The study deals with the dynamics of the evaporation process in the pores of heat pipe wicks. The qualitative effect of increasing evaporation rates in capillary pumped devices on the capillary pressure is measured near the contact line within the representative pores in the wick. A wedgelike approximation of an evaporating meniscus is employed in the analysis along with a regular perturbation technique and first-order correction to the capillary pressure. It is shown that for an increasing evaporation rate, the capillary pressure increases as a result of evaporation. It is suggested that in liquid-metal heat pipes, the capillary pressure may not be adequately represented by the static capillary pressure, and that the driving capillary pressure should include dynamic contributions in the pressure-drop criterion for determining the capillary limit when designing liquid-metal heat pipes.