Hydrodynamics of Moving Contact Lines: Macroscopic versus Microscopic

Thermally assisted mobility of nanodroplets on surfaces with weak defects

HYPOTHESIS

Thermal activation plays an essential role in contact line dynamics on nanorough surfaces. However, the relation between the aforementioned concept and the sliding motion of nanodroplets remains unclear. As a result, thermally assisted motion of nanodroplets on nanorough surfaces is investigated in this work.

EXPERIMENTS

Steady slide and random motion of nanodroplets on surfaces with weak defects are investigated by Many-body Dissipative Particle Dynamics. The surface roughness is characterized by the slip length acquired from the velocity profile associated with the flowing film.

FINDINGS

The slip length is found to decline with increasing the defect density. The linear relationship between the sliding velocity and driving force gives the mobility and reveals the absence of contact line pinning. On the basis of the Navier condition, a simple relation is derived and states that the mobility is proportional to the slip length and the reciprocal of the product of viscosity and contact area. Our simulation results agree excellently with the theoretical prediction. In the absence of external forces, a two-dimensional Brownian motion of nanodroplets is observed and its mean square displacement decreases with increasing the defect density. The diffusivity is proportional to the mobility, consistent with the Einstein relation. This consequence suggests that thermal fluctuations are able to overcome contact line pinning caused by weak defects.

Non-locality of the contact line in dynamic wetting phenomena

HYPOTHESIS

The notion of the contact line is fundamental to capillary science, where in a large category of wetting phenomena, it was always regarded as a one-dimensional object involving only microscopic length scales. This prevailing opinion had a strong impact and repercussions on the developing theories and methodologies used to interpret experimental data. It is hypothesised that this is not the case under certain conditions leading to non-local effects and requiring the development of a modified force balance at the contact line.

THEORY AND SIMULATIONS

Using the first principles of molecular dynamic simulations and a unique combination of steady state conditions and observables, the microscopic structure of the contact region and its connections with macroscopic quantities of capillary flows was revealed for the first time.

FINDINGS

The contact line is shown to become a non-local, macroscopic object involving rather complex interplay between microscopic distributions of density, velocity and friction force. It was established that the non-locality effects, which cannot be in principle captured by localised methodologies, kick off at a universal tipping point and lead to a modified force balance. The developed framework is applicable to a wide range of capillary flows to identify and analyse this regime in applications.

Slip transition in dynamic wetting for a generalized Navier boundary condition

HYPOTHESIS

Computer fluid dynamics simulations of dynamic wetting are often performed using a slip model on the substrate. In previous studies, the generalized Navier boundary condition (GNBC) has shown promising results and could help clear the gap between molecular and continuum scales, but lacks quantitative comparisons to experiments. We seek to investigate the dependence between the contact-line velocity and the slip length in a GNBC, by confronting numerical simulations to experimental data.

EXPERIMENTS

The physical properties of a molten polymer (polyethylene glycol) were assessed thoroughly. Its dynamic contact angle on a cellulosic substrate was measured carefully using the Wilhelmy method. The experiment was reproduced in a finite elements model using a GNBC. It was repeated for capillary numbers between 10^-6 and 10^-1, and slip lengths ranging from 1 μm to 1 mm.

FINDINGS

A realistic value of the slip length was selected by matching the dynamic contact angles issued from numerical simulations and their experimental counterparts. The slip length behavior as a function of contact line velocity displayed a clear transition. The model also reproduced a dynamic wetting transition between frictional and viscous dissipations, which seems to be linked to an increasing difference between microscopic and macroscopic contact angles.

Taking a closer look: A molecular-dynamics investigation of microscopic and apparent dynamic contact angles

HYPOTHESIS

Molecular dynamics (MD) may be used to investigate the velocity dependence of both the microscopic and apparent dynamic contact angles (θ_m and θ_app).

METHODS

We use large-scale MD to explore the steady displacement of a water-like liquid bridge between two molecularly-smooth solid plates under the influence of an external force F⁰. A coarse-grained model of water reduces the computational demand and the solid-liquid affinity is varied to adjust the equilibrium contact angle θ⁰. Protocols are devised to measure θ_m and θ_app as a function of contact-line velocity U_cl.

FINDINGS

For all θ⁰, θ_m is velocity-dependent and consistent with the molecular-kinetic theory of dynamic wetting (MKT). However, θ_app diverges from θ_m as F⁰ is increased, especially at the receding meniscus. The behavior of θ_app follows that predicted by Voinov: (θ_app)³ = (θ_m)³ + 9Ca·ln(L/L_m), where Ca is the capillary number and L and L_m are suitably-chosen macroscopic and microscopic length scales. For each θ⁰, there is a critical velocity U_crit and contact angle θ_crit at which θ_app→0 and the receding meniscus deposits a liquid film. Setting θ_app=0, θ_m=θ_crit and U_cl=U_crit in the Voinov equation yields the value of L/L_m. The predicted values of θ_app then agree well with those measured from the simulations. Since θ_m obeys the MKT, we have, therefore, demonstrated the utility of the combined model of dynamic wetting proposed by Petrov and Petrov.