Capillary rise between parallel plates ($h=2\gamma \cos \theta /(\Delta \rho gd)$)

Two wide vertical plates separated by gap $d$ provide two contact lines per unit width. Upward surface-tension force $2\gamma \cos \theta$ balances column weight $\Delta \rho gdh$. Compared with a circular tube of radius $r$, the height ratio is $r/d$ for the same fluid and contact angle. Equal plate gap and tube diameter give half the tube rise.