Bubble nucleation, growth and departure from a single cavity on the top of a uniformly hydrophilic heater and a uniformly hydrophobic heater at low superheats are investigated numerically based on a recently developed liquid-vapor phase-change lattice Boltzmann method. A conjugate 2D heat transfer problem, including heat conduction in the heated plate with a finite thickness, is considered in this paper. It is found that bubble nucleation starts in the central part of a hydrophilic cavity and at corners of a hydrophobic cavity. In addition, the bubble departure diameter from the single cavity increases with the increase of the contact angle on a uniform wettability surface. It is also found that there is little effect on bubble behaviors if the cavity depth is small, but there is a sudden jump in bubble departure frequency from a hydrophilic cavity when the cavity depth reaches a critical value, causing the formation of a residual bubble in the hydrophilic cavity. There also exists a critical cavity width, beyond which the bubble departure diameter and bubble departure frequency increase with the increase of cavity width, and therefore enhancing boiling heat flux. The three-phase contact line region exhibits the highest local heat flux and lowest local temperature along the rough heating surface, and its location greatly affects the direction of heat transfer on the vertical side walls of the cavity. The three-phase contact line is pinned at the cavity mouth on a uniformly hydrophilic rough surface while it is expanded to outside of the cavity mouth on a uniformly hydrophobic rough surface. For a mixed wettability rough surface with a hydrophobic cavity on a hydrophilic surface, it is shown that the hydrophobic cavity promotes bubble nucleation at low wall superheats while the hydrophilic surface prevents the forward expansion of the three-phase contact line outside of the cavity mouth. (C) 2016 Elsevier Ltd. All rights reserved.