.Yz -Drag reduction. PACS. 82.70.Uv -Surfactants, micellar solutions, vesicles, lamellae, amphiphilic systems (hydrophilic and hydrophobic interactions). PACS. 83.50.Rp -Wall slip and apparent slip.Abstract. -Drag reduction of turbulent flows by surfactant additives is studied. The surfactant forms a shear-induced gel phase in both rheological and turbulent flows. In both flows, the fracture of the gel causes an apparent wall slip. The slipping in turbulent flows decreases the wall friction and therefore immediately leads to drag reduction, providing a detailed mechanism for drag reduction by surfactants.Introduction. -A spectacular reduction of energy losses in turbulent flows can be achieved by the addition of small amounts of certain polymers or surfactants [1, 2]. For polymers, drag reduction is due to the large elongational viscosity of the polymer solution; this stabilizes the turbulent boundary layer, leading to less turbulent energy generation, and hence less dissipation [3,4]. For surfactants, the phenomenon is still ill understood, in spite of the enormous attention the subject attracted over the past few decades, and the fact that due to their reversible degradation of the aggregates, surfactant solutions are better adapted to industrial applications than polymers that degrade irreversibly [5]. Surfactant drag reduction is uniquely found for systems forming wormlike micelles. These micelles are self-assembled structures in which the surfactants form tubular structures with a diameter roughly twice the size of a surfactant molecule and a length that can be thousands of times the molecular size. The flow behavior of dilute solutions of such wormlike micelles in both laminar and turbulent

We ask the question of whether birefringent bands observed during stress plateaus when shearing certain surfactant solutions correspond to shear banding, i.e., a region of high shear rate coexisting with a region of low shear rate. Our experimental observations on one surfactant system agree with the simple idea of a shear-induced transition between a high and a low viscosity ‘phase’. The detailed analysis of the velocity profiles allows us to reach the conclusion that the viscosities of the coexisting phases are those of the homogeneous fluids that exist before and after the stress plateau. The proportion of the shear-induced phase grows in the same fashion as that of the birefringent band, and the fraction of the gap occupied by the shear-induced fluid is found to follow a simple lever rule.