Skip to main content
Open Access Publications from the University of California

UC Berkeley

UC Berkeley Previously Published Works bannerUC Berkeley

On the contact region of a diffusion-limited evaporating drop: A local analysis

  • Author(s): Morris, SJS;
  • et al.

Motivated by experiments showing that a sessile drop of volatile perfectly wetting liquid initially advances over the substrate, but then reverses, we formulate the problem describing the contact region at reversal. Assuming a separation of scales, so that the radial extent of this region is small compared with the instantaneous radius a of the apparent contact line, we show that the time scale characterizing the contact region is small compared with that on which the bulk drop is evolving. As a result, the contact region is governed by a boundary-value problem, rather than an initial-value problem: the contact region has no memory, and all its properties are determined by conditions at the instant of reversal. We conclude that the apparent contact angle θ is a function of the instantaneous drop radius a, as found in the experiments. We then non-dimensionalize the boundary-value problem, and find that its solution depends on one parameter 葦, a dimensionless surface tension. According to this formulation, the apparent contact angle is well-defined: at the outer edge of the contact region, the film slope approaches a limit that is independent of the curvature of bulk drop. In this, it differs from the dynamic contact angle observed during spreading of non-volatile drops. Next, we analyse the boundary-value problem assuming 葦 to be small. Though, for arbitrary 葦, determining θ requires solving the steady diffusion equation for the vapour, there is, for small 葦, a further separation of scales within the contact region. As a result, θ is now determined by solving an ordinary differential equation. We predict that θ varies as a-1/6, as found experimentally for small drops (a < 1 mm). For these drops, predicted and measured angles agree to within 10-30 %. Because the discrepancy increases with a, but 葦 is a decreasing function of a, we infer that some process occurring outside the contact region is required to explain the observed behaviour of larger drops having a > 1 mm.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View