Table 1.

1D, 2D and 3D models for burst frequencies

Model	Equation	Notes
1D [16]	$P=\frac{4\cos {\theta }_{\mathrm{c}}{\gamma }_{\mathrm{la}}}{D}$	Describes the pressure in a capillary channel. (Refer to “Capillary” in Fig. 2)
2D [24]	$P=\frac{2{\gamma }_{\mathrm{la}}}{h_n}\left[\frac{\cos {\theta }_{\mathrm{c}}-\frac{\alpha }{\sin \alpha }\sin \beta }{\cos \beta +\frac{\sin \beta }{\sin \alpha }\left(\frac{\alpha }{\sin \alpha }-\cos \alpha \right)}\right]$	Describes the pressure when liquid begins to expand beyond the opening of the end of a channel (Refer to Stage 3 in Fig. 2)
3D [4]	$P=\frac{2{\gamma }_{\mathrm{la}}}{w}\left[-\frac{w}{h}\cos {\theta }_{\mathrm{c}}-\cos ({\theta }_{\mathrm{c}}+\beta )\right]$	Describes the pressure when liquid begins to expand beyond the opening of the end of a channel (Refer to Stage 3 in Fig. 2)

D is the diameter of a circular channel, D is substituted with the hydraulic diameter, D_h for a channel of any other shape, θ_c is the contact angle of liquid on solid (channel surface), γ_la is the liquid surface energy in contact with air, h_n is the height of the channel, w and h are the width and height of the channel, β is the opening angle of the channel expansion