The Stretching of an Electrified Non-Newtonian Jet: a Model
Feng, J. J.
Phys. Fluids 14, 3912-3926 (2002)
Abstract - Electrospinning uses an external electrostatic
field to accelerate and stretch a charged polymer jet, and may produce
ultrafine ``nanofibers". Many polymers have been successfully electrospun
in the laboratory. Recently Hohman et al.6,7proposed
an electrohydrodynamic model for electrospinning Newtonian jets. A problem
arises, however, with the boundary condition at the nozzle. Unless the
initial surface charge density is zero or very small, the jet bulges out
upon exiting the nozzle in a ``ballooning instability'', which never occurs
in reality. In this paper, we will first describe a slightly different
Newtonian model that avoids the instability. Well-behaved solutions are
produced which are insensitive to the initial charge density except inside
a tiny ``boundary layer'' at the nozzle. Then a non-Newtonian viscosity
function is introduced into the model and the effects of extension-thinning/thickening
are explored. Results show two distinct regimes of stretching. For a ``mildly
stretched" jet, the axial tensile force in the fiber resists stretching,
so that extension-thinning promotes stretching and thickening hinders stretching.
For a ``severely stretched" jet, on the other hand, the tensile force enhances
stretching at the beginning of the jet and suppresses it further downstream.
The effects of extensional viscosity then depend on the competition between
the upstream and downstream dynamics. Finally, we use an empirical correlation
to simulate strain-hardening typical of polymeric liquids. This generally
steepens the axial gradient of the tensile stress. Stretching is more pronounced
at the beginning but weakens later, and ultimately thicker fibers are produced
because of strain-hardening.