Universal evolution of a viscous-capillary spreading drop

A generalized scaling theory for spontaneous spreading of Newtonian fluids on solid substrates

HYPOTHESIS

There exists a generalized solution for the spontaneous spreading dynamics of droplets taking into account the influence of interfacial tension and gravity.

EXPERIMENTS

This work presents a generalized scaling theory for the problem of spontaneous dynamic spreading of Newtonian fluids on a flat substrate using experimental analysis and numerical simulations. More specifically, we first validate and modify a dynamic contact angle model to accurately describe the dependency of contact angle on the contact line velocity, which is generalized by the capillary number. The dynamic contact model is implemented into a two-phase moving mesh computational fluid dynamics (CFD) model, which is validated using experimental results.

FINDINGS

We show that the spreading process is governed by three important parameters: the Bo number, viscous timescale τ_viscous, and static advancing contact angle, θ_s. More specifically, there exists a master spreading curve for a specific Bo and θ_s by scaling the spreading time with the τ_viscous. Moreover, we developed a correlation for prediction of the equilibrium shape of the droplets as a function of both Bo and θ_s. The results of this study can be used in a wide range of applications to predict both dynamic and equilibrium shape of droplets, such as in droplet-based additive manufacturing.

Lattice-Boltzmann simulations of the dynamics of liquid barrels

We study the relaxation towards equilibrium of a liquid barrel-a partially wetting droplet in a wedge geometry-using a diffuse-interface approach. We formulate a hydrodynamic model of the motion of the barrel in the framework of the Navier-Stokes and Cahn-Hilliard equations of motion. We present a lattice-Boltzmann method to integrate the diffuse-interface equations, where we introduce an algorithm to model the dynamic wetting of the liquid on smooth solid boundaries. We present simulation results of the over-damped dynamics of the liquid barrel. We find that the relaxation of the droplets is driven by capillary forces and damped by friction forces. We show that the friction is determined by the contribution of the bulk flow, the corner flow near the contact lines and the motion of the contact lines by comparing simulation results for the relaxation time of the barrel. Our results are in broad agreement with previous analytical predictions based on a sharp interface model.

Morphological classification and dynamics of a two-dimensional drop sliding on a vertical plate

A two-dimensional drop sliding down a plate under the action of gravity is numerically studied. A lattice Boltzmann method coupled with the phase field method is utilized, which can well capture the motion of the three-phase contact line. The morphologies of the sliding drop and corresponding force balance during the process are considered. It is found that there are two basic sliding modes of the drop with various gravitational and viscous effects. The viscous shear stress ( [Formula: see text] from the wall acts on the bottom of the drop, and it is divided in two parts. One is in the contact line region, and the other on the rest part of the solid-liquid interface (contacting area). The former one appears as [Formula: see text] -peaks, which are purely determined by the intrinsic contact angle ( [Formula: see text] and sliding speed. They are very local. When the gravity is small, the drop slides down very slowly, and such shear force can balance the gravity. Meanwhile, the shape of the droplet can be interestingly characterized as a "pendant drop". When the gravity increases, an additional shear force is generated mainly due to the appearing of a trail at the rear part of the drop. The de-wetting failure condition makes the sliding velocity almost constant in this regime. The present study is also valuable to understand the physics of three-dimensional drop sliding.