Flow-induced migration polyethylene-co-methacryhc acid (PE-co-MA) and polystyrene-b-polydimethylsiloxane (PS-b-D) MS) copolymer additives in commercial long-chain branch polyethylene (PE) and narrow-molecular distribution polystyrene (PS) hosts was investigated in a capillary flow device. Attenuated Total Reflection Fourier Transform Infrared (ATR-FITR) spectroscopy and Dynamic Contact Angle (DCA) measurements were used to characterize surface composition of polymer specimen following extrusion through metallic dies with various length-to-diameter (L/D) ratios, (1100 less than or equal to L/D less than or equal to 3000). Results from experiments covering a broad range of shear rates and polymer residence times in the dies are reported. Provided that the polymer residence time in the die is sufficiently long, shear is found to increase the concentrations of low molecular weight copolymer additives on the host polymer's surface. The surface composition of copolymer additive is found to vary strongly with the wall shear rate and die L/D ratio. Decreasing the die diameter at fixed flow rate is found, for example, to be a more effective method for enhancing transport of additive to a polymer's surface than increasing shear rate at fixed diameter. A mechanism based on shear-induced diffusion is proposed to explain the observed migration.