TY - JOUR
T1 - Statics and Dynamics of Liquid Barrels in Wedge Geometries
AU - Ruiz Gutierrez, Elfego
AU - Semprebon, Ciro
AU - McHale, Glen
AU - Ledesma Aguilar, Rodrigo
PY - 2018/5/10
Y1 - 2018/5/10
N2 - We present a theoretical study of the statics and dynamics of a partially wetting liquid droplet, of equilibrium contact angle, confined in a solid wedge geometry of opening angle. We focus on a mostly non-wetting regime, given by the condition, where the droplet forms a liquid barrel – a closed shape of positive mean curvature. Using a quasi-equilibrium assumption for the shape of the liquid–gas interface, we compute the changes to the surface energy and pressure distribution of the liquid upon a translation along the symmetry plane of the wedge. Our model is in good agreement with numerical calculations of the surface energy minimisation of static droplets deformed by gravity. Beyond the statics, we put forward a Lagrangian description of the droplet dynamics. We focus on the overdamped limit, where the driving capillary force is balanced by the frictional forces arising from the bulk hydrodynamics, the corner flow near the contact lines and the contact-line friction. Our results provide a theoretical framework to describe the motion of partially wetting liquids in confinement, and can be used to gain further understanding on the relative importance of dissipative processes that span from microscopic to macroscopic length scales.
AB - We present a theoretical study of the statics and dynamics of a partially wetting liquid droplet, of equilibrium contact angle, confined in a solid wedge geometry of opening angle. We focus on a mostly non-wetting regime, given by the condition, where the droplet forms a liquid barrel – a closed shape of positive mean curvature. Using a quasi-equilibrium assumption for the shape of the liquid–gas interface, we compute the changes to the surface energy and pressure distribution of the liquid upon a translation along the symmetry plane of the wedge. Our model is in good agreement with numerical calculations of the surface energy minimisation of static droplets deformed by gravity. Beyond the statics, we put forward a Lagrangian description of the droplet dynamics. We focus on the overdamped limit, where the driving capillary force is balanced by the frictional forces arising from the bulk hydrodynamics, the corner flow near the contact lines and the contact-line friction. Our results provide a theoretical framework to describe the motion of partially wetting liquids in confinement, and can be used to gain further understanding on the relative importance of dissipative processes that span from microscopic to macroscopic length scales.
KW - Capillary flows
KW - contact lines
KW - liquid bridges
U2 - 10.1017/jfm.2018.116
DO - 10.1017/jfm.2018.116
M3 - Article
VL - 842
SP - 26
EP - 57
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
SN - 0022-1120
ER -