The dialysis method in protein isolation is a separation technique that works on the principle of selective and passive diffusion through a semipermeable membrane. It is used in laboratories for removing contaminants from a solution. 

Dialysis operates through the process of diffusion, which is the natural, thermal movement of molecules within a solution from areas of higher concentration to areas of lower concentration until it reaches a state of equilibrium. To achieve differential diffusion patterns, the sample and dialysate or buffer solution are separated with a semi-permeable membrane. 

Smaller molecules are able to permeate the membrane easily, diffusing into the dialysate, while the larger molecules are unable to traverse the pores of the membrane and thus remain within the sample chamber.