Capillary evaporation (cavitation) has been suggested to be a possible source of long range interactions between mesoscopic hydrophobic surfaces. While evaporation is predicted by thermodynamics, little is known about its kinetics. Glauber dynamics Monte Carlo simulations of a lattice gas close to liquid-gas coexistence and confined between partially drying surfaces are used to model the effect of water confinement on the dynamics of surface-induced phase transition. Specifically, we examine how kinetics of induced evaporation changes as the texture of hydrophobic surfaces is varied. Our results provide guidelines for efficient manipulation of surface properties. We find that evaporation rates can be considerably slowed upon deposition of relatively small amount of hydrophilic coverage. The distribution of hydrophilic patches is however crucial, with the regularly spaced distribution being much more effective in slowing the formation of vapor tubes that trigger the evaporation process. To relate simulation rates to experimental ones, we also perform calculations using the mass-conserving Kawasaki algorithm. We predict evaporation time scales that range from hundreds of picoseconds in the case of mesoscopic surfaces similar to 10(4) nm(2) to tens of nanoseconds for smaller surfaces similar to 2x10(2) nm(2), when the two surfaces are similar to 10 solvent layers apart. The present study demonstrates that cavitation is kinetically viable in real systems and should be considered in studies of processes at confined geometry.