In the study of interactions of blood with artificial surfaces, it is common practice to wet these surfaces with a saline solution before exposing them to blood. The effect of this procedure on subsequent adhesion of blood platelets has been investigated both theoretically and experimentally, with a spinning disc apparatus. A large part of the observed delay in the initiation of platelet adhesion when using this apparatus is attributed to the time involved in displacing the prewetting fluid and bringing platelets near the surface. This observation is relevant to speculations of other researchers about the time course of adhesion-related reactions at the surface-proper. Other theoretical solutions are developed for the transient Leveque problem, which relates to a uniform shear-flow near a surface, and for a stagnation point apparatus. These solutions are compared with delay effects noticed in experimental data published by others.