Electrospinning The Velocity Profile

Taylor identified the critical electric potential for electrostatically forming a cone of liquid (Taylor cone-semivertical sphere) at the end of a capillary tube. The derivation began with the expression for the equilibrium state of a droplet at the end of a pressurized tube, and the coefficients for the electrostatic potential were generated by observing the deflection of charged solutions at the end of an inverted capillary. Taylor showed that the vertical voltage (V in kV) at which the maximum jet fluid instability start, is given by  

The spinning rate was estimated by measuring the length of the polyethylene (PE) fiber obtained in a known interval of time. The rate was of the order of 1 m/min, and it increased with the applied field strength. The relationship between the spinning rate and electric field strength E is found to be as following at 200°C. 

The relationship between the capillary radius plane distance and the applied voltage is given by tbe following equation  

The velocity profile inside the liquid cone at the base of an electrically driven jet was examined by inserting tracer particles into the liquid. Observations of these particles at high magnification demonstrated the presence of an axis5mimetric circulation inside the cone due to interfacial electrical shear stress. An anal3dical solution was presented that predicts the velocity profile inside the cone. The surface velocity were expressed as 

A relationship between the applied voltage, surface tension, air permittivity, and capillary radius was also introduced. The difference between the calculated jet diameter from the equation and the experimentally measured value had been recorded. 

---