Abstract
When a droplet spreads on a solid substrate, it is unclear what the correct boundary conditions are to impose at the moving contact line. The classical no-slip condition is generally acknowledged to lead to a non-integrable singularity at the moving contact line, which a slip condition, associated with a small slip parameter, λ, serves to alleviate. In this paper, we discuss what occurs as the slip parameter, λ, tends to zero. In particular, we explain how the zero-slip limit should be discussed in consideration of two distinguished limits: one where time is held constant, t=O(1), and one where time tends to infinity at the rate t=O(|log λ|). The crucial result is that in the case where time is held constant, the λ → 0 limit converges to the slip-free equation, and contact line slippage occurs as a regular perturbative effect. However, if λ → 0 and t → ∞, then contact line slippage is a leading-order singular effect.
Original language | English (US) |
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Pages (from-to) | 107-126 |
Number of pages | 20 |
Journal | Journal of Fluid Mechanics |
Volume | 772 |
DOIs | |
State | Published - Jun 1 2015 |
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
Keywords
- contact lines
- lubrication theory
- thin films