We consider the flow of a Newtonian fluid in a nano or microchannel with walls that have patterned variations in slip length. We formulate a set of equations to describe the effects on an incompressible Newtonian flow of small variations in slip, and solve these equations for slow flows. We test these equations using molecular dynamics simulations of flow between two walls which have patterned variations in wettability. Good qualitative agreement and a reasonable degree of quantitative

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... is found between the theory and the molecular dynamics simulations. The results of both analyses show that patterned wettability can be used to induce complex variations in flow. Finally we discuss the implications of our results for the design of microfluidic mixers using slip.