The surface of a substrate may be smoothly covered with a liquid when the substrate is fixed in a holder which together with forms, together with the surface of the substrate, a process volume into which the liquid may be introduced onto the surface of the substrate by means of a wetter, and when the holder including the substrate is set in a swaying motion by means of a swayer, so that the liquid will smoothly spread on the surface of the substrate. By the swaying motion, concentration of the volume of liquid at a specific location of the substrate surface is prevented, since the direction of motion of the liquid changes constantly.