The Society of Rheology: 72nd Annual Meeting (Feb 2001) Paper FD8

Dynamics of formation of non-Newtonian drops from capillaries: Comparison of predictions made with generalized Newtonian and viscoelastic constitutive equations

Session:	Non-Newtonian Fluid Dynamics & Flow Stability
Date:	Tuesday - February 13, 2001
Time:	2:20
Room:	Elliott / Track 3

Speaker:	Ozgur E. Yildirim, School of Chemical Engineering, Purdue University
Authors:	Ozgur E. Yildirim, School of Chemical Engineering, Purdue University Osman A. Basaran, Chemical Engineering Department, Purdue University

Abstract

Dynamics of drop formation is important in many applications including ink-jet printing, biochip arraying, spray coating, and crop spraying where the working fluid is often non-Newtonian. Whereas a considerable amount of work has been done to date on the formation of drops of Newtonian liquids from a capillary, such studies of non-Newtonian liquids are virtually nonexistent. Here we present a theoretical study of dynamics of formation and breakup of drops of non-Newtonian liquids from capillaries and compare their response to that of drops of Newtonian liquids. Two types of constitutive equations are considered for describing non-Newtonian response. The first is a Carreau type generalized Newtonian fluid model that takes into account both shear thinning and strain hardening effects (see Song & Xia 1994). The second is a FENE-CR model that accounts for fluid viscoelasticity (see Chilcott & Rallison 1988). The mathematical problem is simplified by means of a regular perturbation or slender-jet analysis which reduces the original set of 2-d equations to a set of 1-d equations. The resulting set of transient, nonlinear equations is solved numerically by a method of lines using the Galerkin/finite element method for discretization in space and an adaptive finite difference method for discretization in time. The computations are carried out beyond the instant of first pinchoff to study the dynamics of any satellites that may be formed and interactions between the satellite(s), the primary drop, and the liquid mass hanging from the capillary. The predictions of the 1-d simulations are compared to experimental measurements. Among other things, the constitutive behavior is shown to have a profound effect on the dynamics. An interesting computational result is the occurrence of "bead-on-string" patterns, which are shown to arise when strain-hardening dominates.