Elongational properties of liquids in contraction flow

Flows through contraction geometries (contraction flows) are found in many fields involving fluids, but they are poorly understood because they have two inseparable aspects as a whole: shear flow and elongational flow. In this paper, we focus on the center line of the contraction flow where the shear component vanishes because of the symmetry of the flow field and clarify elongational properties of liquids using the data obtained to date. First, we show images of contraction flows of water and dilute polymer solutions, and then, the continuity equation is used to obtain expressions for the center-line velocity. The expressions represent either the exponential contraction flow (ECF) or linear contraction flow (LCF) and agree well with experimental results obtained to date. It is suggested that the Deborah number plays an important role in deciding ECF or LCF. For dilute solutions of polyethylene oxide and polyacrylamide, the ratio of the elongational viscosity (μe) to the shear viscosity (μs) is found to be high, of the order of 104 and 103, respectively. On the other hand, molten polyethylene and 5.0-wt. % polyisobutylene in hydrocarbon tetradecane have greatly different values of μe and μs, but their values of μe/μs do not differ much from four. We propose a novel relaxation velocity number (RV) and find that the exponent ai of the ECF velocity-profile is correlated with log10RV for water, polymer solutions, and molten polyethylene. Furthermore, the expressions agree with experimental data for wet spinning. We propose a novel spinning model for the contraction flow of polymer solutions.