Line Motion Research Articles

Validation of a phase-field approach for contact line hysteresis against a sloshing droplet case

AbstractUnderstanding liquid propellants behavior in microgravity conditions is critical for efficient spacecraft design. For a number of operations, ranging from engine restart to orbital propellant storage and transfer, insight is needed to characterize capillary-dominated flows. In such conditions, surface tension and wetting properties, including contact angle hysteresis, can greatly impact the fluid’s behavior and therefore spacecraft performance. Using experimental data from ESA Propulsion Laboratory, a contact line model for the Cahn–Hilliard phase-field method is validated. The case studied is that of a droplet confined between two oscillating plates, which aims to isolate and observe contact angle-driven physics, limiting the effect of gravity on the flow in a simple and reproducible way on ground. The contact line model allows for the prediction of contact line motion without requiring the computation of dynamic contact angles or contact line velocities, thus simplifying implementation and reducing computational overhead. For the validation, contact line pinning and motion under varying oscillation frequencies is investigated. Specifically, the length between the rear and front contact line edges, as well as the shape of the sloshing droplet are compared. The results show good agreement between simulations and experimental data, confirming the model’s accuracy in predicting contact line behavior and pinning.

Comparison of Contact Angle Models in Two‐Phase Flow Simulations Using a Conservative Phase Field Equation

ABSTRACTIn phase field methods based on a second‐order Allen‐Cahn (AC) equation, contact angles are prescribed mostly via a geometric formulation. However, it is of great interest to utilize the surface‐energy formulation, which is often employed in the Cahn‐Hilliard (CH) phase field method, in the AC phase field method. This article thus put forward a surface‐energy formulation of contact angles. The model was compared with the geometric one in a number of impact problems, including both normal and oblique impacts. The governing equations were discretized using a finite difference method on a half‐staggered grid. The Navier–Stokes equation was tackled using an explicit projection method. The major findings are as follows. First, the geometric model can maintain a fixed contact angle throughout contact line motion, while the surface‐energy one predicts a changeable contact angle, with a fluctuation of about 5°. In the oblique drop impact, contact angle hysteresis was captured even if a static contact angle was applied in the surface‐energy formulation.

Influence of wettability and surface tension on bubble formation from a needle

AbstractThe multiphase flow accompanied by contact line motion is a common flow phenomenon in nature and industry. When investigating the bubble formation from a needle, it is generally assumed that the contact line is fixed at the inner diameter of a needle. Namely, the influence of contact line motion on bubble formation is ignored. In this paper, the effects of wettability and surface tension on the characteristics of bubble formation were studied using volume of fluid method. The changes of bubble volume, instantaneous contact angle, contact line radius, and the motion mechanism of contact line were analyzed in detail. It is found that when surface wettability and/or surface tension are different, the motion type of contact line during bubble formation is different, and the stage of bubble formation shows a great difference too. The motion of contact line is mainly affected by the pressure inside a bubble, the adhesion force, and the hydrostatic pressure of liquid outside a bubble. The sum of all forces driving contact line to move inward or outward controls the motion type of contact line.

Observation of super-Alfvénic slippage of reconnecting magnetic field lines on the Sun

AbstractSlipping motions of magnetic field lines are a distinct signature of three-dimensional magnetic reconnection, a fundamental process driving solar and stellar flares. While being a key prediction of numerical experiments, the rapid super-Alfvénic field line slippage driven by the ‘slip-running’ reconnection has remained elusive in previous observations. New frontiers into exploring transient flare phenomena were introduced by recently designed high cadence observing programs of the Interface Region Imaging Spectrograph (IRIS). By exploiting high temporal resolution imagery (~2 s) of IRIS, here we reveal slipping motions of flare kernels at speeds reaching thousands of kilometres per second. The fast kernel motions are direct evidence of slip-running reconnection in quasi-separatrix layers, regions where magnetic field strongly changes its connectivity. Our results provide observational proof of theoretical predictions unaddressed for nearly two decades and extend the range of magnetic field configurations where reconnection-related phenomena can occur.

From Newton's First Law to the Motion of Celestial Bodies

Newton's original work "Principles" was written in Latin. An English version translated two years after his death changed the first law from "in directum" to "in a right line." Later generations think that only static or uniform straight line motion is inertia, while excluding rotational motion. This article proposes that the gravitational potential energy of a planet's revolution is equal to its centrifugal kinetic energy (mυ2). The work done by an object is a process quantity, but kinetic energy is a state variable that can be divided into instantaneous kinetic energy and average kinetic energy. Uniform motion does not do work, and instantaneous kinetic energy in variable speed motion does not also do work, only the average kinetic energy of variable speed motion does work. Only the energy between work and the average kinetic energy of variable speed motion can be converted into each other. We have clarified the relationship between work and kinetic energy, completed the transition of the kinetic energy formula at low and high speeds, achieved the unification of the kinetic energy formula and the mass energy relationship formula, and explained the √2 factor in the escape velocity..

Topology transition description of horseshoe vortex system in juncture flows with velocity characteristic lines

Particle image velocimetry and numerical simulation results of juncture flows were analyzed to parametrically investigate topology transition. The vortex system evolutions from non-vortex to multi-vortex with variations in obstacle bluntness, obstacle width, flow velocity and boundary layer thickness are discussed from the perspective of velocity characteristic lines. The velocity characteristic lines of u=0, v=0, and ∇2v=0 are adopted to describe the vortex system evolution. The motions of the characteristic lines with juncture flow parameters are described in detail, and the corresponding reflections of the vortex system patterns are illustrated. A panoramic picture of the development of velocity characteristic lines corresponding to the HSV topology transition from a non-vortex to a multi-vortex system with variations in the juncture flow parameter is established. Two methods for determining the attachment/separation pattern of the most upstream singularity are proposed. One method is based on the number of intersections of the u=0 and v=0 velocity characteristic curve lines, and the other is based on the relative positions of the most upstream feet of the u=0 and v=0 loop curves with both feet attached to the wall.

Synchronization phenomenon in a vibrating system driven by four eccentric rotors mounted in the orthogonal plane

The engineering application of vibration synchronization of multiple eccentric rotors (ERs) with the same rotational plane in far resonance is limited due to the constraints of motion characteristics and resultant force cancellation. Therefore, a dynamic model of four ERs distributed in two orthogonal planes is proposed in this paper, which is designed to increase the excitation force and drive the vibrating body to achieve the motion in a straight line. Based on the governing equation corresponding to the dynamic model firstly, the synchronous condition of four ERs and its stability condition are deduced. Then, the phase relationship of four ERs is obtained by numerical analysis, and the resultant force of four ERs in each phase difference is further studied to determine the motion trajectory of the vibrating body. Lastly, theoretical results are verified by four sets of experiments, which show that there are two stable motion states of the system. In each motion state, the resultant force of four ERs is increased compared to two ERs, and the system also moves in a straight line. Therefore, the model presented in this paper can provide a theoretical basis for designing large vibration machinery.

Freezing and Capillarity

Ice structures such as accretion on airplanes, wires, or roadways; ice falls; ice stalactites; frozen rivers; and aufeis are formed by the freezing of capillary flows (drops, rivulets, and films). To understand these phenomena, a detailed exploration of the complex coupling between capillary flow and solidification is necessary. Among the many scientific questions that remain open in order to understand these problems are the confinement of the thermal boundary layer by the free surface, the interaction between a freezing front and a free surface, the effect of freezing on the contact line motion, etc. This review focuses mainly on water and ice, discussing the theoretical framework and recent developments in the main areas of the freezing–capillarity interaction. The text deeply explores the freezing of a moving drop or a rivulet and the fundamental problem of wetting water on ice. Additionally, it highlights some of the main open questions on the subject.

Precursor-film-driven ultra-early depinning of the three-phase contact line

Hypothesis: Despite its importance in colloid and interface science, contact line pinning remains poorly understood, especially in the presence of a precursor film. We hypothesized that this is due to a lack of an experimental method capable of directly observing their physics at the nanoscale. MethodsUsing coherence scanning interferometry, we visualized the three-dimensional behavior of contact lines with a precursor film near a nanogroove structure composed of flat terrace surfaces and steps with an inclination angle of 30° while achieving nanoscale vertical resolution. FindingsWe found that even when the contact line is pinned at the edge of the step, the precursor film is not and advances beyond the edge. Furthermore, we discovered that the precursor film has two distinct effects on contact line motion. Specifically, the precursor film facilitates depinning when the contact line descends the step — a contact angle change was 0.9°, only 3.0% of the value predicted by a classical theory of contact angle at a solid edge. This ultra-early depinning is attributed to the formation of a new liquid film past the edge, driven by the progression of the precursor film that overcomes the pinning effect. In contrast, when the contact line ascends the step, the precursor film acts as a resistance to movement due to steric interaction.

A novel procedure to automate the removal of PLI and motion artifacts using mode decomposition to enhance pattern recognition of sEMG signals for myoelectric control of prosthesis

Hand Movement Recognition (HMR) with sEMG is crucial for artificial hand prostheses. HMR performance mostly depends on the feature information that is fed to the classifiers. However, sEMG often captures noise like power line interference (PLI) and motion artifacts. This may extract redundant and insignificant feature information, which can degrade HMR performance and increase computational complexity. This study aims to address these issues by proposing a novel procedure for automatically removing PLI and motion artifacts from experimental sEMG signals. This will make it possible to extract better features from the signal and improve the categorization of various hand movements. Empirical mode decomposition and energy entropy thresholding are utilized to select relevant mode components for artifact removal. Time domain features are then used to train classifiers (kNN, LDA, SVM) for hand movement categorization, achieving average accuracies of 92.36%, 93.63%, and 98.12%, respectively, across subjects. Additionally, muscle contraction efforts are classified into low, medium, and high categories using this technique. Validation is performed on data from ten subjects performing eight hand movement classes and three muscle contraction efforts with three surface electrode channels. Results indicate that the proposed preprocessing improves average accuracy by 9.55% with the SVM classifier, significantly reducing computational time.

Theoretical model of dynamics and stability of nanobubbles on heterogeneous surfaces

Surface nanobubbles have revealed a new mechanism of gas–liquid–solid interaction at the nanoscale; however, the nanobubble evolution on real substrates is still veiled, because the experimental observation of contact line motions at the nanoscale is too difficult. HypothesisThis study proposes a theoretical model to describe the dynamics and stability of nanobubbles on heterogeneous substrates. It simultaneously considers the diffusive equilibrium of the liquid–gas interface and the mechanical equilibrium at the contact line, and introduces a surface energy function to express the substrate’s heterogeneity. ValidationThe present model unifies the nanoscale stability and the microscale instability of surface bubbles. The theoretical predictions are highly consistent to the nanobubble morphology on heterogeneous surfaces observed in experiments. As the nanobubbles grow, a lower Laplace pressure leads to weaker gas adsorption, and the mechanical equilibrium can eventually revert to the classical Young-Laplace equation above microscale. FindingsThe analysis results indicate that both the decrease in substrate surface energy and the increase in gas oversaturation are more conducive to the nucleation and growth of surface nanobubbles, leading to larger stable sizes. The larger surface energy barriers result in the stronger pinning, which is beneficial for achieving stability of the pinned bubbles. The present model is able to reproduce the continual behaviors of the three-phase contact line during the nanobubble evolution, e.g., “pinning, depinning, slipping and jumping” induced by the nanoscale defects.

An axiom system for absolute plane geometry in terms of collinearity and congruence

AbstractWe present an axiom system in terms of collinearity and congruence for plane geometry independent of assumptions about parallels. The line reflections and motions of corresponding geometries are studied, and it is shown that the axiom system characterizes the non-elliptic metric planes in the sense of Bachmann with midpoints. If the hyperbolic axiom is added, we show that the familiar algebraic models of hyperbolic planes result.

The role of an in-plane electric field during the merging formation of spherical tokamak plasmas

Axial merging of two torus plasmas is utilized as a center-solenoid free start-up scheme for a high-beta spherical tokamak (ST) plasma, in which magnetic reconnection under a strong guide field plays dominant roles in energy conversion and equilibrium formation. The ion heating source in magnetic reconnection is the plasma outflow with E×B drift velocity in the downstream region where the reconnected field lines flow out. Since the inductive reconnection electric field is almost parallel to the magnetic field, particularly in the inboard-side downstream region of magnetic reconnection under a strong guide field, a large electrostatic field in the poloidal plane is spontaneously formed to sustain steady plasma outflow motion in the downstream region. In ST plasma merging experiments, the self-generated electrostatic field in the downstream region does not always balance with the inductive electric field to make the total electric field strictly perpendicular to the total magnetic field. The excess electrostatic field will provide an even faster outflow plasma velocity than the magnetic field line motion and a quick reversal of the toroidal plasma current to form convex flux surfaces.

Cracking of submerged beds

We investigate the phenomena of crater formation and gas release caused by projectile impact on underwater beds, which occurs in many natural, geophysical and industrial applications. The bed in our experiment is constructed of hydrophobic particles, which trap a substantial amount of air in the pores of the bed. In contrast to dry beds, the air–water interface in a submerged bed generates a granular skin that provides rigidity to the medium by producing skin over the bulk. The projectile's energy is used to reorganize the grains, which causes the skin to crack, allowing the trapped air to escape. The morphology of the craters as a function of impact energy in submerged beds exhibits different scaling laws than what is known for dry beds. This phenomenon is attributed to the contact line motion on the hydrophobic fractal-like surface of submerged grains. The volume of the gas released is a function of multiple factors, chiefly the velocity of the projectile, depth of the bed and depth of the water column.

Electrostatic Surface Charging by Water Dewetting.

Water dewetting generates static electricity. We reviewed historical experiments of this phenomenon, and we studied the charging of polymer slides and metal electrode supported polymer films withdrawn vertically from a pool of aqueous solutions. For pure water, charging was negative and surface charge densities increased with the speed of dewetting, which we explain by the thermally activated entrainment of nanometer-sized water droplets or clusters charged by unbalanced adsorbed electric double-layer ions. Surface charge densities increased for reduced polymer film thickness following a power law, which we explain by reduced discharge of the entrained water volumes. At low salinity c ≲ 10 μM, charging was proportional to electrokinetic interfacial charge densities: the negative charging was increased for alkaline solutions and for most salts at μM concentrations and the charge polarity was inversed to positive for a cationic surfactant, a salt with a highly positively charged cation, and for a strong acid at approximately pH 4. Charging was reduced again for c ≳ 100 μM, especially at high dewetting speeds and for chaotropic ions, which we explain by the entrainment of larger and more discharged droplets. We determined adsorption energies of the charged water clusters on the dewetted surface from thermally stimulated discharge of the charged polymer slides and we show that the surface charge distribution, imaged by charged toner powders and measured microscopically by Kelvin probe force microscopy, is a record of the dewetting process that provides spatial and kinetic information about the three-phase contact line motion.

Droplet boiling on two-tier hierarchical micro-pillar array surface – Nucleate boiling regime

Although hierarchical structured surfaces have shown great potential in improving heat transfer performance of boiling, the mechanisms associated with structure configuration and structure size remain elusive. In this work, the nucleate boiling regime of droplet on single-tier micro-pillar array (SM) surfaces and three types of two-tier hierarchical micro-pillar array (THM) surfaces is investigated comprehensively using the lattice Boltzmann model. Effects brought by the primary pillar size and the secondary pillar configuration on the development of vapor confined in pillar gaps are emphatically discussed from bubble nucleation through vapor coalescence to vapor expansion. Boiling dynamic characteristics concerning droplet morphological evolution, liquid-vapor interfacial deformation and triple-phase contact line (TPCL) motion are elucidated by the distributions of vapor pressure, fluid temperature and substrate heat flux. It is most efficient for the secondary pillar to enhance boiling heat transfer performance when configured on the side of primary pillar and least efficient when configured on the top of primary pillar.

Well-posedness of a bulk-surface convective Cahn–Hilliard system with dynamic boundary conditions

We consider a general class of bulk-surface convective Cahn–Hilliard systems with dynamic boundary conditions. In contrast to classical Neumann boundary conditions, the dynamic boundary conditions of Cahn–Hilliard type allow for dynamic changes of the contact angle between the diffuse interface and the boundary, a convection-induced motion of the contact line as well as absorption of material by the boundary. The coupling conditions for bulk and surface quantities involve parameters K,L∈[0,∞]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K,L\\in [0,\\infty ]$$\\end{document}, whose choice declares whether these conditions are of Dirichlet, Robin or Neumann type. We first prove the existence of a weak solution to our model in the case K,L∈(0,∞)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K,L\\in (0,\\infty )$$\\end{document} by means of a Faedo–Galerkin approach. For all other cases, the existence of a weak solution is then shown by means of the asymptotic limits, where K and L are sent to zero or to infinity, respectively. Eventually, we establish higher regularity for the phase-fields, and we prove the uniqueness of weak solutions given that the mobility functions are constant.

Numerical Analysis of the Dispersion and Deposition of Particles in Evaporating Sessile Droplets.

Evaporating sessile droplets containing dispersed particles are used in different technological applications, such as 3D printing, biomedicine, and micromanufacturing, where an accurate prediction of both the dispersion and deposition of the particles is important. Furthermore, the interaction between the droplet and the substrate must be taken into account: the motion of the contact line, in particular, must be modeled carefully. To this end, studies have typically been limited to either pinned or moving contact lines to simplify the underlying mathematical models and numerical methods, neglecting the fact that both scenarios are observed during the evaporation process. Here, a numerical algorithm considering both contact line regimes is proposed whereby the regimes are distinguished by predefined threshold contact angles. After a detailed validation, this new algorithm is applied to study the influence of both regimes on the dispersion and deposition of particles in an evaporating sessile droplet. In particular, the presented analysis focuses on the influence of (i) the contact line motion characteristics by varying the limiting contact angle and spreading speed, (ii) the Marangoni number, characterizing the importance of thermocapillarity, (iii) the evaporation number, which quantifies the importance of evaporation, (iv) the Damköhler number, a measure of the particle deposition rate, and (v) the Peclet number, which compares the convection and diffusion of the particle concentration. When thermocapillarity becomes dominant or the limiting contact angle is larger, the particle accumulation near the contact line decreases, which, in turn, means that more particles are deposited near the center of the droplet. In contrast, increasing the evaporation number supports particle accumulation near the contact line, while a larger Damköhler number and/or smaller Peclet number yield more uniform final deposition patterns. Finally, a larger characteristic speed of spreading results in fewer particles being deposited at the center of the droplet.

Contact-angle hysteresis on rough surfaces: mechanical energy balance framework

Using as a starting point conservation of momentum, a multiphase mechanical energy balance equation is derived that accounts for multiple material phases and interfaces present within a moving control volume. This balance is applied to a control volume that is anchored to a three-phase contact line as it advances continuously over the surface of a rough and chemically homogeneous and inert solid. Using semi-quantitative models for the material behaviour occurring within the control volume, an order of magnitude analysis is performed to neglect insignificant terms, producing an equation for predicting contact-angle hysteresis from a knowledge of the interface dynamics occurring around the three-phase contact line. It is shown that the viscous energy dissipation that occurs during the ‘stick–slip’ motion of the three-phase contact line, being the cause of contact-angle hysteresis on rough surfaces, can be calculated from changes in intermediate equilibrium interface states. The balance is applied to the Wenzel, Cassie–Baxter and Fakir (super-hydrophobic) wetting states, showing for the Fakir case that significant dissipation occurs during both interface advance and recede, and relating these dissipations to interfacial area changes that occur around the ‘stick–slip’ events.

Subgrid moving contact line model for direct numerical simulations of bubble dynamics in pool boiling of pure fluids

This contact line vicinity model is conceived as a subgrid model for the DNS of bubble growth in boiling. The model is based on the hydrodynamic multiscale theory and is suitable for the partial wetting case. On the smallest length scale (distance from the contact line) ∼ 100 nm, the interface slope is controlled by the Voinov angle. It is the static apparent contact angle (ACA) that forms due to evaporation, similarly to previous models neglecting the contact line motion. The calculation of the Voinov angle is performed with the generalized lubrication approximation and includes several nanoscale effects like those of Kelvin and Marangoni, vapor recoil, hydrodynamic slip length and interfacial kinetic resistance. It provides the finite values of the heat flux, pressure and temperature at the contact line. The dynamic ACA is obtained with the Cox-Voinov formula. The microscopic length of the Cox-Voinov formula (Voinov length) is controlled mainly by the hydrodynamic slip. The integral heat flux passing through the contact line vicinity is almost independent of the nanoscale phenomena, with the exception of the interfacial kinetic resistance and is mostly defined by the dynamic ACA. Both the dynamic ACA and the integral heat flux are the main output parameters of the subgrid model, while the local superheating and the microscopic contact angle are the main input parameters. The model is suitable for the grid sizes > 1 µm.