When a heat pipe operates, heat applied in the evaporator vaporizes the working fluid, which travels to the condenser and condenses. The condensate is returned passively to the evaporator by capillary forces. As discussed in the capillary limits page, for the heat pipe to function, the maximum capillary force that the wick can generate must be greater than the sum of the vapor pressure drop, the liquid pressure drop, and the gravitational head.
The pressure difference between the liquid and vapor at any location on the interface is known as the capillary pressure, ΔPc.
ΔPc = PVapor – PLiquid
The capillary pressure depends on surface tension and two radii of curvature of the liquid/vapor interface, measured perpendicular to each other:
σ Surface tension, N/m
r1 and r2 are the radii of curvature (m)
where rc is the pore radius.
One of the radii is infinite for grooves, so the equation becomes:
The pressures and curvatures are shown schematically in Figure 3. The vapor pressure drops from its initial value as the vapor travels towards the condenser, while the liquid pressure drops as the liquid travels countercurrently back to the evaporator. Therefore, the vapor pressure is always higher than the liquid pressure (except at the end of the condenser), so a capillary pressure exists along the entire heat pipe. To support this pressure difference, the liquid/vapor interface is curved, with the curvature increasing along the length of the heat pipe, from condenser to evaporator.
 These figures are taken from Dr. Jentung Ku’s excellent Heat Pipe Short Course and are used with his permission.