Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 344 / 3 / a

Table of contents
- Solution a

Solution

The Young–Laplace equation gives a pressure excess

2 σ / R

inside a spherical droplet. Near coexistence, the common chemical-potential shift is

μ ≃ α δ

, where

α = f^{''} (ϕ_{B})

, while changing phase changes the composition by approximately

2 ϕ_{B}

. Balancing the capillary pressure against this thermodynamic shift gives the Gibbs--Thomson relation

2 ϕ_{B} α δ ≃ \frac{2 σ}{R} .

Hence the compositions immediately outside and inside are

ϕ (R^{+}) = - ϕ_{B} + δ (R), ϕ (R^{-}) = + ϕ_{B} + δ (R),

with

δ (R) = \frac{σ}{α ϕ _{B} R} \propto \frac{σ}{R} .

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version