Capillary Forces between Two Spheres with a Fixed Volume Liquid Bridge: Theory and Experiment

The capillary bridge between two spheres: New closed-form equations in a two century old problem

A detailed understanding of the mechanistic role of solid surface microstructures in modulating capillary forces and liquid transport in liquid bridge systems is crucial, for liquid bridges between rough surfaces are omnipresent in nature and various industries. In this work, Gibbs free energy expression was derived for a liquid bridge system confined between a smooth surface and a microstructured surface, based on the principle of minimum thermodynamic potential. Furthermore, by analyzing the energy conversion during spacing variation between the two solid surfaces, an analytical expression for the capillary force of the liquid bridge was derived that incorporates the geometric parameters of the microstructures and the contact angle. Finally, numerical simulations were performed using the Fluent UDFs (User-Defined Functions) to validate the proposed capillary force model. The simulation results validated the analytical expression and revealed the influence of the microstructures on the force distribution on the upper and lower surfaces of the liquid bridge, and on the droplet transport performance.

The angle of repose does affect the behavior of granular materials and has a wide range of applications. The addition of a small amount of liquid can dramatically change the properties of granular media, leading to an increase in the repose angle. This change is mainly attributed to the capillary force resulting from the liquid bridge when the small amount of water was introduced. The capillary force as an attractive force increases the interaction between particles and becomes a dominant factor affecting the angle of repose because it is usually stronger than gravity. In this paper, a new discrete element method (DEM) model was developed in which the capillary force was calculated by the liquid bridge model based on toroidal approximation. The developed DEM model linked the microscopic liquid bridge volume to the macroscopic water content and it also considered the effect of liquid bridge breakage and formation on capillary force. The numerical model was first validated by comparing the experimental and numerical results. Then, the effects of surface tension, volume of the liquid bridge, and the contact angle are studied numerically. Finally, the empirical equation between water content and angle of repose is given under the present simulation conditions. This work will provide a deep understanding for the effect of capillary on the angle of repose.

Study of cyclic waterflooding for improving oil recovery in Lukeqin heavy oil reservoir

Effects of the interaction between neighboring droplets on the stability of nanoscale liquid bridges

Pendular bond strength between unequal-sized spherical particles

Microscale study of particle agglomeration in oil-based food suspensions: The effect of binding liquid

The present article discusses the transient method of calibrating capillary gas flow meters which involves the application of a type of manometric flow meters, which measure the release of a substance by registering changes in the differential pressure on a measuring element. The measurement methodology presented in the article is but a concept proposing actions and calculations aimed at determining the calibration coefficient of a section of a measurement capillary in an outstandingly simple manner. This method is dedicated to capillary flow meters with very small gas flow rates. Calibrating flow meters by means of the transient method involves registering changes in the differential pressure on both ends of a capillary tube while gas flows out of a measuring burette, through a calibrated capillary tube, to be released into the atmosphere. On the basis of a combination of the Hagen–Poiseuille equation and the ideal gas law, a relationship describing the phenomenon of a gas flow through a capillary tube was formulated, which, in turn, served as a basis for determining the calibration coefficients of the two capillary sections measuring 10 cm and 40 cm, with an internal radius of 0.015 cm. The calibration processes of both capillary sections were conducted for 21 different temperature values, using methane. The obtained values of calibration coefficients were juxtaposed with their model values obtained via calculation. The relative differences between the calibration-obtained values and model values did not exceed 7.65% and 4.83% in the case of the 10 cm capillary tube and the 40 cm capillary tube, respectively.

The stability of an isothermal liquid mass of constant properties (density and surface tension) held by capillary forces between two solid disks placed a distance L apart (the so-called liquid bridge model) is considered. For a weightless liquid bridge that is a right circular cylinder, the well-known Rayleigh stability limit holds, and the liquid column becomes unstable when its length is larger than its circumference. Many perturbations from this ideal configuration have been studied in the past, but the supporting disk shape has always been assumed circular. In this Brief Communication the influence of noncircular supports on stability limits of almost cylindrical liquid bridges is analyzed through an asymptotic analysis. Closed form expressions for the stability limits are presented.

Capillary bridge is a common phenomenon in nature and can significantly contribute to the adhesion of biological and artificial micro- and nanoscale objects. Especially, it plays a crucial role in the operation of atomic force microscopy (AFM) and influences in the measured force. In the present work, we study the rupture kinetics and transition pathways of liquid bridges connecting an AFM tip and a flat substrate during a process of pulling the tip off. Depending on thermodynamic conditions and the tip velocity, two regimes corresponding to different transition pathways are identified. In the single-bridge regime, the initial equilibrium bridge persists as a single one during the pulling process until the liquid bridge breaks. While, in the multibridge regime the stretched liquid bridge transforms into an intermediate state with a collection of slender liquid bridges, which then break gradually during the pulling process. Moreover, the critical rupture distance at which the bridges break changes with the tip velocity and thermodynamic conditions, and its maximum value occurs near the boundary between the single-bridge regime and the multibridge regime, where the longest range capillary force is produced. In this work, the effects of tip velocity, tip size, tip-fluid interaction, and humidity on rupture kinetics and transition pathways are also systematically studied.

a Steady spacecraft acceleration f Liquid fill fraction in the tank M Mass of a nearby spacecraft B Bond number Bgg Ratio of gravity gradient and capillary effects Bng Ratio of nearby-spacecraft and capillary effects Bsg Ratio of self-gravitation and capillary effects G Universal gravitational constant, 6.6742× 10−11m3 kg−1 s−2. Pa Pressure difference due to acceleration Pc Pressure difference due to capillary effects Png Pressure difference due to a nearby spacecraft Pgg Pressure difference due to gravity gradient Psg Pressure difference due to self-gravitation Rorb Orbital radius around Earth RT Radius of the spherical tank ∆ Separation distance ρ Mass density of the liquid propellant σ Surface tension of the liquid propellant Ω Orbital period around Earth

Numerical study of gravity-driven droplet displacement on a surface using the pseudopotential multiphase lattice Boltzmann model with high density ratio

We consider a homogeneous chain of spheres linked by liquid bridges under tension. The rupture of a single liquid bridge leads to a fragmentation cascade driven by the inverse relation between the capillary force and the sphere distances. The initial length of the liquid bridges determines the number and size of the fragments and the velocity of the fragmentation front.

When a hot solid particle is submerged into an ambient fluid near a free liquid-gas interface, a non-uniform temperature field around the particle produces surface tension gradients at the interface and generates thermocapillary flow in the surrounding fluid. This flow sets the particle itself in motion towards or away from the interface. In the first part of the paper, the interaction between a hot spherical solid particle and a plane undeformable liquid-gas interface is studied. The velocity of the thermocapillary induced motion of the solid particle is proportional to the surface tension gradient at the liquid-gas interface, and is calculated in the approximation of the Stokes flow and a zero Peclet number as a function of the separation distance between the particle and the interface. The asymptotic cases of both small and large separation distances are studied. In the second part of the paper, the interaction between a hot solid sphere and a gas bubble submerged into an ambient fluid is studied in the limiting case when the separation distance between them tends to zero. The velocity of a pairwise migration of a particle and a bubble in contact is calculated as a function of their radius ratio. The asymptotic values of the individual velocities of a solid particle and a gas bubble in near contact are also computed. The relative velocity of their motion towards each other is found to be proportional to the separation distance between them. In the third part of the paper, we investigate the effect of gravity on the thermocapillary driven motion of a solid particle for the two cases. It is shown that due to the thermocapillary interaction, a particle can move against the buoyancy forces.

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