V. Tirtaatmadja

Drop formation and breakup of low viscosity elastic fluids: Effects of molecular weight and concentration

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 i...

Drop formation dynamics of constant low-viscosity, elastic fluids

The dynamics of drop formation under gravity has been investigated as a function of elasticity using a set of low-viscosity, ideal elastic fluids and an equivalent Newtonian glycerol-water solution. All solutions had the same shear viscosity, equilibrium surface tension, and density, but differed greatly in elasticity. The minimum drop radius in the early stages of drop formation (necking) was found to scale as expected from potential flow theory, independent of the elasticity of the solutions. Thus, during this stage of drop formation when viscous force is still weak, the dynamics are controlled by a balance between inertial and capillary forces, and there is no contribution of elastic stresses of the polymer. However, upon formation of the pinch regions, there is a large variation in the drop development to break-off observed between the various solutions. The elastic solutions formed secondary fluid threads either side of a secondary drop from the necked region of fluid between the upper and lower pinches, which were sustained for increasing amounts of time. The break-off lengths and times increase with increasing elasticity of the solutions. Evolution of the filament, length is, however, identical in shape and form for all of the polymer solutions tested, regardless of differing elasticity. This de-coupling between filament growth rate and break-up time (or equivalently, final filament length at break-up) is rationalised. A modified force balance to that of Jones and Rees [48] is capable of correctly predicting the filament growth of these low-viscosity, elastic fluids in the absence of any elastic contributions due to polymer extension within the elongating filament. The elongation of the necked region of fluid (which becomes the filament) is dominated by the inertia of the drop, and is independent of the elasticity of the solution. However, elasticity does strongly influence the resistance of the pinch regions to break-off, with rapid necking resulting in extremely high rates of surface contraction on approach to the pinch point, initiating extension of the polymer chains within the pinch regions. This de-coupling phenomenon is peculiar to low-viscosity, elastic fluids as extension does not occur prior to the formation of the pinch points (i.e. just prior to break-up), as opposed to the high viscosity counterparts in which extension of polymers in solution may occur even during necking. Once steady-state extension of the polymers is achieved within the pinch at high extension rates, the thread undergoes elasto-capillary break-up as the capillarity again overcomes the viscoelastic forces. The final length at detachment and time-to-break-off (relative to the equivalent Newtonian fluid) is shown to be linearly proportional to the longest relaxation time of the fluid

Rheology of dextran solutions

Commercial dextran samples of molecular weight up to 2 million and concentration up to 30 wt.% in aqueous solutions show Newtonian viscosity behaviour. Plot of shear viscosity as a function of concentration for the 2 million Mw gives a very high critical overlap concentration of approximately 8 wt.%, while the viscosity at 25 wt.% shows a very small molecular weight dependence, in sharp contrast to findings for flexible polymers in the semi-dilute region. All these results point to the conclusion that the dextran molecules are less stiff than most carbohydrates and are highly branched, so that the molecules are in a highly compact configuration in aqueous solution.

Steady shear and dynamic rheological properties of xanthan gum solutions in viscous solvents

An extensive examination of the first normal stress difference and linear viscoelastic properties of xanthan gum solutions has been conducted in relation to molecular theories in the literature. The first normal stress difference, storage modulus, and loss modulus are reported for 0.01–0.04% w/w solutions of xanthan gum in high viscosity (wheat syrup and water) solvents. The average length of the xanthan molecules used was determined by light scattering to be (1.25±0.05)×103 nm. The storage and loss moduli obtained show a frequency dependence consistent with theories that included a relaxation time spectrum, while the first normal stress difference exhibits dependence on shear rate consistent with theories of suspensions of rigid particles. Both the first normal stress difference and the solute contribution to the storage modulus were found to vary linearly with concentration and with the solvent viscosity to the power of 2/3. Extensional viscosity measurements of a xanthan gum solution are in good agreem...

Squeeze film flow of ideal elastic liquids

Abstract An exact solution is presented for the squeeze film flow of an Oldroyd B. fluid. The solution demonstrates that the flow kinematics is similar to the Newtonian (or Maxwellian) one. Theoretical predictions for constant velocity squeezing are compared to experimental observation for well characterized non-shear thinning elastic fluids. It is shown both theoretically and experimentally that the effect of elasticity in a constant velocity squeeze film flow is to always reduce the load relative to the inelastic (Newtonian) prediction and that this load reduction falls between the upper and lower asymptote prediction by the exact solution for the Oldroyd B fluid. The upper load asymptote is given by the Stefan solution for the viscosity of the polymer solution and the lower asymptote is given by the Stefan solution for the viscosity of the solvent. Experimental observations agree with the theoretical prediction for the Oldroyd B fluid at low shear rates where it is shown that the steady and dynamic flow properties of the test fluids used in the experimental program are well represented by the Oldroyd B constitutive equation. With the exception of the work of Lee et al. [6] for constant load squeezing of a Maxwell fluid, this work represents one of the few cases where experimental observation of large effects due to elasticity are indeed predicted with a constitutive equation which actually describes the steady and dynamic shear properties of the fluids used in the experimental program.

Drop Impact of Newtonian and Elastic Fluids

We studied the dynamics of drops of a Newtonian fluid ~water! and a constant viscosity elastic ~Boger! fluid of matched shear viscosities (hN51.1 mPa•s, hE51.3 mPa•s! impacting on hydrophilic and hydrophobic surfaces and on a thin liquid film ~;1 mm! of the same fluid. The elastic solution has a Zimm relaxation time l51.1310 s. During the drop spreading, both solutions have an equivalent surface tension of sDmax572.1 mN/m. At long time, the surface tension of the elastic solution decreases to sE562.0 mN/m. In all experiments, the impact velocity and initial drop diameter are 2.48 m/s and 1.68 mm, respectively. The Reynolds and Weber numbers are Re54166 and We5142 for the Newtonian solution and Re53205, We5166 for the elastic solution. To observe the impact of liquid drops from both bottom and side views, we used a beam splitter cube setup ~Fig. 1! with a high speed video camera. On a hydrophilic surface ~Fig. 2! the spreading of the two solutions occurs over the same time interval. At the maximum diameter, both solutions display a flat disc surface with peripheral fingers with different amplitude and frequency. During recoil, the Newtonian solution exhibits capillary waves from the outer ring to the center of the disc. These waves are dampened in the elastic solution. The rate of retraction and the final shape of the drops at long time differ significantly between the two solutions. Such differences cannot be explained by the difference in surface tension of the solutions and it is believed to be due to the adsorption of the polymer to the surface during spreading FIG. 1. Experimental setup.