A study using the ideas and analytical techniques of fluid mechanics to investigate the role of plasma motion in the transport of species between erythrocytes and surrounding tissue in rather narrow capillaries. It has been widely believed that the plasma circulatory motion in the region between the red blood cells and capillary wall is sufficiently vigorous to augment the low rates of species transport by diffusion alone. This study makes a detailed theoretical and numerical examination of the bolus model of capillary flow. It shows that for this highly idealized situation, the convective motions of the plasma and the enhanced mixing due to these motions do not appreciably augment diffusional species-transport rates for dissolved gases. The results of the equations of motion and the equations of species transport indicate that plasma mixing is important only in the transfer of materials such as macromolecules, which may diffuse more slowly than dissolved gases.