Table 1.

Capillary rise equation for various cross-sections.

Capillary rise equation	Groove cross-section	Non-dimensional equation	References
$h_{\mathit{rec}}=\frac{\sigma \left[\left(2D+W\right)cos\theta -W\right]}{\rho gDWSin\alpha }$ ${\text{P}}_{\text{w}}=2\text{D}+\text{W}$ ${\text{A}}_{\text{c}}=\text{D}\times \text{W}$		$h_{\mathit{rec}}^{\ast }=cos\theta -\frac{W}{P_w}$	21
$h_{\mathit{cyl}}=\frac{\sigma \left[\left(\pi R+2d\right)cos\theta -2R\right]}{\rho g\left[2dR+\pi R^2/2\right]Sin\alpha }$ ${\text{P}}_{\text{w}}=\pi R+2d$ ${\text{A}}_{\text{c}}=2dR+\pi R^2/2$		$h_{\mathit{cyl}}^{\ast }=cos\theta -\frac{W}{P_w}$	23
$h_{\mathit{tri}}=\frac{\sigma \left[2cos\theta \sqrt{D^2+\frac{W^2}{4}}-W\right]}{\rho gWD/2Sin\alpha }$ ${\text{P}}_{\text{w}}=2\sqrt{D^2+\frac{W^2}{4}}$ ${\text{A}}_{\text{c}}=W\times D/2$		$h_{\mathit{tri}}^{\ast }=cos\theta -\frac{W}{P_w}$	24
$h_{\mathit{curv}}=\frac{\sigma \left[\left(\pi R+2d+l\right)cos\theta -2R-l\right]}{\rho g\left[2dR+dl+Rl+\pi R^2/2\right]Sin\alpha }$ ${\text{P}}_{\text{w}}=\pi R+2d+l$ ${\text{A}}_{\text{c}}=2dR+l\left(d+R\right)+\pi R^2/2$		$h_{\mathit{curv}}^{\ast }=cos\theta -\frac{W}{P_w}$	23
$h_{\mathit{trap}}=\frac{\sigma \left[\left(l+2\sqrt{D^2+\frac{{\left(W-l\right)}^2}{4}}\right)cos\theta -W\right]}{\rho g\left(l+W\right)D/2Sin\alpha }$ ${\text{P}}_{\text{w}}=l+2\sqrt{D^2+\frac{{\left(W-l\right)}^2}{4}}$ ${\text{A}}_{\text{c}}=\left(l+W\right)\times D/2$		$h_{\mathit{trap}}^{\ast }=cos\theta -\frac{W}{P_w}$	–
$h_{\mathit{ellip}}=\frac{\sigma \left[\left(2bE\left(\sqrt{1-{\epsilon }^2}\right)\right)cos\theta -2b\epsilon \right]}{\rho g\left[\pi \epsilon b^2/2\right]Sin\alpha }$ ${\text{P}}_{\text{w}}=2bE(\sqrt{1-{\epsilon }^2})$ ${\text{A}}_{\text{c}}=\pi \epsilon b^2/2$		$h_{\mathit{ellip}}^{\ast }=cos\theta -\frac{W}{P_w}$	25