Young's law for a nonlocal isoperimetric model of charged capillarity droplets

Abstract

We study a variational problem modeling equilibrium configurations of charged liquid droplets resting on a surface under a convexity constraint. In the two-dimensional case with Coulomb interactions, we establish the validity of Young's law for the contact angle for small enough charges.

Figures (7)

• Figure 1: Contact sets and contact angles
• Figure 2: Competitor obtained by cutting
• Figure 3: Contact angle $\gamma \in (0, \pi/2)$, $\gamma = \pi/2$ and $\gamma \in (\pi/2, \pi)$.
• Figure 4: Two cases.
• Figure 5: Contact angle $\gamma \in (0, \pi/2)$, $\gamma = \pi/2$ and $\gamma \in (\pi/2, \pi)$.

Theorems & Definitions (50)

• Theorem 1.1
• Theorem 1.2
• Remark 1.3
• Lemma 2.1
• proof
• Lemma 2.2
• Theorem 2.3
• Remark 2.4
• Remark 3.1: Non-existence of minimizers when $\beta \geq 1$
• Remark 3.2: No capillarity phenomena when $\beta \leq -1$