A novel surface-flow filter has been designed to take advantage of a combination of both diffusion and lateral flow permeation, since active coatings, even if porous, tend to be far less permeable than through-flow constructs. The formation of a continuous coating layer virtually excludes any fluid transport into the coating other than by planar diffusion for gases or capillarity for liquids. This study considers the additional potential advantage of creating a pixelated/patterned coating, applied using a pin coater to form printed dots onto a highly permeable cellulose fibrous paper-like substrate. The coating—fine particulate calcium carbonate combined with micro-nanofibrillated cellulose as binder and humectant—reacts on exposure to NO2 gas to form calcium nitrate. Experimental results show an effective doubling of nitrate-forming efficiency using pixelated coating compared with a reference continuous layer coating. To establish an understanding of the comparative mechanisms of gas-coating contact, computational fluid dynamic modelling is used to generate surface pressure profiles combined with a pore network model of the coating to estimate theoretical fluid permeability and gas diffusion coefficients. Although pressure-driven permeation was calculated to be approximately two orders of magnitude less than the diffusive flow, it is concluded that patterned aerofoil pressure differential effects can reduce the impact of surface stagnant layering and so aid fluid transfer, boosting the diffusive transport, which in turn delivers greater contact efficiency based on the increased accessibility to the active coating.