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

Abstract

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.

DNA-based highly tunable particle focuser

“…Finally, the relaxation time of a polymer solution may significantly deviate from its Zimm relaxation time because of polymer-polymer interactions unless the polymer solution is very dilute, and this deviation is particularly relevant in extensional flows [44][45][46] . However, the relaxation times of polymer solutions, which were measured under shear flows, slowly increased until c reaches c* (refs 45,46), which was also observed by single DNA experiments 47 .…”

“…The scale bar denotes the length of 100 mm. 44 , where c is a polymer concentration and [m] is estimated to be 0.77/c* (ref. 48).…”

Sheathless Focusing and Separation of Diverse Nanoparticles in Viscoelastic Solutions with Minimized Shear Thinning

“…However, the focusing efficiencies for M w = 0.3×10 6 g/mol are much lower than those of M w = 0.6×10 6 g/mol for all the investigated c. The solutions with M w = 0.3×10 6 g/mol results in the weak elasticity, whose λ is over 4 times shorter than that for M w = 0.6×10 6 g/mol at the same c ( λ ∝ 2.1 w M ). 29,30 5 Therefore, a good carrier solution should have weak shear thinning and sufficient elasticity at the same time. In the present study, the PEO solution of M w = 0.6×10 6 g/mol is the optimal one.…”

Polymeric Drift Control Adjuvants for Agricultural Spraying

“…[10,11] The enhanced extensional viscosity (or elasticity) of polymer solutions is believed to cause the larger drop size. [12] Increases in other rheological properties such as dynamic surface tension, [3,13] and to a lesser extent static surface tension and zero shear rate viscosity have also been reported to increase spray drop size. [14][15][16] There currently exist an extensive range of commercial drift control adjuvants (DCAs), a selection of which is presented in Table 1.…”