Drag Reduction arising from Adhesive Tapes

Abstract

COSSAR has reported1 that the presence of a uniform layer of double-sided adhesive tape (‘Scotch’ brand) on the floor of a water channel can have a significant influence on the mean-velocity profile in the boundary layer of a turbulent flow. Indeed, Cossar's experiments indicate that, in his operating conditions, the velocity distribution above a layer of adhesive tape is almost the same as that obtained in flow over rough boundaries for which the mean height of roughness is about 0.040 inches (0.116 cm). He accordingly suggested that ‘Scotch’ tape is physically “sticky” towards water. But Cossar's interpretation of his results is open to question: it may be that, rather than increasing the resistance to the flow, the influence of the adhesive tape reduces it. This conclusion can in fact be inferred from Cossar's results. For flows past smooth boundaries, the shear stress τ exerted on the boundary is related to the viscosity η and the normal velocity gradient by where u is the tangential velocity and y is the normal coordinate. But this is a good approximation only for boundaries that are hydraulically smooth, in the sense that the surface irregularities lie within the viscous sublayer of the flow. If, on the other hand, the roughness elements at the boundary are large enough, they can contribute to the shear stress exerted on the boundary through an effective form drag (see ref. 2, page 376), and then equation (1) is invalid. Indeed, it is usual for values of ∂u/∂y near the wall to decrease as the surface roughness increases (compare Cossar's results), although the actual shear stress exerted on the boundary increases. If we now make the assumption that the adhesive tape in Cossar's experiments was hydraulically smooth, it follows that the observed reduction in ∂u/∂y—which presumably extends right up to the wall—is accompanied by a reduction in shear stress, compared with what it would be on a smooth insoluble wall.