Exploring the role of gravity in coffee ring formation: the emergence of a secondary ring #

Madeleine Moore, Alex Wray

11:50 Wednesday in 3Q16.

Part of the Evaporation session.

Abstract #

We consider the role of gravity in solute transport when a thin droplet evaporates. Under the physically-relevant assumptions that the contact line is pinned and that solutal diffusion is dominated by advection in the droplet bulk, we identify two fundamental regimes that depend on the size of the Bond number. When the Bond number is moderate, the asymptotic structure of solute transport follows directly from the surface tension-dominated regime, whereby advection drives solute towards the contact line, only to be countered by local diffusive effects, leading to the formation of the famous ``coffee ring". For larger Bond numbers, where gravity dominates and forms so-called “puddle” or “pancake” drops, we identify a distinguished limit in which the diffusive boundary layer is comparable to the surface tension boundary layer in the liquid flow.

In each regime, we perform a systematic asymptotic analysis of the solute transport and compare our predictions to numerical simulations of the full model. Our analysis identifies the effect of gravity on the nascent coffee ring, providing quantitative predictions of the size, location and shape of the solute mass profile. Furthermore, we reveal that, for certain values of the Bond and Péclet numbers, a secondary peak may exist inside the classical coffee ring. We discuss the onset of this secondary peak and show that it is linked to the change in behaviour of the critical point in the droplet centre. Both the onset and the peak characteristics are shown to be driven by gravity, but solutal diffusion may act to remove the secondary peak when the classical coffee ring becomes so large as to subsume it.