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Electrospinning electric field simulation

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During electrospinning, a polymer solution is ejected from a spinning syringe and deposited at the target plate placed at some distance from the needle. High voltage is applied between the needle and the plate, which generates the electrostatic forces pulling the ejected polymer flow into the fine stream.

Problem Type
Axisymmetric problem of electrostatics.

Geometry
Electrospinning electric field simulation Polymer solution is ejected from a spinning syringe and deposited at the target plate Taylor cone HV Polymer solution Target plate Air

Given
Relative permittivity of air ε = 1;
Relative permittivity of polymer ε = 3.
Deposition plate electric potential = 0.
Needle electric potential = 10 kV.

Task
Simulate the electric field distribution around the needle tip in the electrospinning experiment.

Solution
Problem has a rotational symmetry and may be set up as an axisymmetric Electrostatic problem. Two electrodes are formed by the hollow needle (where the high voltage is applied) and a grounded deposition plate. It is assumed that the liquid polymer extruded from the needle forms a conical shape (Taylor Cone) having a half angle of 49.3 degrees.

Results
Equipotential lines and electric field vectors around the tip of the Taylor Cone in the Electrospinning experiment simulation
Electrospinning experiment simulation Taylor Cone Equipotential lines