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

TL;DR

This paper compares the interface formation model with the Navier-slip model for droplet spreading, showing they are mathematically equivalent under quasistatic conditions and analyzing their physical implications.

Contribution

It demonstrates the equivalence of the interface formation model and slip models for droplet spreading, clarifying the role of the dynamic contact angle and boundary conditions.

Findings

The droplet radius evolution reduces to a slip model with a velocity-dependent contact angle.

The interface formation model predicts a dynamic contact angle correction.

Pressure and contact line motion features are analyzed in the prototype system.

Abstract

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. Multiphas. Flow 19, 589 (1993)], 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.