Parallel plate devices for hemofiltration or hemodialysis are provided. A parallel plate device includes a parallel plate assembly having an aligned stack of stackable plate subunits, each stackable plate subunit having a through channel for blood, where the blood channels are opened up at opposite ends of the parallel plate assembly. The parallel plate assembly is configured to form filtrate/dialysate channels interleaved with the blood channels, adjacent channels being separated by a silicon nanoporous filtration membrane. A blood conduit adaptor is attached to the parallel plate assembly at each of the ends, and is configured to distribute blood to or collect blood from the blood channels. Also provided are systems and methods for using the parallel plate devices.