The invention provides a microfluidic apparatus for performing 2-D biomolecular separations. The microfluidic 2-D device may include first and second planar substrates which include at least a first dimension microchannel extending in a first direction and an array of second dimension microchannels extending in a second direction, preferably, orthogonal to the first dimension. The ends of at least some of the microchannels are in fluid communication with a plurality of reservoirs. The substrates may further include a number of microchannels and reservoirs. The reservoirs are in electrical communication with a plurality of electrodes and voltage power sources. The device enables two dimensional separations of proteins, DNA and other biomolecules. According to another aspect of the invention, an array of tertiary microchannels extending in a third direction may be utilized.