In this study the interaction of human erythrocytes in suspension with a planar ice-liquid interface is investigated. Due to a repulsive van der Waals force repelling the cells from the crystal and an attractive force resulting from the viscous drag of melt flow around the cell a velocity was determined below which the cell is pushed by the growing crystal and above which it is entrapped by the solid phase. The critical velocity for erythrocytes suspended in 0.85 wt% NaCl-D2O solution can be derived from measuring the time periods of pushing and is calculated to be 1.1 microns/s at a temperature gradient of 15.3 K/mm.