Computing the viscous effect in early-time drop impact dynamics

TL;DR

This paper investigates how liquid viscosity and interfacial tension influence early-time dynamics of drop impact on solid surfaces, using numerical simulations to reveal complex dependencies beyond simple scaling laws.

Contribution

It introduces a coupled Navier-Stokes and lubrication model to analyze the viscous and interfacial effects during early drop impact, providing new insights into lift-off timing.

Findings

Viscosity affects lift-off time with a more complex relationship than the square root law.

Interfacial tension plays a significant role in mediating impact dynamics.

Numerical results align with experimental observations of early-time effects.

Abstract

The impact of a liquid drop on a solid surface involves many intertwined physical effects, and is influenced by drop velocity, surface tension, ambient pressure and liquid viscosity, among others. Experiments by Kolinski et al. (2014b) show that the liquid-air interface begins to deviate away from the solid surface even before contact. They found that the lift-off of the interface starts at a critical time that scales with the square root of the kinematic viscosity of the liquid. To understand this, we study the approach of a liquid drop towards a solid surface in the presence of an intervening gas layer. We take a numerical approach to solve the Navier-Stokes equations for the liquid, coupled to the compressible lubrication equations for the gas, in two dimensions. With this approach, we recover the experimentally captured early time effect of liquid viscosity on the drop impact, but our results show that lift-off time and liquid kinematic viscosity have a more complex dependence than the square root scaling relationship. We also predict the effect of interfacial tension at the liquid-gas interface on the drop impact, showing that it mediates the lift-off behavior.