Stokes flow in a drop evaporating from a liquid subphase
arXiv:1212.3986 · doi:10.1063/1.4823710
Abstract
The evaporation of a drop from a liquid subphase is investigated. The two liquids are immiscible, and the contact angles between them are given by the Neumann construction. The evaporation of the drop gives rise to flows in both liquids, which are coupled by the continuity of velocity and shear-stress conditions. We derive self-similar solutions to the velocity fields in both liquids close to the three-phase contact line, where the drop geometry can be approximated by a wedge. We focus on the case where Marangoni stresses are negligible, for which the flow field consists of three contributions: flow driven by the evaporative flux from the drop surface, flow induced by the receding motion of the contact line, and an eigenmode flow that satisfies the homogeneous boundary conditions. The eigenmode flow is asymptotically subdominant for all contact angles. The moving contact-line flow dominates when the angle between the liquid drop and the horizontal surface of the liquid subphase is smaller than , while the evaporative-flux driven flow dominates for larger angles. A parametric study is performed to show how the velocity fields in the two liquids depend on the contact angles between the liquids and their viscosity ratio.
submitted to Physics of Fluids
References in corpus (6)
- Order-to-disorder transition in ring-shaped colloidal stains
- Universal deformation of soft substrates near a contact line and the direct measurement of solid surface stresses
- Static wetting on deformable substrates, from liquids to soft solids
- How water droplets evaporate on a superhydrophobic substrate
- Contact angles on a soft solid: from Young's law to Neumann's law
- Stokes flow near the contact line of an evaporating drop