In this thesis the effect of gas diffusion between bubbles on the bubble-size distribution and capillary resistance to foam flow in a bubble train is investigated using an idealized 2D pore model. First the shape of the model pore is discussed and how a lamella moves through it. Then the physical forces (lamella curvatures and pressure differences between bubbles) in the pores are explained and how they affect capillary resistance to foam flow. Next the parameters of the dimensionless model are related to measured fluid properties. Under certain conditions (large film permeability to gas, large surface tension, low pressure, small pores, and low velocity of flowing gas) it is possible that characteristic diffusion rate can be greater than imposed convection rate, and that all gas transport is from diffusion across lamellae, not bubble movement. We present model results for different ratios of characteristic diffusion to convection rates. If bubbles are smaller than pores, diffusion reduces the number of bubbles and increases average bubble size, whether convection is imposed on the foam or not. If convection is imposed, lamellae disappear not in pore throats but after first colliding in jumps across pore bodies. If bubbles are larger than pores, diffusion does not increase average bubble size. Diffusion increases the capillary resistance to flow; the increase is greatest when the characteristic rate of diffusion is close to the convection rate. Diffusion increases capillary resistance to flow because lamellae spend more time in positions of greater curvature than in the absence of diffusion. For characteristic diffusion rates much greater or much less than the imposed convection rate the effect of diffusion on capillary resistance to foam flow is modest. These results suggest that by itself, an increase in diffusion rate through lamellae does not make foam flow with less resistance. With diffusion lamellae spend more time in pore throats where capillary resistance to flow is greatest.