Uptake of Low Density Lipoproteins (LDL) by the arterial wall is likely to play a key role in the process of atherosclerosis initiation. Not only can such an uptake account for the lipid rich nature of atherosclerotic lesions, it can also explain their patchy distribution, via mechanisms that spatially mediate the rate of trans-endothelial LDL transport. A particular mechanism that may facilitate the non-uniform uptake of LDL is the formation of a flow-dependent LDL concentration polarisation on the luminal side of the endothelium. In the study presented here the effect of a spatially non-uniform transmural water flux (passing through intercellular clefts only) on such a concentration polarisation is investigated computationally. Results of the study show that under certain physiological conditions, a non-uniform transmural flux will cause significant and shear-dependent sub-cellular scale variations in LDL concentration polarisation. Further results indicate that this can lead to a considerable shear-dependence of LDL influx into the arterial wall, in addition to the shear-dependence due to larger scale flow features affecting the overall degree of concentration polarisation. This additional effect (~23% decrease in uptake as shear rate is increased from 0s^-1 to 3000s^-1 ) is seen when assuming transcytosis of LDL occurs only in regions within one micron of intercellular clefts. This is a reasonable assumption since caveolae have been shown to occur most frequently near cell edges.