The dynamics of filaments of complex liquids analyzed by continuum and mixed continuum-stochastic methods
Bhat, Pradeep Prabodha
Doctor of Philosophy
Formation and breakup of filaments of liquids is of fundamental importance in established and cutting edge technologies such as ink-jet printing, atomization of coolants in electronic systems, and micro-arraying of DNA. Most of the liquids encountered in these processes have macromolecules (e.g., DNA) which make them viscoelastic. The dynamics of such viscoelastic filaments is analyzed in this thesis using state-of-the-art numerical techniques. A transient flow solver, based on the finite element algorithm of Pasquali and Scriven (2002), is developed and used in the computations. Viscoelasticity is modeled using a single macroscopic variable, the conformation tensor, which is computed by solving a generalized constitutive equation (Pasquali 2000). The dynamics of stretching filaments in the low capillary number regime is analyzed using three different weakly strain hardening models. Among thern, Giesekus filaments show the most drastic necking. The dependence of the transient Trouton ratio on the capillary number in this model is demonstrated. Cohesive necking failure due to elastic unloading in the filaments is investigated using both kinematic (Yao et al. 1998) and energy arguments. The thinning in the Giesekus filaments is aided by the elastic unloading, which increases with growing elasticity. The analysis of pinch-off of viscoelastic filaments, to date, relied on simple one-dimensional approximations. In this work, two-dimensional analysis o fpinch-off of FENE-P filaments is conducted for the first time. Scalings of physical variables calculated near pinch-off accord with asymptotic theoretical results. The liquid-gas interface in the neck region of low viscosity FENE-P filaments overturn before breakup when the Ohnesorge number, suitably redefined with the maximum extensional viscosity, is lower than a critical value. A multi-scale algorithm, in which viscoelasticity is modeled using an ensemble of Brownian configuration fields (Hulsen et al. 1997), is developed to solve axisymmetric free surface flows. The new method reproduces filament stretching results with Hookean dumbbells, within statistical error bars, when compared with equivalent macroscopic calculations. Inclusion of hydrodynamic interactions reduces the extension of the dumbbells thereby decreasing the growth of extensional stresses in the filaments.
Applied mechanics; Chemical engineering