We study the deformation of oil droplets of varying viscosity adhering to a solid, rigid wall in a rectangular channel induced by a pressure-driven, laminar flow of water. Our experimental investigation involves the systematic study of the effects of initial droplet volume, flow rate and viscosity ratio on the various modes of droplet motion and deformation; this is performed via direct visualisation of the flow in a glass cell using a high-speed camera. Our results are used to construct flow maps that delineate the critical conditions for droplet 'sliding', 'crawling' and detachment from the channel wall as a function of system parameters. Comparisons of our experimental results with numerical predictions obtained using a procedure based on the diffuse-interface method yield reasonably good agreement for certain flow regimes. (C) 2010 Elsevier Ltd. All rights reserved.