Immiscible or miscible gas injection and steam assisted gravity drainage are well known examples of gravity dominated recovery processes under isothermal and non-isothermal conditions, respectively. It is commonly observed in these processes that field scale applications yield less recovery than estimated. In order to clarify the reasons associated with the amount of the remaining oil in these processes, especially for the non-isothermal ones such as steam assisted gravity drainage (SAGD), pore scale experimental analysis of the mechanics is needed. In this paper, as complementary to our previous work (Argüelles and Babadagli, 2011) that used horizontally positioned circular capillaries, we studied the gravity drainage dominated flow of heavy-oil at pore scale using vertically positioned square and circular capillary tubes. Heavy crude oil samples were used and an elementary volume in the swept zone of SAGD was simulated using a single capillary tube. Detailed experiments were carried out to analyze: (1) the effects of oil viscosity on non-isothermal gravity drainage (including free fall), (2) behavior of co-current gravity driven displacement, (3) interplay among capillary, gravity and viscous (injection rates) forces and wettability, and (4) residual oil saturation and phase distribution in the capillaries. Also, we compared the residual oil saturation development results obtained for square capillaries with those for the circular ones having a diameter approximately equal to the side of the square capillary tube.