The nascent coffee ring: how solute diffusion counters advection

Author: 

Moore, M
Vella, D
OLIVER, J

Journal: 

Journal of Fluid Mechanics

Last Updated: 

2021-08-17T09:48:18.14+01:00

abstract: 

We study the initial evolution of the coffee ring that is formed by the
evaporation of a thin, axisymmetric, surface tension-dominated droplet
containing a dilute solute. When the solutal P\'{e}clet number is large, we
show that diffusion close to the droplet contact line controls the coffee-ring
structure in the initial stages of evaporation. We perform a systematic matched
asymptotic analysis for two evaporation models -- a simple, non-equilibrium,
one-sided model (in which the evaporative flux is taken to be constant across
the droplet surface) and a vapour-diffusion limited model (in which the
evaporative flux is singular at the contact line) -- valid during the early
stages in which the solute remains dilute. We call this the `nascent coffee
ring' and describe the evolution of its features, including the size and
location of the peak concentration and a measure of the width of the ring.
Moreover, we use the asymptotic results to investigate when the assumption of a
dilute solute breaks down and the effects of finite particle size and jamming
are expected to become important.

Symplectic id: 

1148477

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article