= Solution
The <Young–Laplace equation> is $p_l-p_v=\gamma(1/R_1+1/R_2)$ with signed principal curvatures positive for a convex <liquid> droplet. A <wetting> bridge between plates has a strongly concave meridional curvature. If the <contact angle> through the <liquid> is $\theta$, the plate separation is $d$, and the bridge radius is approximately $a\gg d$, then
$$
p_v-p_l\simeq\frac{2\gamma\cos\theta}{d}+O(\gamma/a).
$$
\b[For complete <wetting>, the leading suction is $p_v-p_l\simeq2\gamma/d$.] The neglected azimuthal curvature is of order $1/a$. A numerical <pressure> cannot be specified without the separation, <surface tension> and <wetting> condition. The full signed-curvature expression remains valid when the narrow-gap approximation is unsuitable.
\Image[/past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2017/paper-1-capillary-bridge.png]
{title=<capillary pressure> suction in an original narrow liquid-bridge schematic}
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