Journal of Non-Newtonian Fluid Mechanics, Vol.62, No.1, 81-94, 1996
Flow past a sphere in polystyrene-based Boger fluids: The effect on the drag coefficient of finite extensibility, solvent quality and polymer molecular weight
This study experimentally investigates how the drag behavior of a sphere falling in a Boger fluid is affected by the fluid's extensibility, solvent quality and chain molecular weight. By means of terminal velocity measurements under conditions of creeping flow, deviations from Newtonian drag behavior in a homologous series of three polystyrene-based Boger fluids were measured as a function of Weissenberg number (We). The polymer-solvent quality and polymer molecular weight of each of the Boger fluids were manipulated in a manner that produced a systematic variation in the degree of extensibility of the fluids. Here, we define extensibility in terms of the FENE model parameter L, the ratio of a fully extended coil length to an equilibrium coil length. It is expected that L varies by nearly a factor of three over this series of Boger fluids. The compositions and ranking of the degree of extensibility of the three Boger fluids are the following: a high extensibility fluid of 2.0 x 10(7) g mol(-1) polystyrene in a poor, dioctyl phthalate (DOP)-based solvent, a medium extensibility fluid of 2.0 x 10(7) g mol(-1) polystyrene in a good, tricresyl phosphate (TCP)-based solvent and a low extensibility fluid of 2.0 x 10(6) g mol(-1) polystyrene in a poor DOP-based solvent. The principal result of the falling sphere experiments is that while the low extensibility fluid shows only small deviations from Newtonian behavior at all tested We, the two fluids of greater extensibility show drag enhancement of more than 300% for We > 1. These experiments are in agreement with the earlier work of Tirtaatmadja et al. and Chmielewski et al., indicating that the drag does not correlate with We alone. Here, by using monodisperse polymers and systems in which the polymer-solvent interactions have been characterized, we are also able to determine the sensitivity of the dimensionless drag to polymer molecular weight and polymer-solvent quality.
Keywords:VISCOELASTIC FLOW;EXTENSIONAL VISCOSITY;CYLINDRICAL TUBE;CREEPING FLOW;CYLINDERS;EQUATION;BUBBLES;MOTION;NUMBER