The Effect of Surface Treatment on the Drag Characteristics in Laminar Flow

In this study, we explore the clear idea of drag change when the surface contains roughness. For that purpose, we performed a simple terminal velocity experiment using small solid spheres. The terminal velocity of Cu spheres is measured before and after they are surface treated to form superhydrophilic or superhydrophobic nanostructures and appreciable increase in the terminal velocity for both cases is observed. An analytic solution is derived to evaluate the corresponding slip length in an external flow and the result is comparable to values reported in previous studies of lithographically patterned superhydrophobic surfaces. To gain useful physical insight, incompressible Navier-Stokes equations are solved. From the solution, a simple explanation for the experimental observation is developed using the concept of friction drag and form drag. The total drag can be reduced when the reduction of the friction drag is larger than the increase of the form drag.