Microscopic Dynamic Contact Angle Research Articles

Moving contact line dynamics for capillary-driven microfluidics in wetting transition regime

The dynamics of moving contact lines (MCLs) dominate the behavior of capillary-driven microfluidics, which underlie many applications including microfluidic chips. The capillary displacement dynamics in the quasi-static regime has been extensively studied. However, the behavior of MCLs in the dynamic wetting transition regime remains largely unexplored, and previously established MCL dynamic models may be inadequate. In this study, a novel capillary displacement experiment is introduced, which is achieved by reversely introducing microfluidics with surface tension differences, where the one with low surface tension undergoes the wetting transition. In addition, a generalized Navier boundary condition (GNBC)-based model of capillary displacement dynamics is developed within the framework of diffusive interface theory to investigate the MCL dynamics in the wetting transition regime. The oscillation-relaxation process is experienced for phase interface and microscopic dynamic contact angle θd in the wetting transition regime. Spontaneous filling distance follows dfill*∼t1/2, and reaching quasi-static stage follows dfill*∼t1. The previously neglected mechanism of inertial-viscous competition dominates the early dynamics of such dynamic wetting transition processes. θd∝ucl is observed to be valid solely under conditions where viscosity dominates, but it breaks down in the presence of dominant inertial effects. An escalation in slip substantially diminishes the influence of inertia, with frictional dissipation mediated by slip emerging as the predominant factor in the capillary-driven early dynamics. The origin of uncompensated Young's stress in the GNBC and its correlation with capillary forces is unified, unveiling the underlying physical mechanism governing the dynamics at the MCL. Finally, by decoupling the analysis of viscosity and slip, a new θd-viscous-slip formulation is proposed, in agreement with the model predictions.

Thermodynamically consistent phase-field modelling of contact angle hysteresis

Abstract

Theoretical model of a finite force at the moving contact line

In theoretical analyses of the moving contact line, an infinite force along the solid wall has been reported based off the non-integrable stress along a single interface. In this investigation we demonstrate that the stress singularity is integrable and results in a finite force at the moving contact line if the contact line is treated as a one-dimensional manifold and all three interfaces that make up the moving contact line are taken into consideration. This is due to the dipole nature of the vorticity and pressure distribution around the moving contact line. Mathematically, this finite force is determined by summing all the forces that act over an infinitesimally small cylindrical control volume that encloses the entire moving contact line. With this finite force, we propose a new dynamic Young’s equation for microscopic dynamic contact angle that is a function of known parameters only, specifically the interface velocity, surface tension, and fluid viscosity. We combine our model with Cox’s model for apparent dynamic contact angle and find good agreement with published dynamic contact angle measurements.

A level-set method for moving contact lines with contact angle hysteresis

We develop a level-set method in the finite-element framework. The contact line singularity is removed by the slip boundary condition proposed by Ren and E (2007) [6], which has two friction coefficients: βN that controls the slip between the bulk fluids and the solid wall and βCL that controls the deviation of the microscopic dynamic contact angle from the static one. The predicted contact line dynamics from our method matches the Cox theory very well. We further find that the same slip length in the Cox theory can be reproduced by different combinations of (βN,βCL), based on which we come up with a computational strategy for mesh-independent results that can match the experiments. There is no need to impose the contact angle condition geometrically, and the dynamic contact angle automatically emerges as part of the numerical solution. With a little modification, our method can also be used to compute contact angle hysteresis, where the tendency of contact line motion is readily available from the level-set function. Different test cases, including code validation and mesh-convergence study, are provided to demonstrate the efficiency and capability of our method.

Role of the rate of surface dilatation in determining microscopic dynamic contact angle

The factors determining the degree of dynamic wetting, which is characterized by the microscopic dynamic contact angle, have been the subject of much discussion. In this manuscript, it is analytically determined that the microscopic dynamic contact angle is dependent on the rate of surface dilatation in addition to the thermodynamic surface tension. It is argued that, in the vicinity of a moving contact line, this rate of surface dilatation results in a disparity between the thermodynamic and mechanical surface tensions, which are almost always assumed to be equal. It is also found that, in the case of forced wetting, the difference between the receding and advancing contact angles is primarily due to the rate of surface compression at the receding contact line and the rate of surface expansion at the advancing contact line. These findings, which are validated using molecular dynamics simulations, demonstrate that surface dilatation is an important factor responsible for the deviation of the microscopic dynamic contact angle from its static equilibrium value.

Contact-line fluctuations and dynamic wetting

HypothesisThe thermal fluctuations of the three-phase contact line formed between a liquid and a solid at equilibrium can be used to determine key parameters that control dynamic wetting. MethodsWe use large-scale molecular dynamics simulations and Lennard-Jones potentials to model a liquid bridge between two molecularly smooth solid surfaces and study the positional fluctuations of the contact lines so formed as a function of the solid–liquid interaction. FindingsWe show that the fluctuations have a Gaussian distribution and may be modelled as an overdamped one-dimensional Langevin oscillator. Our analysis allows us to extract the coefficients of friction per unit length of the contact lines ζ, which arise from the collective interaction of the contact-line’s constituent liquid atoms with each other and the solid surface. We then compare these coefficients with those obtained by measuring the dynamic contact angle as a function of contact-line speed in independent simulations and applying the molecular-kinetic theory of dynamic wetting. We find excellent agreement between the two, with the same dependence on solid–liquid interaction and, therefore, the equilibrium contact angle θ0. As well as providing further evidence for the underlying validity of the molecular-kinetic model, our results suggest that it should be possible to predict the dynamics of wetting and, in particular, the velocity-dependence of the local, microscopic dynamic contact angle, by experimentally measuring the fluctuations of the contact line of a capillary system at equilibrium. This would circumvent the need to measure the microscopic dynamic contact angle directly.

Dipole model of vorticity at the moving contact line

In theoretical analyses of the moving contact line, an infinite force along the solid wall has been reported based off the non-integrable stress along a single interface. In this investigation we demonstrate that the stress singularity is integrable and results in a finite force at the moving contact line if the contact line is treated as a one-dimensional manifold and all three interfaces that make up the moving contact line are taken into consideration. This is due to the dipole nature of the vorticity and pressure distribution around the moving contact line. Mathematically, this finite force is determined by summing all the forces that act over an infinitesimally small cylindrical control volume that encloses the entire moving contact line. With this finite force, we propose a new dynamic Young’s equation for microscopic dynamic contact angle that is a function of known parameters only, specifically the interface velocity, surface tension, and fluid viscosity. We combine our model with Cox’s model for apparent dynamic contact angle and find good agreement with published dynamic contact angle measurements.

Modeling of the dynamic wetting behavior in a capillary tube considering the macroscopic–microscopic contact angle relation and generalized Navier boundary condition

In this study, dynamic wetting phenomena in a capillary tube were studied by using numerical simulations based on the front-tracking method employing the generalized Navier boundary condition (GNBC) and by experimental measurements. For the GNBC, based on molecular dynamics simulations, the microscopic dynamic contact angle is estimated from the grid-scale contact angle using Cox’s macroscopic–microscopic relation. The experimentally measured correlation between the apparent dynamic contact angle and the moving velocity of the contact line is well reproduced by the present simulation technique considering Cox’s macroscopic–microscopic relation. Thus, we found that the dynamics of wetting are well described by combining molecular-scale behavior and macroscopic–microscopic relations.

Slip or not slip? A methodical examination of the interface formation model using two-dimensional droplet spreading on a horizontal planar substrate as a prototype system

We consider the spreading of a thin two-dimensional droplet on a planar substrate as a prototype system to compare the contemporary model for contact line motion based on interface formation of Shikhmurzaev [Int. J. Multiphase Flow 19, 589–610 (1993)]10.1016/0301-9322(93)90090-H, to the more commonly used continuum fluid dynamical equations augmented with the Navier-slip condition. Considering quasistatic droplet evolution and using the method of matched asymptotics, we find that the evolution of the droplet radius using the interface formation model reduces to an equivalent expression for a slip model, where the prescribed microscopic dynamic contact angle has a velocity dependent correction to its static value. This result is found for both the original interface formation model formulation and for a more recent version, where mass transfer from bulk to surface layers is accounted for through the boundary conditions. Various features of the model, such as the pressure behaviour and rolling motion at the contact line, and their relevance, are also considered in the prototype system we adopt.

Fluid epitaxialization effect on velocity dependence of dynamic contact angle in molecular scale

Molecular dynamics simulations were used to investigate the effect of epitaxial ordering of the fluid molecules on the microscopic dynamic contact angle. The simulations were performed in a Couette-flow-like geometry where two immiscible fluids were confined between two parallel walls moving in opposite directions. The extent of ordering was varied by changing the number density of the wall particles. As the ordering becomes more evident, the change in the dynamic contact angle tends to be more sensitive to the increase in the relative velocity of the contact line to the wall. Stress components around the contact line is evaluated in order to examine the stress balance among the hydrodynamic stresses (viscous stress and pressure), the deviation of Young's stress from the static equilibrium condition, and the fluid-wall shear stress induced by the relative motion between them. It is shown that the magnitude of the shear stress on the fluid-wall surface is the primary contribution to the sensitivity of the dynamic contact angle and that the sensitivity is intensified by the fluid ordering near the wall surface.

Dynamics of Partial Wetting and Dewetting of an Amorphous Fluoropolymer by Pure Liquids

We report velocity dependencies of dynamic contact angles for CCl4 and tert-butyl alcohol on the amorphous fluoropolymer AF 1600 and compare them with our previous results for octamethylcyclotetrasiloxane (OMCTS) on the same substrate. The molecules of these liquids have well-defined form and the solid surface is almost smooth and homogeneous, which enables checking the assumptions of the main theories of wetting dynamics. We find that the molecular-kinetic theory well represents the data for CCl4 in the characteristic cos ϑ/V scale but qualitatively disagrees with the experiment for tert-butyl alcohol and OMCTS at high velocities. The CCl4 data do not fulfill the requirement of the hydrodynamic theory for symmetric advancing and receding branches. For the other two systems, the hydrodynamic theory works better at high velocities, but the nonlinear initial sections of the ϑ3/V plots require consideration of the velocity dependence of the microscopic dynamic contact angle ϑc(V). This is done by the molecular-hydrodynamic theory accounting for both contact line and bulk viscous friction. This theory shows agreement with the experimental data in the entire velocity range for all systems compared. It fits the receding and advancing ϑ/V branches simultaneously, yielding unique values of the microscopic dynamic parameters λ, Ko,s, and Lc,max that do not depend on direction of the contact line motion. Only this theory describes the wetting−dewetting asymmetry observed for tert-butyl alcohol and OMCTS. However, it yields inadequately large values of λ and too small hopping frequencies Ko,s for CCl4 and tert-butyl alcohol. Such results, also reported previously, might mean that not λ and Ko,s but their combinations better serve for description of wetting dynamics. Here we analyze the characteristic molecular-kinetic velocity Vo,s = λKo,s and the coefficient of friction of a unit contact line length ξc = kT/Ko,sλ3 and find a significant difference between the studied systems.