Moving contact line problem: Advances and perspectives

The solid-liquid interface, which is ubiquitous in nature and our daily life, plays fundamental roles in a variety of physical-chemical-biological- mechanical phenomena, for example in lubrication, crystal growth, and many biological reactions that govern the building of human body and the functioning of brain. A surge of interests in the moving contact line （MCL） problem, which is still going on today, can be traced back to 1970s primarily because of the exis- tence of the ＂Huh-Scriven paradox＂. This paper, mainly from a solid mechanics perspective, describes very briefly the multidisciplinary nature of the MCL problem, then summarizes some major advances in this exciting research area, and some future directions are presented.

Measurement of the friction coefficient of a fluctuating contact line using an AFM-based dual-mode mechanical resonator

A dual-mode mechanical resonator using an atomic force microscope （AFM） as a force sensor is developed. The resonator consists of a long vertical glass fiber with one end glued onto a rectangular cantilever beam and the other end immersed through a liquid-air interface. By measuring the resonant spectrum of the modified AFM cantilever, one is able to accurately determine the longitudinal friction coefficient ξv along the fiber axis associated with the vertical oscillation of the hanging fiber and the traversal friction coefficient ξh perpendicular to the fiber axis associated with the horizontal swing of the fiber around its joint with the cantilever. The technique is tested by measurement of the friction coefficient of a fluctuating （and slipping） contact line between the glass fiber and the liquid interface. The experiment verifies the theory and demonstrates its applications. The dual-mode mechanical resonator provides a powerful tool for the study of the contact line dynamics and the rheological property of anisotropic fluids.

NUMERICAL SIMULATION OF THE FLOW WITH CONTACT LINES

The paper proposes a physical model for the motion of the contact line and the gas-liquid interface. The local motion of the contact line at the solid wall is assumed and the interface between gas and liquid is traced by a level function. The finite volume method and staggered grids are used to solve the governing equation numerically. The motion of the water column in a vertical pipe is computed and the results are in good agreement with experimental data.

Load distribution of involute gears along time-varying contact line

Base on the theory of energy minimization, a numerical algorithm is established to calculate load distribution, and the relationship curve of spur gear load distribution is obtained, and the load distribution ratio changes from 033 to 067 in double contact zone. This theory is adopted to compute the load distribution of helical gear along time-varying contact line, and the load distribution varies with the instantaneous position of the meshing point and the length of contact line, and the maximum value of load appears at the pitch point. Compared with the load distribution results, the helical gear changes more smoothly than spur gear. The load distribution provides a basis for calculate tooth bending deformation and critical stress.

Development and tests of sliding contact line-powered track transporter

In order to solve the problems of complexity of control systems and the limited power supply of traditional fuelpowered and battery-driven transporters operating in mountainous orchards,a sliding contact line-powered track transporter was designed and manufactured based on theoretical calculations.Key components of the transporter were developed such as a PLC-based(programmable logic controller)control system,a sliding contact power supply,and transmission system,and a position limit device.The functions and performance of designed transporter were tested.The test results showed that the transporter exhibited a high stability of operation with an average operation velocity of 0.70 m/s,the maximum working slope of 48°,the maximum load of 400 kg,and the maximum remote control distance reaching 1482 m.When the power supply circuit of sliding contact line was 108.8 m in length,the maximum voltage drop was 2.4 V,and the maximum power loss was 174.72 W,which were close to the theoretical calculation values.With a single power supply cabinet,the transporter can operate normally for a maximum track distance of 175.69 m.All the technical indicators of the transporter met the design requirements,and the above-mentioned problems such as complexity of the control system and limited energy supply of the traditional mountain orchard transporter were well solved.This study can provide reference for the design and optimization of mountain orchard transporter.

DECOUPLED, ENERGY STABLE SCHEME FOR HYDRODYNAMIC ALLEN-CAHN PHASE FIELD MOVING CONTACT LINE MODEL

In this paper, we present an efficient energy stable scheme to solve a phase field model incorporating contact line condition. Instead of the usually used Cahn-Hilliard type phase equation, we adopt the Allen-Cahn type phase field model with the static contact line boundary condition that coupled with incompressible Navier-Stokes equations with Navier boundary condition. The projection method is used to deal with the Navier-Stokes equa- tions and an auxiliary function is introduced for the non-convex Ginzburg-Landau bulk potential. We show that the scheme is linear, decoupled and energy stable. Moreover, we prove that fully discrete scheme is also energy stable. An efficient finite element spatial discretization method is implemented to verify the accuracy and efficiency of proposed schemes. Numerical results show that the proposed scheme is very efficient and accurate.

A Level Set Method for the Simulation of Moving Contact Lines in Three Dimensions

We propose an efficient numerical method for the simulation of the twophase flows with moving contact lines in three dimensions.The mathematical model consists of the incompressible Navier-Stokes equations for the two immiscible fluids with the standard interface conditions,the Navier slip condition along the solid wall,and a contact angle condition(Ren et al.(2010)[28]).In the numerical method,the governing equations for the fluid dynamics are coupledwith an advection equation for a level-set function.The latter models the dynamics of the fluid interface.Following the standard practice,the interface conditions are taken into account by introducing a singular force on the interface in themomentum equation.This results in a single set of governing equations in the whole fluid domain.Similarly,the contact angle condition is imposed by introducing a singular force,which acts in the normal direction of the contact line,into theNavier slip condition.The newboundary condition,which unifies the Navier slip condition and the contact angle condition,is imposed along the solid wall.The model is solved using the finite difference method.Numerical results are presented for the spreading of a droplet on both homogeneous and inhomogeneous solid walls,as well as the dynamics of a droplet on an inclined plate under gravity.

Numerical Simulation of Moving Contact Lines with Surfactant by Immersed Boundary Method

In this paper,we present an immersed boundary method for simulating moving contact lines with surfactant.The governing equations are the incompressible Navier-Stokes equations with the usual mixture of Eulerian fluid variables and Lagrangian interfacial markers.The immersed boundary force has two components:one from the nonhomogeneous surface tension determined by the distribution of surfactant along the fluid interface,and the other from unbalanced Young’s force at the moving contact lines.An artificial tangential velocity has been added to the Lagrangian markers to ensure that the markers are uniformly distributed at all times.The corresponding modified surfactant equation is solved in a way such that the total surfactant mass is conserved.Numerical experiments including convergence analysis are carefully conducted.The effect of the surfactant on the motion of hydrophilic and hydrophobic drops are investigated in detail.

Molecular Hydrodynamics of the Moving Contact Line in Two-Phase Immiscible Flows

The no-slip boundary condition,i.e.,zero fluid velocity relative to the solid at the fluid-solid interface,has been very successful in describing many macroscopic flows.A problem of principle arises when the no-slip boundary condition is used to model the hydrodynamics of immiscible-fluid displacement in the vicinity of the moving contact line,where the interface separating two immiscible fluids intersects the solid wall.Decades ago it was already known that the moving contact line is incompatible with the no-slip boundary condition,since the latter would imply infinite dissipation due to a non-integrable singularity in the stress near the contact line.In this paper we first present an introductory review of the problem.We then present a detailed review of our recent results on the contact-line motion in immiscible two-phase flow,from molecular dynamics(MD)simulations to continuum hydrodynamics calculations.Through extensive MD studies and detailed analysis,we have uncovered the slip boundary condition governing the moving contact line,denoted the generalized Navier boundary condition.We have used this discovery to formulate a continuum hydrodynamic model whose predictions are in remarkable quantitative agreement with the MD simulation results down to the molecular scale.These results serve to affirm the validity of the generalized Navier boundary condition,as well as to open up the possibility of continuum hydrodynamic calculations of immiscible flows that are physically meaningful at the molecular level.

Numerical Simulation for Moving Contact Line with Continuous Finite Element Schemes

In this paper,we compute a phase field(diffuse interface)model of CahnHilliard type for moving contact line problems governing the motion of isothermal multiphase incompressible fluids.The generalized Navier boundary condition proposed by Qian et al.[1]is adopted here.We discretize model equations using a continuous finite element method in space and a modified midpoint scheme in time.We apply a penalty formulation to the continuity equation which may increase the stability in the pressure variable.Two kinds of immiscible fluids in a pipe and droplet displacement with a moving contact line under the effect of pressure driven shear flow are studied using a relatively coarse grid.We also derive the discrete energy law for the droplet displacement case,which is slightly different due to the boundary conditions.The accuracy and stability of the scheme are validated by examples,results and estimate order.

Stick-Slip Motion of Moving Contact Line on Chemically Patterned Surfaces

Based on our continuum hydrodynamic model for immiscible two-phaseflows at solid surfaces, the stick-slip motion has been predicted for moving contactline at chemically patterned surfaces [Wang et al., J. Fluid Mech., 605 (2008), pp. 59-78].In this paper we show that the continuum predictions can be quantitatively verifiedby molecular dynamics (MD) simulations. Our MD simulations are carried out fortwo immiscible Lennard-Jones fluids confined by two planar solid walls in Poiseuilleflow geometry. In particular, one solid surface is chemically patterned with alternating stripes. For comparison, the continuum model is numerically solved using material parameters directly measured in MD simulations. From oscillatory fluid-fluidinterface to intermittent stick-slip motion of moving contact line, we have quantitativeagreement between the continuum and MD results. This agreement is attributed tothe accurate description down to molecular scale by the generalized Navier boundary condition in our continuum model. Numerical results are also presented for therelaxational dynamics of fluid-fluid interface, in agreement with a theoretical analysisbased on the Onsager principle of minimum energy dissipation.

To improve alignment of isoindigo-based conjugated polymer film by controlling contact line receding velocity

The macroscopic alignment of conjugated polymers with low grain boundary is essential to carrier transport. During film forming process, the match between contact line receding velocity and the critical alignment velocity is essential to get the alignment polymer film. In this paper, the contact line receding velocity of a D-A conjugated polymer film, isoindigo and bithiophene（IIDDT-C3）, was adjusted by solvent vapor content and film-formation temperature. Only when solvent vapor content was 0.3 m L and the film-formation temperature was 90C, the contact line receding velocity was in accordance with the critical alignment velocity, and the highest degree of alignment was attained in the IIDDT-C3 film, with the dichroic ratio up to 4.08. Fibers were aligned parallel with the direction of the contact line receding and the molecules of IIDDT-C3 adopted an edge-on orientation with the backbone parallel with the direction of fiber long axis. The p-p stacking distance between adjacent molecules was 3.63 ？.

Simulation of flows with moving contact lines on a dual-resolution Cartesian grid using a diffuse-interface immersed-boundary method

In this paper, we investigate flows with moving contact lines on curved solid walls on a dual-resolution grid using a diffuse-interface immersed-boundary（DIIB） method. The dual-resolution grid, on which the flows are solved on a coarse mesh while the interface is resolved on a fine mesh, was shown to significantly improve the computational efficiency when simulating multiphase flows. On the other hand, the DIIB method is able to resolve dynamic wetting on curved substrates on a Cartesian grid, but it usually requires a mesh of high resolution in the vicinity of a moving contact line to resolve the local flow. In the present study, we couple the DIIB method with the dual-resolution grid, to improve the interface resolution for flows with moving contact lines on curved solid walls at an affordable cost. The dynamic behavior of moving contact lines is validated by studying drop spreading, and the numerical results suggest that the effective slip length λ_n can be approximated by 1.9Cn, where Cn is a dimensionless measure of the thickness of the diffuse interface. We also apply the method to drop impact onto a convex substrate, and the results on the dual-resolution grid are in good agreement with those on a single-resolution grid. It shows that the axisymmetric simulations using the DIIB method on the dual-resolution grid saves nearly 60% of the computational time compared with that on a single-resolution grid.

Effect of triple-phase contact line on contact angle hysteresis

Recent studies have shown that the triple-phase contact line has critical effect on the contact angle hysteresis of surfaces.In this study,patterned surfaces with various surface structures of different area fractions were prepared by electron etching on a silicon wafer.The advancing angle,receding angle and hysteresis angle of these surfaces were measured.Our experimental results showed that while the geometry of microstructure and contact line have a minor effect on the advancing angle,they have a significant effect on the receding angle and thus the hysteresis angle.We have shown that the effect of microstructure and the contact line can be described by a quantitative parameter termed the triple-phase line ratio.The theoretical predictions were in good agreement with our experimental results.

Quasi-static motion of microparticles at the depinning contact line of an evaporating droplet on PDMS surface

In this paper, evaporation of sessile water droplets containing fluorescent polystyrene(PS) microparticles on polydimethylsiloxane(PDMS) surfaces with different curing ratios was studied experimentally using laser confocal microscopy. At the beginning, there were some microparticles located at the contact line and some microparticles moved towards the line. Due to contact angle hysteresis, at first both the contact line and the microparticles were pinned. With the depinning contact line, the microparticles moved together spontaneously. Using the software ImageJ, the location of contact lines at different time were acquired and the circle centers and radii of the contact lines were obtained via the least square method. Then the average distance of two neighbor contact lines at a certain time interval was obtained to characterize the motion of the contact line. Fitting the distance-time curve at the depinning contact line stage with polynomials and differentiating the polynomials with time, we obtained the velocity and acceleration of both the contact line and the microparticles located at the line. The velocity and the maximum acceleration were,respectively, of the orders of 1 μm/s and 20-200 nm/s^2, indicating that the motion of the microparticles located at the depinning contact line was quasi-static. Finally, we presented a theoretical model to describe the quasi-static process, which may help in understanding both self-pinning and depinning of microparticles.

Effect of upper contact line on sliding behavior of water droplet on superhydrophobic surface

With a low surface energy, high apparent contact angle(>150°) and low sliding angle(<5°), superhy- drophobic surface has recently been attracting a great deal of attention. The true factor determining the sliding angle still remains unclear. In this paper, various superhydrophobic silicon surfaces with pillars are fabricated by photolithography and hydrophobized with octadecyltrichlorosilane (OTS). Relations between sliding angles and micro-structured surfaces are being investigated in detail with 10 mg water droplets in C-B state and mixed state. Experimental pictures and data show that the sliding angle is independent of pillar heights from 20 to 80 μm, increasing the space between pillars causes decrease in sliding angle, and increasing the side lengths of pillars causes increase in sliding angle. Moreover, the sliding angle is irrelevant to the state of interfacial contact area of water-solid and lower contact line. It is concluded that the sliding angle of water droplet on the micro-structured surface is merely deter-mined by the upper contact line.

ESTIMATION OF RESIDUAL CONTACT PRESSURE IN HYDRAULICALLY EXPANDED CRA-LINED PIPE

The mechanically bonded CRA-lined pipe is developed to meet the need forcorrosion-resistant alloy steel pipe. Residual contact pressure at the interface of lined pipe isimportant factor that governs the quality of lined pipe. A simplified theoretical method ispresented to predict the residual contact pressure created by hydraulic pressure. The calculatingequation related hydro-forming pressure to the residual contact pressure between two metal faces isderived. And the validation of the proposed equation is accomplished by comparing its result tothose obtained by experimental investigation.

ANALYSIS OF THE SINGULARITY FOR THE VERTICAL CONTACT PROBLEM OF LINE CRACK-INCLUSION

Taking the short-fiber composite materials as engineering back-ground, utilizing the existing basic solutions of single inclusion and single crack, the plane problem of vertical contact interactions between line crack and rigid line inclusion in infinite plane (matrix) from the viewpoint of crack fracture mechanics is studied. According to boundary conditions, a set of standard Cauchy-type singular integral equations of the problem is obtainable. Besides, singular indexes, stresses and stress intensity factors around the contact point are expressed. Numerical examples are given to provide references to engineering.

基于角度传感器的弓网相对坐标检测技术研究

在电气化公路弓网相对坐标的检测中,基于机器视觉的非接触式检测技术的检测精度受图像采集环境的影响较大,基于光电传感器的接触式检测技术的检测精度受传感器安装密度限制。提出了一种基于角度传感器的接触式相对坐标检测技术,用于电气化公路的弓网相对坐标检测。首先,基于双接触线的电气化公路接触网,搭建弓网相对坐标检测实验台,建立弓网相对坐标与角度信息关联函数;然后,研究系统刚度、角度传感器线性度对实验台检测误差的影响规律,建立多项式修正函数对关联函数进行修正;最后,基于修正的弓网相对坐标关联函数,进行弓网相对坐标检测实验,得到实验台检测的绝对误差为±1 mm,相对误差为±0.5%,具备较高的检测精度。

Dynamics of Low-Viscosity Liquids Interface in an Unevenly Rotating Vertical Layer

The behavior of two immiscible low-viscosity liquids differing in density and viscosity in a vertical flat layer undergoing modulated rotation is experimentally studied.The layer has a circular axisymmetric boundary.In the absence of modulation of the rotation speed,the interphase boundary has the shape of a short axisymmetric cylinder.A new effect has been discovered,under the influence of rotation speed modulation,the interface takes on a new dynamic equilibrium state.A more viscous liquid covers the end boundaries of the layer in the form of thin films,which have the shape of round spots of almost constant radius;with increasing amplitude of the velocity modulation,the wetting boundary expands.It is found that upon reaching the critical amplitude of oscillations,the film of a viscous liquid loses stability,and the outer edge of the wetting spot collapses and takes on a feathery structure.It is shown that this threshold is caused by the development of the Kelvin-Helmholtz oscillatory instability of the film.The spreading radius of a spot of light viscous liquid and its stability are studied depending on the rotation rate,amplitude,and frequency of rotation speed modulation.The discovered averaged effects are determined by different oscillatory interaction of fluids with the end-walls of the cell,due to different viscosities.The effect of films forming can find application in technological processes to intensify mass transfer at interphase boundaries.