridges and moisture migration in solid bulk cargo liquefaction. We experimentally investigate the stability of liquid bridges in static and dynamic particles. The liquid-holding capacity of static particles is determined, and the formation and fracturing of liquid bridges are related to the particle distribution and particle radius. The spacing of the bottom particles determines the maximum liquid-holding capacity, while the space between the upper particles and the bottom particles determines the fracture position. The particles with larger radii have an increased liquid-holding capacity and a low volumetric moisture content, which confirms that cargo that consists entirely of large particles would be apt to have seepage and would not liquefy. Moisture migration for pendular and funicular liquid bridges during stretching and squeezing is captured. We indicate that the fusion behavior of liquid bridges is an important inducement for moisture migration, and it dramatically decreases the liquid-holding capacity. The findings suggest that cargo with low water content would still cause liquefaction, and that the water content should be reduced further for the safe transport of solid bulk cargo.

Influence of volume and aspect ratio of liquid bridges on capillary breakup rheometry

Capillary thinning of liquid bridges is routinely used for extensional rheology of Newtonian and complex fluids. Although it is expected that the volume and aspect ratio of a liquid bridge significantly influence its dynamics, the role played by these parameters in rheological characterization has not been previously studied. We perform numerical simulations of Newtonian as well as viscoelastic liquid bridges with the one-dimensional slender-filament approximation of Eggers and Dupont [“Drop formation in a one-dimensional approximation of the Navier–Stokes equation,” J. Fluid Mech. 262, 205–221 (1994)] and Ardekani et al. [“Dynamics of bead formation, filament thinning and breakup in weakly viscoelastic jets,” J. Fluid Mech. 665, 46–56 (2010)]. Sample volume and bridge aspect ratio control two phenomena that can adversely impact rheological characterization: the tendency to form satellite drops at the necking plane and the slowing down of capillary thinning due to the proximity (in parameter space) of the liquid-bridge stability boundary. The optimal range of these parameter values to avoid drop formation and slowdown is discussed.

Extensional Magnetorheology of Viscoelastic Human Blood Analogues Loaded with Magnetic Particles.

This study represents a pioneering work on the extensional magnetorheological properties of human blood analogue fluids loaded with magnetic microparticles. Dynabeads M-270 particles were dispersed in Newtonian and viscoelastic blood analogue fluids at 5% wt. Capillary breakup experiments were performed, with and without the influence of an external magnetic field aligned with the flow direction. The presence of the particles increased the viscosity of the fluid, and that increment was larger when embedded within a polymeric matrix. The application of an external magnetic field led to an even larger increment of the viscosity of the working fluids, as the formation of small aggregates induced an increment in the effective volume fraction of particles. Regarding the liquid bridge stability, the Newtonian blood analogue fluid remained as a Newtonian liquid exhibiting a pinch-off at the breakup time in any circumstance. However, in the case of the viscoelastic blood analogue fluid, the presence of the particles and the simultaneous application of the magnetic field enhanced the formation of the beads-on-a-string structure, as the Ohnesorge number remained basically unaltered, whereas the time of the experiment increased due to its larger viscosity, which resulted in a decrease in the Deborah Number. This result was confirmed with fluids containing larger concentrations of xanthan gum.

Analysis of evaporating liquid bridge in horizontal fractures

The formation of liquid bridge is pertinent to many fields including seepage into underground fractured rocks as an environmental issue and capillary continuity between matrix blocks which controls oil recovery in fractured reservoirs. Evaporation from the surface of liquid bridge into the surrounding gas could affect the stability of liquid bridge and fracture capillary pressure, which is not well discussed in the available literatures. In this research, by the aid of analogy between the diffusive flux and electrostatic potential, a new model for predicting evaporation rate from a liquid bridge inside a horizontal fracture is presented. The proposed model is then coupled with Young-Laplace equation to evaluate volume, shape and capillary pressure of liquid bridge as evaporation proceeds. Close agreement (R2 = 0.994) observed between model predictions and experimental data of evaporating liquid bridge, confirms reliability of the assumptions and the methodology made in model development. For the first time the impact of presence of solid substrate on evaporation rate as a function of liquid bridge volume, length and contact angle is described by a new mathematical expression. It has been found that transient behavior of fracture capillary pressure for a more realistic mode of evaporating liquid bridge, in which both contact angle and contact line change, indicates an initial increase, reaching to a maximum value, and finally a sharp decrease before rupture of bridge. In some cases, the capillary pressure of evaporating liquid bridge might reach to twice/half of its initial value. For liquid bridges with sufficient initial volume in thin fractures, stability period is prolonged and fracture capillary pressure values are greater, resulting a higher degree of capillary continuity. Results of this work help to better understand the gas-liquid transport in fractured porous media incorporating mass transfer between liquid bridge and surrounding gas for possible application in simulation models.

Evaporation driven detachment of a liquid bridge from a syringe needle in repose

In this paper, a study of the stability of an evaporating semi-unbounded axisymmetric liquid bridge that forms between a syringe needle tip and a horizontal interface by using both theory and experiments is presented. Here, the evaporation produces slow quasistatic motion such that it allows one to use hydrostatics to analyze interface profiles via solutions to the Young–Laplace equation. The two main parameters, in the hydrostatic limit, are the familiar Bond number and a slenderness parameter that often appears in the literature that studies liquid bridge stability. The axisymmetric Young–Laplace equation yields a semi-analytical solution for capillary pressure at zero Bond number using boundary conditions appropriate for this study. At finite Bond numbers, computation of interface profiles is used to estimate the maximum slenderness. Experiments using water for Bond numbers 0.01 < Bo < 0.1 show good agreement for the maximum slenderness when comparing those results with predictions based on solutions to the Young–Laplace equation.

De-pinning instability of an evaporating-bounded liquid bridge: Experiments and axisymmetric analysis

In this manuscript we examine the stability of an evaporating-bounded axisymmetric liquid bridge confined between parallel-planar similar substrates by using both theory and experiments. From classical stability analysis appearing in the literature it is now generally understood that a bounded liquid bridge stability diagram contains; a region of low slenderness where instability is caused by de-pinning; a region of low to large slenderness and small liquid bridge volume where axisymmetric minimum volume instabilities occur; and a low to large slenderness region with large liquid bridge volume where non-axisymmetric maximum volume instabilities are present. Under a quasistatic assumption we use hydrostatics via the Young–Laplace equation to estimate the minimum stable volume before either de-pinning or rupture occur for a range of axial and radial Bond numbers. To examine liquid bridge stability from the Young–Laplace equation for bounded-axisymmetric liquid bridges we analyzed zero capillary pressure solutions, and their transition, as stability limits. Observable trends show good agreement for critical behavior when comparing experiments and theory.

Modeling of capillary pressure in horizontal rough-walled fractures in the presence of liquid bridges

Capillary continuity between adjacent matrix blocks through formation of liquid bridge controls the recovery factor of gravity drainage process in fractured reservoirs. However, stability of liquid bridges as well as related capillary pressure in horizontal rough fractures is not well discussed in the available literature. In this work, new models of rough-walled fracture are developed and the role of roughness size and frequency on formation of liquid bridge and fracture capillary pressure are investigated. The Young-Laplace equation is numerically solved to characterize the liquid bridge formed in the proposed models of rough fractures. Critical fracture aperture for a range of liquid saturations, various roughness models and wettability conditions, is computed. Moreover, an expression is proposed to predict critical fracture aperture as a function of liquid saturation and contact angle for different models of rough fracture. Thereafter, as an interesting result, variation of fracture capillary pressure with liquid saturation, fracture aperture and wettability is evaluated for different models of rough fractures. It has been found that the trend of obtained fracture capillary pressure is similar to a typical matrix capillary pressure curve. The results also revealed that fracture capillary pressures as high as 1 psi (6.9 KPa) are viable when liquid saturation in the fracture is low (<5%) and fracture is sufficiently thin. Increasing wettability to liquid phase decreases the critical fracture aperture and enhances the fracture capillary pressure. At last, a semi-empirical model for capillary pressure as a function of effective fracture aperture, fracture roughness, contact angle and liquid saturation is proposed. The findings of this work help to better understand how liquid bridge stability and fracture capillary pressure may change in rough-walled horizontal fractures.

A novel method for the analysis of particle coating behaviour via contact spreading in a tumbling drum: Effect of coating liquid viscosity

Spray coating is a common method of distributing liquids over powders, especially in the pharmaceutical, detergent and food industries. During this process, liquid drops are deposited on the surface of particles. Liquid is then transferred between particles via particle collisions, in a process called liquid contact spreading. This contact spreading process facilitates inter-particle coating, in which wetting, de-wetting, mixing and drying are occurring simultaneously. This work presents the first experimental study of the mechanism of liquid contact spreading. In this work, a novel experimental method has been developed to investigate the mechanism of contact spreading, incorporating a newly developed image analysis technique, based on colourimetric measurements, to quantitatively determine coating behaviour via contact spreading.Here, experiments designed to isolate the contact spreading coating mechanism were performed in a tumbling drum using a model material system; alumina particles and dyed polyethylene glycol solutions of varying viscosities. The coating uniformity was quantified by the variation in inter-particle coating; the coefficient of variation (CoV). For all systems, the uniformity of the coating increased with time until the CoV decreased to an asymptotic value. The rate of the decrease in the CoV was successfully fitted using an exponential decay function.The viscosity of the coating solution had a significant effect on the rate of liquid transfer; the lower the viscosity the faster the contact spreading process. This effect is attributed to differences in the formation and stability of liquid bridges between the particles, influencing the extent of liquid transfer. The results also show that in most cases examined here, viscous forces play a main role in the contact spreading process, and the contribution of capillary forces are minimal. This understanding could assist with the design and scale up of wet coating processes.

Stability of liquid bridges with elastic interface

Experimental demonstration that the enhanced elastic response of the brine–crude oil interface under low-salinity conditions increase the stability of the oil–brine interface as shown by uniquely designed bridge experiments.

Stability of a liquid bridge under vibration.

We examine the stability of a vertical liquid bridge between two vertically vibrating, coaxial disks. Assuming that the vibration amplitude and period are much smaller than the mean distance between the disks and the global timescale, respectively, we employ the method of multiple scales to derive a set of asymptotic equations. The set is then used to examine the stability of a bridge of an almost cylindrical shape. It is shown that, if acting alone, gravity is a destabilizing influence, whereas vibration can weaken it or even eliminate altogether. Thus, counter-intuitively, vibration can stabilize an otherwise unstable capillary structure.

Liquid-bridge stability and breakup on surfaces with contact-angle hysteresis.

We study the stability and breakup of liquid bridges with a free contact line on surfaces with contact-angle hysteresis (CAH) under zero-gravity conditions. Non-ideal surfaces exhibit CAH because of surface imperfections, by which the constraints on three-phase contact lines are influenced. Given that interfacial instabilities are constraint-sensitive, understanding how CAH affects the stability and breakup of liquid bridges is crucial for predicting the drop size in contact-drop dispensing. Unlike ideal surfaces on which contact lines are always free irrespective of surface wettability, contact lines may undergo transitions from pinned to free and vice versa during drop deposition on non-ideal surfaces. Here, we experimentally and theoretically examine how stability and breakup are affected by CAH, highlighting cases where stability is lost during a transition from a pinned-pinned (more constrained) to pinned-free (less constrained) interface-rather than a critical state. This provides a practical means of expediting or delaying stability loss. We also demonstrate how the dynamic contact angle can control the contact-line radius following stability loss.

Static Stability of Liquid Bridges Between Matrix Blocks of a Gas Invaded Zone of Naturally Fractured Reservoirs

A large portion of oil and gas reservoirs in the world are located in naturally fractured reservoirs. Despite such importunity, the production mechanisms of these reservoirs are not completely well defined. Gas–oil gravity drainage that takes place in the gas-invaded zone of this type of reservoirs is one instance of such a weakness. The density difference between gas-filled fractures in contact with oil-saturated matrix blocks brings the oil out of the matrix blocks into the fracture. The drained oil can reach the production well through two different paths: continues fracture network and block-to-block path. These two different paths require different approaches to modeling of gravity drainage. Single-block approaches are used when drained oil only travels through the fracture network, which totally formulated before. But when oil prefers to travel through the matrix blocks, continuum approaches such as Darcy's law may not work in their basic forms any more. Liquid bridges and film that form in the horizontal fracture between matrix blocks usually transfer the wetting phase across the fracture. Stability condition and duration of stability can help better understanding of gravity drainage in stacks of blocks. In this article, the stability of liquid bridges between the matrix blocks studied and a minimum length of stability is predicated. The results show that this stable length of liquid bridges formed between adjacent matrix blocks is 2r0π, which is a function of the pore throat. This critical length can be used in modeling of capillary continuity and wetting phase transfer across matrix blocks.

Bridging transitions for spheres and cylinders.

We study bridging transitions between spherically and cylindrically shaped particles (colloids) of radius R separated by a distance H that are dissolved in a bulk fluid (solvent). Using macroscopics, microscopic density-functional theory, and finite-size scaling theory, we study the location and order of the bridging transition and also the stability of the liquid bridges, which determines spinodal lines. The location of the bridging transitions is similar for cylinders and spheres, so that at bulk coexistence, for example, the distance H_{b} at which a transition between bridged and unbridged configurations occurs is proportional to the colloid radius R. However, all other aspects, particularly the stability of liquid bridges, are very different in the two systems. Thus, for cylinders the bridging transition is typically strongly first-order, while for spheres it may be first-order, critical, or rounded as determined by a critical radius R_{c}. The influence of thick wetting films and fluctuation effects beyond mean field are also discussed in depth.

Liquid-bridge breakup in contact-drop dispensing: Liquid-bridge stability with a free contact line.

The static stability of weightless liquid bridges with a free contact line with respect to axisymmetric and nonaxisymmetric perturbations is studied. Constant-volume and constant-pressure stability regions are constructed in slenderness versus cylindrical volume diagrams for fixed contact angles. Bifurcations along the stability-region boundaries are characterized by the structure of axisymmetric bridge branches and families of equilibria. A wave-number definition is presented based on the pieces-of-sphere states at branch terminal points to classify equilibrium branches and identify branch connections. Compared with liquid bridges pinned at two equal disks, the free contact line breaks the equatorial and reflective symmetries, affecting the lower boundary of the constant-volume stability region where axisymmetric perturbations are critical. Stability is lost at transcritical bifurcations and turning points along this boundary. Our results furnish the maximum-slenderness stability limit for drop deposition on real surfaces when the contact angle approaches the receding contact angle.

Using Parabolic Flights to Examine Quantitatively the Stability of Liquid Bridges under Varying Total Body Force

Liquid bridges were flown aboard a Boeing 727-200 aircraft in a series of parabolic arcs that produced multiple periods of microgravity. During the microgravity portion of each arc, geff, the effective total body acceleration due to external forces became negligibly small so that cylindrical liquid bridges could be suspended across two coaxial support posts. Near the bottom of each arc, geff slowly increased to a maximum of 1.84g, causing the liquid bridges to deform and in some cases collapse. Although the physics of liquid bridges subject to varying total body force is well-established and has been analyzed extensively both theoretically and experimentally, specific hardware was designed to vary geff in a precise way that overcomes the gravity-related limitations and high g-jitter associated with parabolic flights. Bridge-stability was examined for axial and lateral orientations with respect to geff by measuring the slenderness ratio as a function of Bond number at the instant of bridge collapse. Results exhibit remarkable agreement with theory as well as with the experimental results obtained in a magnetic levitation-based experiment. The parabolic flight method offers technical originality and provides experimental insights for researchers in the microgravity field. Here we present hardware development, experimental considerations, and results, and demonstrate that parabolic flight is a viable alternative to extant techniques for quantitative experiments on fluids.

On the stability of a cylindrical liquid bridge

The problem of the stability of a liquid bridge stretched between parallel plates with a wetting contact angle of 90◦ is revisited. A closed form expression is derived for the height of the bridge, in terms of its volume, within which a cylindrical and various types of unduloidal equilibrium configurations can exist. For a given volume of the liquid and specified height of the bridge, the lateral surface of a uniform cylindrical bridge is smaller than the surface area of any unduloidal equilibrium shape. The lateral surface of the unduloidal shapes increases with the increase in the number of their inflection points. The force required to keep the bridge in equilibrium is evaluated in each case. All unduloidal equilibrium configurations are unstable, the only stable configuration being that of a cylindrical bridge whose height is less than one-half of its circumference. A lower bound estimate is also derived based on a simple energy consideration. The stretching force required for the equilibrium at the onset of instability is compared with its upper bound estimate. For a given height of the bridge, the force required to keep a cylindrical bridge in equilibrium is greater than the force required for equilibrium of any unduloidal configuration of the same height. The opposite is true for the capillary pressure.

An Experimental Investigation of Fracture Tilt Angle Effects on Frequency and Stability of Liquid Bridges in Fractured Porous Media

Liquid bridges are believed to play an important role in improving the recovery of fractured reservoirs. However, little is known about the stability of liquid bridges in fractured media at the pore scale. In this work, a glass micromodel representing a stack of two blocks was used at different tilt angles to monitor the frequency and stability of liquid bridges formed during free-fall gravity drainage as a function of tilt angle. It was observed that by increasing the tilt angle, the liquid bridge frequency decreased but its stability increased. This resulted in higher ultimate recovery. In addition, it was found that during the first half of the experiments, the number of bridges was higher but their stability was lower than during the second half of the tests. Moreover, no more than one stable liquid bridge was observed at tilt angles above 20°, and the bridge cross-sectional area was gradually decreased as the stability was maintained. A sequence of bridges that were formed and broken one after the other results in a higher drainage rate than a single bridge with stability equal to the overall stability of the sequence.

Stability of Liquid Bridges Between Coaxial Equidimensional Disks to Axisymmetric Finite Perturbations: A Review

This paper reviews the dynamics of breaking or oscillating axisymmetric liquid bridges, and estimates of the energy which is needed to break a liquid bridge. We consider a liquid bridge spanning two coaxial equal disks with sharp edges and held by surface-tension forces. The liquid volume is assumed to be conserved under perturbations, and the contact lines are pinned to the disk edges. The perturbations are finite and axisymmetric. An analysis is based on the one-dimensional models previously used in capillary jet theory and last several decades for study a liquid bridge dynamics. According to the scientific project JEREMI (Japanese and European Research Experiment on Marangoni Instabilities), the first stage of the space experiment on ISS will involve an isothermal liquid bridge with a gas blowing parallel to the axial direction of the bridge. The geometry corresponds to a cylindrical volume liquid bridge coaxially placed into an outer cylinder with solid walls. The gas enters the annular duct bounded by the outer cylinder and the internal system consisting of supporting vertical rods and the liquid bridge. Considering that the bridge is small (the rod’s radii are 3 mm) and the gas velocity is typically (0.25 ÷ 0.37) m/s, the perturbations cannot be considered small. Thus, one may assume that the amplitude of the liquid bridge perturbations is sufficiently large that departures from linearity must be considered.

Discrete microfluidics transfer across capillaries using liquid bridge stability

Discrete microfluidics offers distinct advantages over continuous microfluidics since the need for flow presents significant problems. Here, we demonstrate a method of achieving the gentle transfer of liquid samples between two capillaries with the use of air actuation which limits flow and is amenable to automation. Since the stability of liquid bridges is in operation, there is a relationship established between the gap distance and the liquid volume, thereby resulting in three physical response types that were identified. Only one of these allows for efficient liquid transfer. We advance a model for the optimal gap distance and show that it is in good agreement with the experimental data. During the process of liquid transfer, favorable mixing is also achieved.

Pore-Level Observation of Free Gravity Drainage of Oil in Fractured Porous Media

This work presents results from two sets of experiments conducted to study, in pore level, the role of fracture aperture and tilt angle on the stability of liquid bridges and the shape of a front during free gravity drainage process. Glass micromodels of two different aperture sizes were used to monitor the mechanism of gravity drainage of air–crude oil system, rotating around a bottom corner to create different tilting angles. Oil content within the matrix blocks was determined as a function of time using a series of images obtained during the experiments, from which net drainage rate from the upper and lower matrix blocks is calculated. Liquid bridges are more frequent but less stable at early time of drainage. The liquid bridges, which have widths as thin as 50 μm, can resist instability to maintain continuity. Liquid bridges formed in stacks with higher tilt angles are more stable, enhancing oil drainage from the upper matrix block and causing higher recoveries. Quantitative analysis of the results shows that a wider fracture aperture increases the oil production rate, but reduces the ultimate recovery. Furthermore, stacks with higher tilt angles present larger ultimate recoveries and smaller production rates. The front geometry in the lower block deviates from linearity due to formation of liquid bridges in the middle fracture. The results of this work can be helpful to better understand the interaction between fractures and matrix blocks.