Early stages of spreading and sintering

TL;DR

This paper investigates the early stages of sintering in viscous droplets, drawing an analogy to droplet spreading and elastic contact, and derives a scaling law for contact radius growth over time.

Contribution

It introduces a novel scaling law for the initial growth of contact radius in viscous droplet sintering, extending the analogy to elastic contact and including viscoelastic effects.

Findings

Derived a scaling law: a=(3 π γ R^2 t/(32 η))^{1/3}

Established the relation between contact radius growth and creep compliance for viscoelastic fluids

Complemented existing Tanner law for low contact angles with new early-stage results.

Abstract

The early stages of sintering of highly viscous droplets are very similar to the early stages of a viscous droplet spreading on a solid substrate. The flows in both problems are closely analogous to the displacements in a Hertzian elastic contact. We exploit that analogy to provide both a scaling argument and a calculation for the early growth of the contact radius $a$ with time, namely $a=(3 \pi \gamma R^2 t/(32 \eta))^{1/3}$. (This result is complementary to the well-known Tanner law for spreading, $a \sim t^{1/10}$, which holds in the regime of low contact angles.) For viscoelastic fluids, the linear scaling of $a^3$ with time is replaced by the general result that $a^3(t)$ is proportional to the creep compliance $J(t)$.