Recent studies have demonstrated an increased concentration of several macromolecules in the anterior corneal stroma as compared to the posterior stroma. Possible mechanisms generating these gradients include volume exclusion, preferential binding and/or convection. One of these potential causes, convective flow driven by a combination of evaporation from the tear film and intraocular pressure, is examined here numerically. A one-dimensional, corneal transport model is used to estimate the average posterior-to-anterior (PA) flow rate. This fluid velocity is then applied to a simpler advection-diffusion model to estimate the magnitude of an albumin gradient in the PA direction. It was found that the influence of convection on the distribution of soluble albumin may contribute significantly to observed gradients in the corneal stroma. These results suggest that alteration of either the supply of a given protein to the cornea (e.g. granular corneal dystrophy (GCD)) or the convective flow rate (e.g. contact lens wear) may enhance the normal gradient of soluble macromolecules in the corneal tissue. The possibility that gradients in the local chemical composition of the stroma are driven ultimately by tear film evaporation has important clinical implications. It is concluded that a full understanding of the mechanisms behind some poorly understood corneal disorders (GCD) or responses to contact lens wear may require the consideration of the physiological phenomena that combine to establish the local stromal chemical milieu.