Molecular origin of contact line friction in dynamic wetting

A hydrophilic liquid, such as water, forms hydrogen bonds with a hydrophilic substrate. The strength and locality of the hydrogen bonding interactions prohibit slip of the liquid over the substrate. The question then arises how the contact line can advance during wetting. Using large-scale molecular dynamics simulations we show that the contact line advances by single molecules moving ahead of the contact line through two distinct processes: either moving over or displacing other liquid molecules. In both processes friction occurs at the molecular scale. We measure the energy dissipation at the contact line and show that it is of the same magnitude as the dissipation in the bulk of a droplet. The friction increases significantly as the contact angle decreases, which suggests suggests thermal activation plays a role. We provide a simple model that is consistent with the observations.

Figure 1

The simulated systems are droplet cylinders with $R=50$ nm, consisting of 1.2 million water molecules. After making contact with the hydrophilic substrates they spread out with a base radius $r\left(t\right)$. Zooming in shows the molecular nature of the droplets, which is particularly important at the contact line.

Figure 2

(a) A sampled 2D number density plot of hydrogen atoms in the first layer of water molecules shows that they are localized (hydrogen bonded) to the underlying ${\mathrm{SiO}}_2$ “molecules.” (b) A snapshot of hydrogen-bonded molecules. All but the water molecules in gray are hydrogen bonded.

Figure 3

Measurements of the wetting radius $r\left(t\right)$ (left) and the dynamic contact angle $\theta \left(t\right)$ (right) for simulations on all involved substrates. The dashed lines denote the two equilibrium states of angles ${36}^{\circ }$ and ${70}^{\circ }$.

Figure 4

The measured contact line friction coefficient ${\mu }_f$ in units of viscosity $\mu$ for all substrates. When the liquid cannot slip, the coefficient increases as the droplet wets the substrate.

Figure 5

Contact line dissipation rate ${\dot{E}}_{{\mu }_f}$ as a fraction of the energy gained as the droplet wets the substrate ${\dot{E}}_{\gamma }$. For the no-slip substrates around half of the gained energy is dissipated at the contact line.

Figure 6

Modes of contact line advancement for a no-slip system. The bottom layer of liquid molecules are hydrogen bonded to the substrate. (a) A molecule A rolls in from an upper layer to advance the contact line. To advance from I it has to pass the intermediate state II. Its interactions with neighboring molecules lead to an energy barrier that has to be crossed through a thermal fluctuation of the interface. After crossing it, it is pulled towards the substrate III. (b) The outermost molecule B jumps to a neighboring lattice site. This is described by molecular kinetic theory.

Figure 7

The contact line friction modeled as a geometry-dependent energy barrier through the contact angle $\theta$. A good agreement is reached between such a model (lines) and the measured velocities (circles) in late-stage wetting for all bar the extremely hydrophilic system. The bars mark measurements using a Couette flow setup for the no-slip ${36}^{\circ }$ substrate: from right to left the ticks, respectively, show measurements of the contact angle $\theta$ at 0.5 nm, 0.7 nm, and 1.0 nm above the substrate.