Asymptotes of maximum friction and heat transfer reductions for drag-reducing surfactant solutions

A new maximum drag reduction asymptote (MDRA) for surfactant solutions is presented. Various concentrations including cationic and non-ionic surfactant solutions were used to experimentally determine this asymptote. It is shown that if solvent viscosity is used to compute Reynolds and Prandtl numbers for viscous solutions, it leads to underestimations of the friction coefficient. To avoid uncertainties in the selection of the fluids viscosity, most solutions used were intentionally conditioned so their shear viscosity was water-like in the ranges covered. Using the same solutions, a maximum heat transfer reduction asymptote (MHTRA) was also determined – a correlation that did not exist for surfactants until now. Finally, by using slightly modified definitions to quantify the heat transfer and drag reductions (TRH and TRD), it is possible to express the ratio between the MHTRA and MDRA with a constant value of 1.06, independent of Reynolds number. This relationship can be used as an auxiliary criterion to determine whether or not a solution is asymptotic when there is an uncertainty about the shear viscosity.