An electrophoresis device is described which separates cells, particles, proteins and other separands by collecting samples having decreasing electrophoretic mobility in a train of inverted cavities while an electric field is applied between the inverted cavities and a sample cuvette containing a mixture of cells, particles, proteins or other separands. A circular plate is provided for the inverted cavities, and this circular plate is rotated to collect fractions. The system utilizes an innovative purification method that combines free electrophoresis and multistage extraction in an instrument capable of separating living cells, particles, and proteins in useful quantities at high concentrations. Most multistage processes are based on equilibrium separations, but electrophoresis is a kinetic separation; therefore, a pseudoequilibrium paradigm was developed for use in optimizing separation parameters including number of stages and electrophoresis time per stage. This paradigm allows the application of McCabe-Thiele type analysis, and it was calculated, for example, that two separands differing by 20% in electrophoretic mobility can be purified to 95% purity with acceptable yield in about seven stages. Laboratory experiments demonstrated a 95% purification in four stages of a separand originally present at 4% when electrophoretic mobilities differed by 80%.