A way of harvesting water from the air that avoids the discontinuity of the adsorption/desorption cycles is theoretically analyzed. A rectangular prism-shaped adsorbent bed is immersed in low-humidity air, at an angle to the horizontal and subject to a temperature gradient between two opposite and open faces. The other four faces of the prism remain isolated. Water is adsorbed on the adsorbent colder face, causing a density gradient in the surrounding air, parallel to the surface, that results in a self-sustained continuous air flow. On the opposite face, a self-sustained continuous air flow parallel to the surface also arises, but this time due to a temperature gradient in the air surrounding the hot bed face. In addition, its higher temperature causes the desorption of water from the adsorbent. This overall water exchange produces the enrichment of water content in one of the air streams that is crucial to produce water harvesting. The performance of Al-Fumarate, MOF-303, SAPO-34 and Zeolite 13X is tested, unveiling the key factors that increase flow rate and water concentration at the enriched phase. It has been found that the diffusive mass transport at the air-solid interphase is the bottleneck of water harvesting in continuous flow conditions. Therefore, if high concentration of water is desired, it is necessary to use porous materials with very high diffusitivities. These findings provide the foundations for the design of continuous water harvesting devices.