A. Introduction

Drag reduction is observed with many surfactant solutions, but the results differ from those obtained with polymers in a number of ways which include:

1. With surfactants, the mechanism of drag reduction is the formation of micelles (sub-microscopic structural units built up from the surfactant molecules). Though the micellular structures may be broken up in passage, say, through a centrifugal pump, they can reform downstream of the pump, reinstating the drag reduction effect. This contrasts with polymers where degradation is permanent (Hoyt, 1989).
   
   
2. Drag reduction with surfactants increases with Reynolds number, but then decreases with high Reynolds number, presumably because the thread-like micelles break up in the higher shear fields. This effect is illustrated by the data of Zhang et al. (2005) shown in Figure 1.
   
   
3. For surfactants, the drag reduction can be higher than the maximum obtained for polymers (namely the Virk maximum illustrated in Figure 234.7 and described by Equation 234.9). Results for drag reduction in a wide variety of surfactant systems are shown in Figure 2 (Zakin et al., 1996) and there is a corresponding increase in dimensionless velocity above the Virk maximum (Equation 234.14) as shown in Figure 3 (Chara et al., 1993). For surfactants, equations equivalent to Equation 234.9 and Equation 234.14 for maximum drag reduction are as follows:

\[\label{eq1}f=0.315\,\mbox{Re}^{-0.55}\tag{1}\]