Moving Contact Line Dynamics 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.

Thermocapillary migration of a droplet on a substrate with wettability difference: A comparison between slip and precursor film models in three dimensions

Moving contact line dynamics calculations include two models: precursor film models and slip models. The lubrication approximation method is used to establish a three-dimensional mathematical model to analyze the droplet thermocapillary migration behavior on a non-uniformly heated solid substrate with a wettability track. The contact line dynamics in the slip model and the disjoining pressure effect in the precursor model are proposed to regulate the substrate wettability. Both models are numerically implemented to investigate droplet spreading for three cases: free spreading on an isothermal substrate, thermocapillary migration on a uniform wettability substrate, and thermocapillary migration on a wettability-confined track. For the case of free spreading on an isothermal substrate, the three-dimensional results of the slip and precursor contact line models are essentially consistent with two-dimensional slip model results. For the case of thermocapillary migration on a uniform wettability substrate, the results of the two models essentially agree with the experimental results. Decreasing the thermal gradient reduces the discrepancies between the two models that result from the coordinate transformation method used in the slip model, which reduces the contact angles measured in the y-direction and enlarges the advancing contact angle in the migration direction. For the case of thermocapillary migration on a wettability-confined track, the slip model gradually shows a “dynamic-pinning” behavior with increasing equilibrium contact angle in the hydrophobic region. By contrast, the precursor film model maintains a stationary pinning behavior but separates a residual liquid outside the track. The precursor film model is preferred over the slip model in lubrication approximations for three-dimensional fluids when calculating complex moving contact dynamics caused by wettability differences. However, the precursor film model must be further optimized to prevent numerical instability.

A review of physics of moving contact line dynamics models and its applications in interfacial science

Despite several decades long research on moving contact line dynamics due to its remarkable role in interfacial science and technological fields, there is still a significant lack of comprehensive knowledge about the true nature of the contact line. The moving contact line is much more complex than just a geometric flow condition. Given the role of moving contact line physics in numerous emerging advanced technologies including bioprinting, tissue engineering, pharmaceutical industry, smart functional coatings, flexible electronics, and healthcare, it is needed for scientific community to direct their focus in advancement on better understanding of interfacial science and physics of moving contact line. Therefore, this review primarily concentrates on the current physical theories which describe the moving contact line dynamics. Moreover, numerous potential and ongoing applications of moving contact line dynamics linked to the interfacial science are thoroughly discussed. Finally, this review presents the future perspectives related to the current challenges in moving contact line dynamics.

Thermodynamically consistent modelling of two-phase flows with moving contact line and soluble surfactants

Droplet dynamics on a solid substrate is significantly influenced by surfactants. It remains a challenging task to model and simulate the moving contact line dynamics with soluble surfactants. In this work, we present a derivation of the phase-field moving contact line model with soluble surfactants through the first law of thermodynamics, associated thermodynamic relations and the Onsager variational principle. The derived thermodynamically consistent model consists of two Cahn–Hilliard type of equations governing the evolution of interface and surfactant concentration, the incompressible Navier–Stokes equations and the generalized Navier boundary condition for the moving contact line. With chemical potentials derived from the free energy functional, we analytically obtain certain equilibrium properties of surfactant adsorption, including equilibrium profiles for phase-field variables, the Langmuir isotherm and the equilibrium equation of state. A classical droplet spread case is used to numerically validate the moving contact line model and equilibrium properties of surfactant adsorption. The influence of surfactants on the contact line dynamics observed in our simulations is consistent with the results obtained using sharp interface models. Using the proposed model, we investigate the droplet dynamics with soluble surfactants on a chemically patterned surface. It is observed that droplets will form three typical flow states as a result of different surfactant bulk concentrations and defect strengths, specifically the coalescence mode, the non-coalescence mode and the detachment mode. In addition, a phase diagram for the three flow states is presented. Finally, we study the unbalanced Young stress acting on triple-phase contact points. The unbalanced Young stress could be a driving or resistance force, which is determined by the critical defect strength.

Electrothermally actuated moving contact line dynamics over chemically patterned surfaces with resistive heaters

In this paper, we explore the moving contact line dynamics of two Newtonian immiscible fluids over substrates patterned with two different alternative chemical patches. The bulk fluid motion is actuated using electrothermal kinetics where the thermal field is generated by incorporating resistive heaters on the substrate. The electrothermal forces, which arise from the local gradient in electrical conductivity and permittivity, strongly depend on the local temperature and potential distributions. The thermal field and the potential distribution can be modulated by altering the heater characteristics and electrode patterning. The contact line motion and its intricate physics can be effectively tuned by altering the geometrical parameters of the heaters and electrode arrangement. Further, a comparison is executed between conventional electrothermal and heater-assisted electrothermal processes. The interfacial dynamics of the immiscible binary fluids is greatly affected by the present electrothermal mechanism and shows advantages over the conventional electrothermal process. The results presented here are effective for developing various smart devices involving multiphase flow dynamics within an electrokinetic paradigm.

Numerical investigations of electrothermally actuated moving contact line dynamics: Effect of property contrasts

This article reports interfacial electro-thermo-chemical-hydrodynamics of binary fluids with contrasting viscosity, thermal conductivity, and electrical conductivity of fluids under AC electrokinetics, called alternating current electrothermal (ACET) mechanism, over wetted substrates. The interfacial kinetics of the two phases are modulated by the coupled influence of electrothermal, viscous, and capillary forces. Numerical investigations of contact line dynamics reveal that at low viscosity of displaced fluid, viscous drag force significantly reduces leading to faster progression of the contact line. Larger viscous drag force at higher viscosity of the displaced fluid resists the interface motion to travel along the capillary. ACET forces are the direct consequences of the thermal and electric fields. For low thermal conductivity of the displaced fluid, the temperature gradient becomes much stronger leading to higher ACET forces and contact line velocity. Below a threshold limit of thermal conductivity, stronger electrothermal forces cause misbalance between contact line velocity and bulk fluid velocity, which, in turn, trigger an interesting phenomena of interface breaking. Mismatch in electrical conductivity generates electrical stresses across the interface that deforms the interface profile and causes boosting impact across the interface leading to an increase in contact line velocity. The net force across the interface changes the direction depending on the deviation of electrical conductivity ratio from unity. Finally, we observe that larger channel height and wider electrode spacing decrease the net force on the bulk fluid and contact line velocity.

Alternating current electrothermal modulated moving contact line dynamics of immiscible binary fluids over patterned surfaces.

In this paper, we report the results of our numerical study on incompressible flow of a binary system of two immiscible fluids in a parallel plate capillary using alternating current electrothermal kinetics as the actuation mechanism for flow. The surfaces of the capillary are wetted with two different alternating wettability patches. The dynamic motion of the interface of the two fluids is tracked using a phase-field order parameter-based approach. The results exhibit a stick-slip behavior involving acceleration and deceleration of the interface due to the interplay of electrothermal (Coulomb and dielectric) and surface tension forces. Controlling the interface motion through effective tuning of the chemical characteristics of the surfaces and forcing parameters was explored in detail. Finally, we were able to find a critical value of the dimensionless strength of the alternating current electrothermal force above which the interface "breaks", resulting in the formation of isolated droplets. These results have the potential to improve fundamental understanding and design optimization of various biomedical and physiological systems that involve flow of two or more immiscible fluids over chemically wetted surfaces.

Moving contact line dynamics: from diffuse to sharp interfaces

We reconcile two scaling laws that have been proposed in the literature for the slip length associated with a moving contact line in diffuse interface models, by demonstrating each to apply in a different regime of the ratio of the microscopic interfacial width $l$ and the macroscopic diffusive length $l_{D}=(M{\it\eta})^{1/2}$, where ${\it\eta}$ is the fluid viscosity and $M$ the mobility governing intermolecular diffusion. For small $l_{D}/l$ we find a diffuse interface regime in which the slip length scales as ${\it\xi}\sim (l_{D}l)^{1/2}$. For larger $l_{D}/l>1$ we find a sharp interface regime in which the slip length depends only on the diffusive length, ${\it\xi}\sim l_{D}\sim (M{\it\eta})^{1/2}$, and therefore only on the macroscopic variables ${\it\eta}$ and $M$, independent of the microscopic interfacial width $l$. We also give evidence that modifying the microscopic interfacial terms in the model’s free energy functional appears to affect the value of the slip length only in the diffuse interface regime, consistent with the slip length depending only on macroscopic variables in the sharp interface regime. Finally, we demonstrate the dependence of the dynamic contact angle on the capillary number to be in excellent agreement with the theoretical prediction of Cox (J. Fluid Mech., vol. 168, 1986, p. 169), provided we allow the slip length to be rescaled by a dimensionless prefactor. This prefactor appears to converge to unity in the sharp interface limit, but is smaller in the diffuse interface limit. The excellent agreement of results obtained using three independent numerical methods, across several decades of the relevant dimensionless variables, demonstrates our findings to be free of numerical artefacts.

Wetting and spreading

Wetting phenomena are ubiquitous in nature and technology. A solid substrate exposed to the environment is almost invariably covered by a layer of fluid material. In this review, the surface forces that lead to wetting are considered, and the equilibrium surface coverage of a substrate in contact with a drop of liquid. Depending on the nature of the surface forces involved, different scenarios for wetting phase transitions are possible; recent progress allows us to relate the critical exponents directly to the nature of the surface forces which lead to the different wetting scenarios. Thermal fluctuation effects, which can be greatly enhanced for wetting of geometrically or chemically structured substrates, and are much stronger in colloidal suspensions, modify the adsorption singularities. Macroscopic descriptions and microscopic theories have been developed to understand and predict wetting behavior relevant to microfluidics and nanofluidics applications. Then the dynamics of wetting is examined. A drop, placed on a substrate which it wets, spreads out to form a film. Conversely, a nonwetted substrate previously covered by a film dewets upon an appropriate change of system parameters. The hydrodynamics of both wetting and dewetting is influenced by the presence of the three-phase contact line separating ``wet'' regions from those that are either dry or covered by a microscopic film only. Recent theoretical, experimental, and numerical progress in the description of moving contact line dynamics are reviewed, and its relation to the thermodynamics of wetting is explored. In addition, recent progress on rough surfaces is surveyed. The anchoring of contact lines and contact angle hysteresis are explored resulting from surface inhomogeneities. Further, new ways to mold wetting characteristics according to technological constraints are discussed, for example, the use of patterned surfaces, surfactants, or complex fluids.

Contact-line dynamics of a diffuse fluid interface

An investigation is made into the moving contact line dynamics of a Cahn–Hilliard–van der Waals (CHW) diffuse mean-field interface. The interface separates two incompressible viscous fluids and can evolve either through convection or through diffusion driven by chemical potential gradients. The purpose of this paper is to show how the CHW moving contact line compares to the classical sharp interface contact line. It therefore discusses the asymptotics of the CHW contact line velocity and chemical potential fields as the interface thickness ε and the mobility κ both go to zero. The CHW and classical velocity fields have the same outer behaviour but can have very different inner behaviours and physics. In the CHW model, wall–liquid bonds are broken by chemical potential gradients instead of by shear and change of material at the wall is accomplished by diffusion rather than convection. The result is, mathematically at least, that the CHW moving contact line can exist even with no-slip conditions for the velocity. The relevance and realism or lack thereof of this is considered through the course of the paper.The two contacting fluids are assumed to be Newtonian and, to a first approximation, to obey the no-slip condition. The analysis is linear. For simplicity most of the analysis and results are for a 90° contact angle and for the fluids having equal dynamic viscosity μ and mobility κ. There are two regions of flow. To leading order the outer-region velocity field is the same as for sharp interfaces (flow field independent of r) while the chemical potential behaves like r−ξ, ξ = π/2/max{θeq, π − θeq}, θeq being the equilibrium contact angle. An exception to this occurs for θeq = 90°, when the chemical potential behaves like ln r/r. The diffusive and viscous contact line singularities implied by these outer solutions are resolved in the inner region through chemical diffusion. The length scale of the inner region is about 10√μκ – typically about 0.5–5 nm. Diffusive fluxes in this region are O(1). These counterbalance the effects of the velocity, which, because of the assumed no-slip boundary condition, fluxes material through the interface in a narrow boundary layer next to the wall.The asymptotic analysis is supplemented by both linearized and nonlinear finite difference calculations. These are made at two scales, experimental and nanoscale. The first set is done to show CHW interface behaviour and to test the qualitative applicability of the CHW model and its asymptotic theory to practical computations of experimental scale, nonlinear, low capillary number flows. The nanoscale calculations are carried out with realistic interface thicknesses and diffusivities and with various assumed levels of shear-induced slip. These are discussed in an attempt to evaluate the physical relevance of the CHW diffusive model. The various asymptotic and numerical results together indicate a potential usefullness for the CHW model for calculating and modelling wetting and dewetting flows.