The dynamics of drop formation and pinch-off have been investigated for a series of low viscosity elastic fluids possessing similar shear viscosities, but differing substantially in elastic properties. On initial approach to the pinch region, the viscoelastic fluids all exhibit the same global necking behavior that is observed for a Newtonian fluid of equivalent shear viscosity. For these low viscosity dilute polymer solutions, inertial and capillary forces form the dominant balance in this potential flow regime, with the viscous force being negligible. The approach to the pinch point, which corresponds to the point of rupture for a Newtonian fluid, is extremely rapid in such solutions, with the sudden increase in curvature producing very large extension rates at this location. In this region the polymer molecules are significantly extended, causing a localized increase in the elastic stresses, which grow to balance the capillary pressure. This prevents the necked fluid from breaking off, as would occur in the equivalent Newtonian fluid. Alternatively, a cylindrical filament forms in which elastic stresses and capillary pressure balance, and the radius decreases exponentially with time. A (0+1)-dimensional finitely extensible nonlinear elastic dumbbell theory incorporating inertial, capillary, and elastic stresses is able to capture the basic features of the experimental observations. Before the critical “pinch time” tp, an inertial-capillary balance leads to the expected 2∕3-power scaling of the minimum radius with time: Rmin∼(tp−t)2∕3. However, the diverging deformation rate results in large molecular deformations and rapid crossover to an elastocapillary balance for times t>tp. In this region, the filament radius decreases exponentially with time Rmin∼exp[(tp−t)∕λ1], where λ1 is the characteristic time constant of the polymer molecules. Measurements of the relaxation times of polyethylene oxide solutions of varying concentrations and molecular weights obtained from high speed imaging of the rate of change of filament radius are significantly higher than the relaxation times estimated from Rouse-Zimm theory, even though the solutions are within the dilute concentration region as determined using intrinsic viscosity measurements. The effective relaxation times exhibit the expected scaling with molecular weight but with an additional dependence on the concentration of the polymer in solution. This is consistent with the expectation that the polymer molecules are in fact highly extended during the approach to the pinch region (i.e., prior to the elastocapillary filament thinning regime) and subsequently as the filament is formed they are further extended by filament stretching at a constant rate until full extension of the polymer coil is achieved. In this highly extended state, intermolecular interactions become significant, producing relaxation times far above theoretical predictions for dilute polymer solutions under equilibrium conditions.

The rheological properties of 1 wt % aqueous solutions (at pH between 8.7 and 9.5) of model associative (HASE) polymers are presented. These polymers are the polymerization product of methacrylic acid, ethyl acrylate, and macromonomers which contain hydrophobes with the alkyl chain ranging in length from C12 to C20. At high pH, the polymers form a network of temporarily associating hydrophobic junctions, resulting in an enhancement of the shear viscosity which increases with the hydrophobe chain length. Strain amplitude sweep results show that the strength of the hydrophobic association increases with the length of the hydrophobe. This is also reflected in the increase in the ratio of the elastic to viscous components of the linear viscoelastic properties. When sheared beyond its equilibrium state, the associative polymers display a terminal (second-order) viscoelastic behavior at higher frequencies as the network is increasingly being disrupted by higher applied stresses. The general behavior of the polymers changes from Zimm-like to Rouse-like, and to reptation-type with a crossover between the storage and loss moduli curves, as the alkyl chain of the hydrophobes increases from 12 to 16, and to 20, carbon atoms. It is believed that in the unstressed state, other relaxation processes with much longer times are involved, and it is these long relaxation times which are greatly curtailed as the network is disrupted by an applied stress.

A filament stretching device for measuring the extensional viscosity of low-viscosity liquids is presented. The fluid sample is held between two disks which move apart at an increasing velocity so that the extension rate, based on the filament midpoint diameter, is constant. The device was used to measure the extensional stress growth coefficients of three ideal elastic solutions, including the model fluid M1 and a shear-thinning model fluid A1. The results indicate that all solutions containing high molecular weight polymer exhibit significant strain hardening as the fluid is extended. For the ideal elastic fluids, steady state in extensional stress was observed at strain above 4.5 and the steady Trouton ratio obtained for the fluids range from 2 to 5×103. For the fluid M1 the extensional viscosities obtained are higher than the apparent extensional viscosity obtained by other methods. This is the first time that the steady extensional viscosity has been measured for polymer solutions. The results obtained enable one to evaluate the numerous constitutive equations that have been proposed for polymer solutions.

The viscoelastic properties over a range of steady shear conditions of an alkali-swellable associative polymer have been determined using the technique of superposition of oscillations upon steady shear flow, thus enabling the structure of the polymer to be investigated. The associative polymer studied consists of a backbone of methacrylic acid and ethyl acrylate to which is attached macromolecules containing C20 hydrophobes via an ethylene oxide−isocyanate linkage. A 1 wt % solution with its pH adjusted to 9.5 was used. At high pHs, the polymer solubilizes to form a network of both intra- and intermolecular associating hydrophobic junctions. The solution shows a non-power-law shear-thinning behavior:  the viscosity flow curve, when plotted against shear stress, shows two distinct regions where network rupture is prominent, at stress of 2 Pa and between 40 and 50 Pa. By superimposing small amplitude oscillations on to shear flow at constant stresses, the network structure of the polymer is unperturbed and linear viscoelastic properties of the polymer under the applied stress conditions can be obtained. At an applied stress of 2 Pa and above, both the storage and loss moduli of the polymer are greatly reduced at low frequencies, with the G‘ approaching second-order behavior and η‘ tending toward constant values. By analogy to Maxwell relaxation time, an estimate of the relaxation time of the associative polymer at different stress conditions can be made. The results show that the relaxation time is reduced by up to 4 orders of magnitude as the stress is increased from 1 to 60 Pa, while a much smaller decrease in viscosity is observed. At sufficiently high frequencies, both the storage and loss moduli show an increase above their linear viscoelastic values as the strain amplitude is increased. This behavior is believed to be dependent on the relaxation time of the polymer which is a function of the state of network disruption. Thus the technique may prove to be a powerful tool for probing the structure of network polymer in solution.

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