A micro-reactor is provided with a mixture of channels having larger cross-sectional areas (17,22,25,27,31,33) and channels having smaller cross-sectional areas (40a,40b,40c). The smaller channels (40a,40b,40c) resist liquid movement driven by hydrostatic force but allow liquid movement driven by electro-osmotic force. Accordingly liquid flow is almost entirely driven by electro-osmotic force. The smaller channels (40a,40b,40c) are formed by etched grooves which are closed by a planar surface 13. This allows the cross-sectional areas of the smaller channels to be closely and reproducibly controlled.