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)
Figure 1. When the vapor pressure is greater than the liquid pressure across and interface, the interface curves so that the surface tension can accommodate the pressure difference. Figure used with permission of Dr. Jentung Ku.
Due to these capillary forces, liquid drops and vapor bubbles both have a pressure higher than the surrounding fluid. The smaller the drop or bubble, the smaller the radii of curvature, and the higher the pressure difference between inside and outside. In a heat pipe, the core of the heat pipe is filled with vapor, while the liquid is retained in the wick by capillary forces; see Figure 2.
Figure 2. A curved vapor/liquid interface forms when the vapor pressure is greater than the liquid pressure. Figure used with permission of Dr. Jentung Ku.
The heat pipe wick allows the capillary force to vary along the length of the heat pipe, returning liquid from the condenser to the evaporator. For sintered and screen wicks, the two radii of curvature are identical, so the capillary pressure equation reduces to:
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 counter currently 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 the condenser to evaporator.
Figure 3. (Top) The vapor/liquid interface is flat at the end of the condenser, where the vapor pressure is equal to the liquid pressure. The curvature increases until it is maximum at the end of the evaporator, due to the pressure drops in the countercurrent vapor and liquid flows. (Bottom) Pressure and capillary pressure along the length of the heat pipe. An adverse elevation increases the pressure drop (and curvature), due to the hydrostatic heat. Figure used with permission of Dr. Jentung Ku.
 These figures are taken from Dr. Jentung Ku’s excellent Heat Pipe Short Course and are used with his permission.