Drag Reduction of Straight and Branched Chain Aluminum Disoaps

Review on Drag Reduction and Its Heat Transfer by Additives

“…For most polymer solutions, drag reduction curves (both friction factors and mean velocities) are located in a domain bounded by the Newtonian line and by Virk's line. It is interesting to note that some systems other than polymer solutions have reported drag reduction which exceeds this asymptote [45,68,69]. The reason for that is the polymer equation was empirically derived from polymer drag reduction data [66].…”

Polymer and Surfactant Drag Reduction in Turbulent Flows

“…For surfactant drag reducers, however, the friction factor can be lower than that predicted by Virk's asymptote [McMillan, 1970;McMillan et al, 1971;Hershey et al, 1975;Chara et al, 1993]. Based on data for cationic surfactants in water and aluminum disoaps in hydrocarbons, Zakin et al [1996] proposed a new asymptote for nonpolymeric drag reducers:…”

A review on drag reduction with special reference to micellar systems

“…These two kinds of behaviour can be reconciled if one can realise that (a) the flexible polymer molecule needs to be elongated be a large velocity gradient before its full drag reducing ability is developed, and (b) the surfactant particles are oriented much more easily at lower velocity gradients, but are broken down at the high shear stresses associated with large velocity gradients. Further, in terms of equivalent molecular weight, micelles are known to have larger values [305] than polymers and hence they would naturally shift the onset of drag reduction to a lower shear stress value.…”