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ELECTROSPINNING PROCESS MODEL
Terry Shetter
Delia Garcia
Department of Materials Engineering
Drexel University
ABSTRACT
The emerging technology of electrospinning has found the interest of many because of the breakdown that occurs during processing. In this paper, a model has been used to describe this behavior and the major factors that affect it have been varied. The factors that most affect this process are viscosity, surface tension and electric current.
INTRODUCTION
Polymer breakdown in electrospinning has attracted much attention. The problem is attributed to electrohydrodynamics in the capillary tube. In this paper, an analytical model of steady state electrospinning in a single jet regime is invoked and the effects of secondary factors are studied. This model was chosen to supplement a senior design project so that the student would better understand what factors affected the electrospinning process. Included is a brief description of the background, problem, and discussion about the results that were attained by using a differential equation for the jet radius.
BACKGROUND INFORMATION
Thin polymer fibers can be made by electrospinning. This process involves ejecting a charged polymer solution from a capillary tube and applying an external electric field to elongate and accelerate the polymer. The polymer is deposited on a substrate and dried and/or can be chemically treated to become a thin fiber.
Electrospinning is an emerging technology and is not understood well. The parameters that control the process are hydrostatic pressure in the capillary tube and the external electric field. The viscosity, conductivity, dielectric permeability, and surface tension of the polymer solution also affect the process. Rayleigh instabilities can describe the breakdown of the polymer solutions. However, this is not typically expected in electrospinning because polymers are highly viscous and exhibit non-rheological behavior.
STATEMENT OF THE PROBLEM
An asymptotic model of the electrospinning process is considered to evaluate and control the diameters of the polymer fibers.
NUMERICAL SIMULATION
Equations taking into consideration the steady state flow of an infinite viscous jet, linear momentum balance, and electric stress tensor (three-dimensional) were reduced to a one- dimensional problem by averaging physical quantities over the jet cross-section.
The following differential equation is used to model the jet radius:
d
dz
R N R N R N
dR
w E R dz
m
(^)
4 1 1 2 1
2
In this equation, Rbar = R/Ro is the dimensionless jet radius, Ro is the normalization constant, zbar = z/zo is the dimensionless axial coordinate and zo is the normalization length. The dimensionless Weber number Nw describes the ration of inertia forces to surface tension in the jet:
Nw = Q^2 /2^2 Ro 3 S
The dimensionless parameter NE, reciprocal of the Euler number, describes the ration of inertial forces to electrostatic field pressure:
NE = 4oQ^4 /^2 J^2 Ro 6
The effective Reynolds number NR for the fluid characterized by the power-law describes the ration of inertia forces to viscous forces:
NR = Q^2 /2^2 Ro 4 [6EJ Ro 2 / Q^2 ]m
where: : fluid density S: coefficient of surface tension E : electric field o: permittivity of vacuum Q: volumetric flow rate J : electric current
The constants in these equations are: = 2.3 x 10^3 cP S= 50 mN/m Ro = 45 m E = 40 kV/m J = 95 nA Q = 15 l/s
The boundary condition is Rbarzbar = 0 = 1. The method of solution used for this analysis is Euler Backward. This method for the analysis was chosen because the differential equation for the jet radius is a non-linear equation. For the Euler Backward method, the generalized equation
deformation are applied, the molecules are stretched and become less tangled. Reduction in the viscosity of the polymer reduced the degree of entanglement, leading to an increase in Nr.
The Weber number Nw describes the ratio of inertial forces to surface tension in the jet. A decrease in the surface tension increased Nw. At the tip of the capillary tube, a drop of polymer is formed that is held together by surface tension. Once the surface tension is decreased, the droplet is no longer able to stay formed which allows the formation of the polymer jet to be formed more easily. The increase of Nw decreased the point at which R begins to curve, approaching zero quicker.
Varying the electric current contributed to a change in the ratio of inertial forces to electrostatic field pressure. Decreasing the value of the electric current increased the overall value of Ne. The position of the curve didn’t change but does approach zero quicker than the original parameters
Changing the size of the radius of the capillary tube proved to make no significant changes to the graph.
The accuracy of the results were limited to the computer programs that were used (Maple and Excel). The CPU time was not a factor in Maple. The program solved the differential equation in a minimal amount of time. Quite a bit of computer memory was used for making the graphs in Excel. This was because any changes seen on the graph were minimal and weren’t seen until thousands of values were plotted. Limitations came mainly from the memory requirements in saving the plots that were made when parameters were changed.
The variance of such parameters would help in better understanding the process of electrospinning. The influence of how such parameters affect the flow of the polymer solution would help to produce fibers of a desired range consistently. The consistent production of fibers would help in determining their applications.
REFERENCES
[1] A. Spivak, Y. Dzenis, D. Reneker. Modeling of Steady State Jet in the Electrospinning Process, Mechanics Research Communications, Vol. 27, No. 1, pp37-42, Elsevier Science Ltd.,
[2] A. Spivak, Y. Dzenis. Asymptotic decay of radius of a weakly conductive viscous jet in an external electric field. Applied Physics Letters. Volume 73, No 21, pp. 3067-3069, American Institues of Physics, 1998.
original parameters
0
1
0.00E+00 5.00E+05 1.00E+06 1.50E+06 2.00E+06 2.50E+06 3.00E+06 3.50E+06 4.00E+06 4.50E+ z
Figure 1. The original parameters in the mathematical model.
Nw=0.
0
1
0 50 100 150 200 250 300 350 z
r
Nw =
0
1
0 50 100 150 200 250 300 350 z
r
Nr=2200, r=0.
0.00E+
2.00E-
4.00E-
6.00E-
8.00E-
1.00E-
1.20E-
0.00E+00 5.00E+04 1.00E+05 1.50E+05 2.00E+05 2.50E+05 3.00E+05 3.50E+05 4.00E+ z
r
Nr=2500, r=0.
0
0 50 100 150 200 250 300 350 z
r
z=
0
0 50 100 150 200 250 300 350 z
r
