Liquid Bridge Volume Research Articles

The simplification and analytical verification of the static liquid bridge force model for particle adhesion in inferior seedling substrates

This study examines the adhesion mechanism in varying water contents of inferior seedling substrate blocks, focusing on the adhesion between particles‒particles and particles‒wall of the seedling tray. A simplified static liquid bridge force model based on the Young–Laplace equation is proposed. The correlation between the liquid bridge force and volume is derived and validated against existing experimental. The results indicate that the static liquid bridge force between particles decreases as the distance increases. A critical distance region is identified, where below this distance, a smaller liquid bridge volume results in a greater static liquid bridge force, and beyond this, the trend reverses, except when the solid–liquid contact angle is 50°. Additionally, the solid‒liquid contact angle has a minimal influence on the liquid bridge force between the particles and the inner sidewall of the seedling tray. This study also analyses the change in critical rupture distance during the transition of liquid bridges from pendulum to ring rope type, and this change increases with the liquid bridge volume.

Shear characteristics of root–matrix composites under various interface friction and moisture content conditions

Analysing the composite's adhesion mechanism is necessary to gain a deep understanding of the pipeline blockage phenomenon encountered during negative pressure matrix removal. This study considers the interface suction and liquid bridge changes between the roots and the matrix. In particular, the liquid bridge volume and the interface's effective stress parameters were combined to establish a theoretical model of the shear strength of the root–matrix composite. The main factors affecting root–matrix composite adhesion stability were the root friction coefficient and the composite moisture content. Regarding the influence of the root friction coefficient, the surface structures of the primary and lateral roots were observed using a laser confocal microscope. Using the principal component analysis method, the main factors influencing the friction properties of the root system were identified as the taproot's maximum valley depth (Rv) and the average roughness (Ra) of the profile, as well as the lateral root's maximum peak-to-valley height (Rz) and the average roughness (Rq) of the lateral root profile. The influence of both the main and lateral roots cannot be overlooked when removing inferior seedlings from the substrate. Furthermore, the bond efficiency of the root–matrix composite was calculated, revealing values of 16.03%, 49.87%, and 58.31% under low, medium, and high moisture content conditions, respectively. Finally, direct shear tests were conducted on the complex under dry-wet-dry conditions, yielding an internal friction angle of 14.1656° and a cohesion force of 1.738 ± 0.3 kPa at a water content of 20% (dry-wet). In conclusion, it is recommended to perform the negative pressure removal of inferior seedling substrate blocks during the seedling stage with low water content and underdeveloped root systems. Related research lays the foundation for preventing blockages in negative pressure pipelines.

One-dimensional hydrodynamic model for the isothermal-evaporation of an axisymmetric-unbounded liquid bridge

In this manuscript, we examine the isothermal-evaporation of an unbounded axisymmetric liquid bridge confined between parallel-planar similar or chemically different substrates using both theory and experiments for axial Bond numbers 0.04 and 0.16. A perturbation analysis of the governing equations of motion produced a one-dimensional equation model, and this model made it possible to compute the interface profile evolution. Glass-acrylic or acrylic-acrylic substrate pairs (top-bottom) were used in experiments, with purified water as the liquid. Transient liquid-bridge volume estimates and contact angle data were extracted via image analysis at fixed time intervals and compared with results from the profiles that were computed using the one-dimensional equation model. There was good agreement when comparing the volume estimates and contact angle data.

Experimental investigations of liquid bridge rupture between a sphere and a spherical concave

The formation and rupture of liquid bridges between solid surfaces have widespread applications in micro gripping, self-alignment, and particles wetting. The axisymmetric liquid bridge rupture between a sphere and a spherical concave is systematically investigated in this study. Detailed analysis was conducted to examine the effects of the radius ratio, liquid bridge volume, and contact angles on the rupture distance and transfer ratio. When the radius ratio is smaller than 2, it exerts a substantial impact on the rupture distance and transfer ratio. The experimental studies support the effectiveness of the simulation modeling based on a minimal energy approach. Theoretical findings of the shooting method and simulated results exhibit great agreement. The maximum absolute errors for rupture distance and transfer ratio were 0.001 and 0.0175, respectively. The simulated and theoretical results are helpful to predict the rupture distance and transfer ratio.

Agglomeration behavior of the dense medium in a gas–solid separation fluidized bed

In this study, the atomic force microscopy (AFM) was used to measure the micro-forces between different particles and study the influence of different operating parameters on the formation of particle clusters in the gas–solid fluidized bed separation process. In this way, the mechanism of liquid bridge formation and fracture can be elucidated, thereby providing a theoretical basis for inhibiting the formation of particle clusters. The results indicated that for relative humidity (RH) < 40%, the extrusion liquid bridge is the dominant factor for the formation of the particle liquid bridge, and the liquid film thickness, h, and liquid film volume, Vsq, vary linearly with RH; however, once the RH is > 40%, these relationships become nonlinear. The adhesion force between magnetite powder particles was found to be the largest and that between pulverized coal particles was found to be the smallest, with the mixture of the two particle types being in between. Further, the adhesion between particles increased monotonically with RH, while showing a maximum value with increasing particle separation. A theoretical analysis of the critical fracture distance, Drupture*, of the particle liquid bridge showed that, as the liquid bridge volume, V*, and contact angle, θ, increase, Drupture* gradually increases, but its rate of increase rate. The theoretical analysis was found to be largely consistent with the experimental data, only deviating at low RH.

Creating lifting force in liquids via thermal gradients

In this paper, we explore a concept and present the first experimental evidence to show that it is possible to form a stable liquid film and create lifting force at the interface via thermal gradient to minimize interfacial rubbing of surfaces and the associated wear. The approach is based on manipulating the flow behavior via thermocapillary, which describes how a liquid can be made to flow from warm to cold regions purely by inducing a thermal gradient. We show that liquid bridges between two parallel plates can be manipulated and stabilized under a combined effect of the thermocapillary flow and the Couette flow, which describes the motion of a viscous fluid between two parallel plates in a relative sliding motion. The equilibrium stage is confirmed under different experimental conditions of a thermal gradient, interfacial gap, liquid viscosity, and liquid bridge volume. A strategy is proposed to control liquid motion and create lifting force between two plates. A theoretical model is also presented to illustrate the principle of the equilibrium stage. Creating lifting forces at the interface offers a new thermo-hydrodynamic tool for manipulating liquids behavior. This approach has the potential for controlling liquid motion in mechanical components and nature.

Investigation of the influence of impact velocity and liquid bridge volume on the maximum liquid bridge length

Several models exist to predict the capillary forces due to liquid bridges during static particle contacts. However, for dynamic impacts, there is still a lack of knowledge to accurately describe the geometry and rupture of liquid bridges. This is essential in order to calculate correctly the energy dissipation in numerical models. Therefore, the liquid bridge volume during the rebound phase of collision, the restitution coefficient, the rupture time and the maximum liquid bridge length were analyzed for a wide range of contact velocities from 0.0001to4.0 m∙s−1. To perform experiments at different velocities three experimental setups were developed. First, free-fall experiments with spherical particles colliding on a glass pane covered with a water layer were performed at different impact velocities from 0.3 to 1.5 m∙s−1 and water layer thicknesses. Secondly, a pneumatic setup was developed for investigating the maximum liquid bridge length at constant liquid bridge volume and contact velocities from 0.3 to 4.0 m∙s−1. A third setup was used to investigate the liquid bridge behavior during low velocities from 0.0001 to 0.04 m∙s−1. Based on the experimental results, a new model is presented to account for the significant influence of impact velocity on the maximum liquid bridge length.

Wet Adhesion of Soap Bubble Bridge between Two Curved Surfaces

Wet adhesion phenomenon of the soap bubble bridge is widespread in the climbing behaviors of geckos and insects, and the surface shapes generally have important impact on the adhesion behavior of soap bubble bridge. In order to focus on the effect of the shape on the wet adhesion, we study the adhesion behavior between two rigid surfaces containing different shapes such as concave, flat, and convex. For a given soap bubble bridge, the relationship between adhesion force and separation is numerically calculated, and the corresponding configuration of soap bubble bridge is also given. The results show that the adhesion force of soap bubble bridge decreases with the increase of separation. This trend is the same as the case of liquid bridge, although the volume of liquid bridge is constant while the volume of soap bubble bridge varies. The adhesion force with concave rigid surfaces is bigger than that of the other two kinds of rigid surfaces at the same separation. The wetting radius of the soap bubble bridge decreases with the increase of separation. The appearance of this phenomenon results from the equation of state for the gas in the soap bubble bridge. This research may improve the understanding of the mechanical mechanism of wet adhesion.

Surface Evolver Simulation of Droplet Wetting Morphologies on Fiber Without Gravity

Droplet wetting phenomenon is encountered in many engineering applications. Three wetting morphologies, namely, barrel, clamshell, and liquid bridge, are investigated by the finite element method, Surface Evolver (SE) simulations. The barrel shape shrinks gradually as contact angle increases. In the shrinkage process, the dimensionless wetting length reduces, and maximum diameter increases. As the increase of the contact angle, the gas–liquid contact line of clamshell droplets bends and contracts inward gradually. The geometry parameters are extracted from the results from simulations. In addition, the critical spacing of liquid bridge rupture is determined. The critical spacing increases rapidly with the expanding of liquid bridge volume. The liquid bridge volume has a significant effect on critical spacing.

Effect of liquid size on vertical liquid bridge freezing

Liquid bridge solidification has important applications in industry. In this paper, the solidification process of vertical axisymmetric liquid bridges between two horizontal discs is numerically simulated with the effects of supercooling and gravity. The mathematical model consists of two parts: one is to use the equivalent heat capacity method to obtain the thermophysical properties and ice mass fraction of the liquid bridge after recalescence, and the other is to solve the Young-Laplace equation to obtain the geometric profile of liquid bridge. The simulated results of freezing front evolution and freezing time are in good agreement with the experiment. It is found that there are two dramatical temperature drops during the freezing process, respectively, corresponding to the initial freezing and the complete freezing of the liquid bridge. Higher disc temperature, larger liquid volume or higher liquid bridge decreases the temperature cooling rate and the development of freezing front height, thus prolonging the freezing time. A correlation is established for estimating the freezing time with the use of simulation results. The disc temperature and the liquid bridge height show more significant influence on the freezing process than the liquid bridge volume.

An improved model for predicting the critical velocity in the removal of hydrate particles from solid surfaces

Understanding the critical velocity at which hydrate particles can be removed from a solid surface is crucial for flow assurance issues. An improved model is proposed to predict the critical velocity in hydrate particle removal process by considering a deformed liquid bridge. In situ experiments were performed for validation, and it was observed that hydrate particle decomposition occurred during the removal process. The particle diameter was determined to be a more dominant factor influencing the critical velocity than the initial liquid bridge volume. The resulting confidence level was 95% within a 30% error, showing its robust capability for engineering applications.

Separation efficiency of liquid–solid undergoing vibration based on breakage of liquid bridge

Vibrating separation is a significant method for liquid–solid separation. A typical example is the vibrating screen to dewater wet granular matter. The properties of granular matter and the vibrating parameters significantly affect the separation efficiency. This study investigates the effect of vibration parameters in separation based on the breakage of large-scale liquid bridge numerically by using a calibrated simulation model. Through analysing the simulation results, the liquid bridge shape and the volume between two sphere particles for various particle sizes and particle distances were studied in the static condition under the effect of gravity. The results show a general reducing trend of liquid bridge volume when the radius ratio of two particles increases, particularly when the ratio increases to 5. Additionally, a set of vibrating motion was applied to the liquid bridge in the simulation model. A group of experiments were also performed to validate the simulation model with vibration. Then, the effect of vibrating peak acceleration, distance between spheres and radius on the separation efficiency which was reflected by the residual water were investigated. It is found that separation efficiency increased obviously with the peak acceleration and the increase slowed down after the peak acceleration over 1 m/s2.

Capillary Forces between Concave Gripper and Spherical Particle for Micro-Objects Gripping.

The capillary action between two solid surfaces has drawn significant attention in micro-objects manipulation. The axisymmetric capillary bridges and capillary forces between a spherical concave gripper and a spherical particle are investigated in the present study. A numerical procedure based on a shooting method, which consists of double iterative loops, was employed to obtain the capillary bridge profile and bring the capillary force subject to a constant volume condition. Capillary bridge rupture was characterized using the parameters of the neck radius, pressure difference, half-filling angle, and capillary force. The effects of various parameters, such as the contact angle of the spherical concave gripper, the radius ratio, and the liquid bridge volume on the dimensionless capillary force, are discussed. The results show that the radius ratio has a significant influence on the dimensionless capillary force for the dimensionless liquid bridge volumes of 0.01, 0.05, and 0.1 when the radius ratio value is smaller than 10. The effectiveness of the theorical approach was verified using simulation model and experiments.

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.

Stretching and rupture of a viscous liquid bridge between two spherical particles

AbstractIn this paper, the stretching and rupture of liquid bridge are studied by experiment and numerical simulation. In the experiment, the relationship between the critical rupture distance of the liquid bridge and four factors, including volume of liquid bridge, particle initial distance, liquid bridge stretching velocity and liquid bridge viscosity, is quantitatively studied. It is found that the liquid bridge critical rupture distance can be described by the modified Bond number, where the critical distance shows a maximum value when this number is about 0.6. As the Capillary number of liquid bridge increases, the effect of the liquid bridge stretching velocity on the critical rupture distance increases, while the influence of the liquid bridge viscosity on the critical rupture distance increases with the volume of liquid bridge. Mesh overset is used to describe the profile change of liquid bridge, and based on the simulation the pressure field is applied in calculating the capillary fore in the liquid bridge. The rupture energy of liquid bridge can be mainly related with the Capillary number, showing two different functions when Ca = 0.01 is the turning point. Finally, two empirical formulas are proposed to predict the rupture energy of liquid bridge.

Numerical simulation of semi-dry desulfurization spouted bed using the discrete element method (DEM)

A research on semi-dry FGD technology using CFD-DEM method is conducted to study the motion of wet particles and their performance on SO2 remove. The liquid bridge force model proposed by Mikami (1998) et al. is introduced to estimate the interactionamong wet particles. The reaction rate of desulfurization is calculated depended on the two-film theory. The profiles of particle volume fractions, velocities and the main forces on particles are obtained. Simulation results indicate that liquid bridge force facilitates the formation of particle aggregation. Meanwhile, the distributions of particles are more inhomogeneous, which result in a decrease on SO2 removal efficiency. Furthermore, the effect of humidity on the desulfurization is also investigated by adjusting the parameter of dimensionless liquid bridge volume. As the humidity increases, the agglomerate grows and the SO2 removal efficiency increases first and gradually decreases. Simulation results of SO2 removal efficiency are in a good agreement with the experimental data from Kunio Kato (1999) et al.

Improved analytical energy balance model for evaluating agglomeration from a binary collision of identical wet particles

Particle agglomeration is a common phenomenon in a large number of industries. The presence of a liquid bridge between colliding wet particles is the principal source of agglomeration in such processes as wet granulation and thermal conversion of fuels in a high temperature gas–solid fluidized bed reactor. A comprehensive agglomeration model for wet particles must incorporate both liquid capillary and viscous contributions, as well as the liquid bridge volume effect. Darabi et al. (Chem. Eng. Sci. 64 (2009) 1868–1876) developed a coalescence model for a binary collision of identical wet particles. The model provides reasonable results for wet particles with a low viscosity liquid layer, i.e., under capillary limiting conditions. However, application of this model for collisions of particles coated with a high viscosity liquid layer, i.e., under viscous limiting conditions, results in unreliable outcomes. The current study presents an improved version of Darabi et al.’s model, which (i) corrects viscous energy loss equations in the original model, thus providing reasonable outcomes under both capillary and viscous limiting conditions with highly wetting systems, (ii) accounts for the contribution of capillary force in the approach stage when estimating the initial particle speed for the separation stage, (iii) accounts for the collision of particles having different initial speeds with respect to the laboratory reference frame, (iv) employs a more reliable correlation to estimate the liquid bridge rupture distance, and (v) evaluates the collision outcome in three steps based on the values of kinetic energy parameters. We compared experimental particle-plate collision data with the predictions from agglomeration models and it showed that considering the liquid bridge volume effect and the liquid bridge rupture distance can be essential for the accurate prediction of collision outcomes. The results of sensitivity analyses with the improved agglomeration model revealed that the agglomeration outcome under capillary limiting conditions is most sensitive to the thickness of the coating layer, particle inertia, liquid surface tension, and dry restitution coefficient. Under viscous limiting conditions, proper measurement or estimation of the thickness of the coating layer, liquid viscosity, asperity height, and particle inertia are critical for evaluating the particle collision outcome.

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.

Stress wave in monosized bead string with various water contents

Wet granular materials exhibit unique physical and mechanical properties, especially in relation to wave propagation, which is quite different from dry granular materials. In this paper, by introducing the capillary bridge force into the discrete element method, the stress wave in mono-sized bead string with various water content has been studied. First the vibration of two particles with liquid bridge has been analyzed. The presence of the liquid bridge force causes the kinetic response of the particles to exhibit completely different properties than that of the dry particles. The equilibrium position is affected by both the physical properties of the particles and the liquid bridge properties. Then the wave propagation behaviors in a mono-sized bead string have been analyzed. According to whether the liquid bridge volume has an effect on granular motion, the whole process can be divided into two stages. Stage I, particles are physically contacted with each other directly. The influence of liquid bridge force is independent of the bridge volume. Stage II, particles start to oscillate back and forth at their equilibrium positions, the influence of the liquid bridge force becomes related to the bridge volume. The kinetic energy dissipation first decreases and then increases. A U-shaped trend appears throughout the dissipation process. In our work, the mechanical properties of wet granular materials are studied from two levels: particle vibration and wave propagation, which will provide theoretical guidance for the application of granular materials in aqueous environment.

Dynamic fracture behaviour and evolution mechanism of soft coal with different porosities and water contents

Determining the effect of water content and porosity on the dynamic mechanics of soft coal is a key problem in reinforcing soft coal seams by water injection. In this study, soft coal specimens with different water contents and porosities were successfully prepared and tested using a Split Hopkinson Pressure Bar (SHPB). The results show that the effect of water content on the strength of soft coal can be divided into two stages based on the critical point of optimum water content. With the effects of increasing porosity, the optimum water content gradually increased, while the peak strength corresponding to the optimum water content gradually decreased. In addition, based on the analysis of the dynamic failure process of the coal recorded using a high-speed camera, the dynamic mechanical model varies with the distance, and the liquid bridge volume between particles was established according to the water-bearing unequal spheres models. Moreover, the mechanism of the effects of porosity and water content on the fracture expansion and dynamic strength of soft coal were further discussed.