We present a new type of free-flow electrophoresis (FFE) device for performing on-chip microfluidic isotachophoresis and zone electrophoresis. FFE is performed using metal gallium electrodes, which are isolated from a main microfluidic flow channel using thin micron-scale polydimethylsiloxane/carbon black (PDMS/CB) composite membranes integrated directly into the sidewalls of the microfluidic channel. The thin membrane allows for field penetration and effective electrophoresis, but serves to prevent bubble generation at the electrodes from electrolysis. We experimentally demonstrate the ability to use this platform to perform on-chip free-flow electrophoretic separation and isotachophoretic concentration. Due to the small size and simple fabrication procedure, this PDMS/CB platform could be used as a part of an on-chip upstream sample preparation toolkit for portable microfluidic diagnostic applications.