Dynamics of formation of a drop of a Newtonian liquid from a capillary tube
into an ambient gas phase is studied computationally and experimentally. W
hile this problem has previously been studied computationally either (a) us
ing a set of one-dimensional equations or (b) treating the dynamics as that
of irrotational flow of an inviscid fluid or creeping flow, here the full
nonlinear, transient Navier-Stokes system subject to appropriate initial an
d boundary conditions is solved in two dimensions to analyze the dynamics a
t finite Reynolds numbers. The success of the computations rests on a finit
e element algorithm incorporating a multiregion mesh which conforms to and
evolves with the changing shape of the drop. The new algorithm is able to c
apture both the gross features of the phenomenon, such as the limiting leng
th of a drop at breakup and the volume of the primary drop, and its fine fe
atures, such as a microthread that develops from a main thread or a neck in
a viscous drop approaching breakup. The accuracy of the new calculations i
s verified by comparison of computed predictions to old and new experiments
. With the new algorithm, it is shown for the first time that the interface
of a viscous drop can overturn before the drop breaks. Calculations have a
lso been carried out to determine the range of parameters over which algori
thms that treat the drop liquid as inviscid and the flow inside it as irrot
ational can accurately predict the dynamics of formation of drops of low vi
scosity liquids. Limiting lengths of drops and primary drop volumes are com
puted over a wide range of the parameter space spanned by the relevant dime
nsionless groups. (C) 1999 American Institute of Physics. [S1070-6631(99)01
812-7].