Effect of Temperature, Composition, and Shear Rate on Polyvinylidene Fluoride/ Dimethylacetamide Solution Viscosity Nayef M. Ghasem,* Mohamed H. Al-Marzouqi, and Muftah H. El-Naas Department of Chemical & Petroleum Engineering, UAE University, Al-Ain, P.O. Box 17555, U.A.E Viscosity required for casting or spinning dope polymeric solution plays an essential role in the formulation of flat sheets and hollow fiber membranes. A flat sheet membrane can be casted from a polymer dope with viscosity as low as a few hundred centipoises; by contrast, a few thousand are required to spin polymeric hollow fibers. In this study, an empirical correlation describing the effect of temperature, polymer mass fraction, and shear rates on the viscosity of polyvinylidene fluoride polymer in dimethylacetamide solvent was derived. The dope polymer was used in the fabrication of polymeric hollow fiber membranes engaged in building membrane contactors for water treatment and the removal of carbon dioxide from natural gas. Data were obtained for (0.10, 0.15, 0.20, and 0.25) mass fraction of polyvinylidene fluoride in dimethylacetamide solvent at temperatures of (25, 35, 45, 55, 65, and 80) °C. The predicted values by the correlation were in good agreement with the experimental data. This empirical correlation accounts for temperature dependencies in the power law shear-thinning exponent. The correlation was derived using a nonlinear regression technique and statistical analysis software. Introduction Fluids are usually classified based on their behavior between shear stress and shear rate into Newtonian and non-Newtonian. Newtonian fluids are defined as those exhibiting a direct proportionality relationship between shear stress and shear rate, whereas for non-Newtonian fluids, the relationship between shear stress and shear rate is not linear. Pseudoplastic fluids are called shear thinning fluids because their apparent viscosity decreases with shear rate. Increasing shear breaks down the internal structure within the fluid very rapidly and reversibly, and no time dependence is manifested. The power law is a model for the shear dependency of the viscosities of polymer melts and solutions. τ ) Kγ ˙ n (1) Viscosity, η, is the ratio of shear stress to shear rate, hence η ) τ/ γ ˙ (2) where τ is the shear stress; γ ˙ is the shear rate; and K and n are fitted parameters. The power law is accurate for the prediction of various viscosity shear rates for molten polymers. 1 It may be deduced that the applicability of the power law gets better with increasing solution concentration. If n ) 1, the flow is Newtonian, and the viscosity does not change with shear rate. The flow is pseudoplastic or shear thinning if n < 1. Most polymer melts and solutions are pseudoplastic. The flow is dilatants or shear-thickening if n > 1. At very low or very high shear rates, Newtonian flow prevails. The melt or solution viscosity is constant; therefore, the power law applies only at intermediate rates of shear. If the polymer molecules are rigid rods or dumbbells which orient themselves in response to the shear forces, the dependence of viscosity on shear rate results from the extra molecular alignment that comes with each increase in shear rate. 2 At very low shear rates, the molecular orientation is random, and therefore, the viscosity is shearing independent. Molecular orientation does not occur below a threshold shear rate. At extremely high shear rates, the alignment process is complete, and additional shear makes no difference. The Andrade equation 3 describes the temperature reliance of liquid viscosities. η ) A 1 e C/T (3) where η is viscosity in Pa and A 1 and C are fitted parameters. Viscosity also increases with increasing polymer concentration in exponential form η ) A 2 e DW (4) where A 2 and D are fitted parameters while W is the polymer mass fraction. The above equations (eqs 1, 3, and 4) can be combined to study the effect of polymer melts and solution viscosities as a function of shear rates, temperature, and polymer concentrations τ ) (K·A 1 ·A 2 )γ ˙ n e C/T e DW (5) Combining the empirical constant of eq 5 leads to τ ) Aγ ˙ n e C/T e DW (6) The effect of temperature and shear rate on a polyisoimide solution viscosity was investigated. 4 Data were obtained for 0.20, 0.30, and 0.40 mass fraction polyisoimide solutions in the ratio of 20:80 tetrahydrofuran/diglyme and for a 0.30 mass fraction solution in N-methyl-pyrrolidone at temperatures of (25, 35, 55, and 75) °C. The measurements were taken on a Brookfield cone and plate viscometer at shear rates ranging from (9.59 to 383.4) reciprocal seconds. Experimental data fits proposed model reasonably well. In some cases, the model provides a better fit. This model accounts for temperature dependencies in the power law shear-thinning exponent. The coefficients depend on the material lot that is being tested even * Corresponding author. E-mail: nayef@uaeu.ac.ae. J. Chem. Eng. Data 2009, 54, 3276–3280 3276 10.1021/je900248a CCC: $40.75  2009 American Chemical Society Published on Web 07/31/2009