TY - JOUR
T1 - Stokes flow near the contact line of an evaporating drop
AU - Gelderblom, Hanneke
AU - Bloemen, Oscar
AU - Snoeijer, Jacco H.
PY - 2012/10/1
Y1 - 2012/10/1
N2 - The evaporation of sessile drops in quiescent air is usually governed by vapour diffusion. For contact angles below 90 , the evaporative flux from the droplet tends to diverge in the vicinity of the contact line. Therefore, the description of the flow inside an evaporating drop has remained a challenge. Here, we focus on the asymptotic behaviour near the pinned contact line, by analytically solving the Stokes equations in a wedge geometry of arbitrary contact angle. The flow field is described by similarity solutions, with exponents that match the singular boundary condition due to evaporation. We demonstrate that there are three contributions to the flow in a wedge: the evaporative flux, the downward motion of the liquid-air interface and the eigenmode solution which fulfils the homogeneous boundary conditions. Below a critical contact angle of 133. 4 , the evaporative flux solution will dominate, while above this angle the eigenmode solution dominates. We demonstrate that for small contact angles, the velocity field is very accurately described by the lubrication approximation. For larger contact angles, the flow separates into regions where the flow is reversing towards the drop centre.
AB - The evaporation of sessile drops in quiescent air is usually governed by vapour diffusion. For contact angles below 90 , the evaporative flux from the droplet tends to diverge in the vicinity of the contact line. Therefore, the description of the flow inside an evaporating drop has remained a challenge. Here, we focus on the asymptotic behaviour near the pinned contact line, by analytically solving the Stokes equations in a wedge geometry of arbitrary contact angle. The flow field is described by similarity solutions, with exponents that match the singular boundary condition due to evaporation. We demonstrate that there are three contributions to the flow in a wedge: the evaporative flux, the downward motion of the liquid-air interface and the eigenmode solution which fulfils the homogeneous boundary conditions. Below a critical contact angle of 133. 4 , the evaporative flux solution will dominate, while above this angle the eigenmode solution dominates. We demonstrate that for small contact angles, the velocity field is very accurately described by the lubrication approximation. For larger contact angles, the flow separates into regions where the flow is reversing towards the drop centre.
KW - capillary flows
KW - contact lines
KW - drops
UR - http://www.scopus.com/inward/record.url?scp=84869782348&partnerID=8YFLogxK
U2 - 10.1017/jfm.2012.321
DO - 10.1017/jfm.2012.321
M3 - Article
AN - SCOPUS:84869782348
VL - 709
SP - 69
EP - 84
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
SN - 0022-1120
ER -