Velocity, acceleration & jerk in electrospinning

Abstract

Electrospinning can produce nano-fibers by drawing a polymer jet through a virtual spatio-temporal orifice. The diameter of the virtual orifice at any time or space depends on the velocity at that point, the velocity being determined by the continuity equation. Velocity profiles on silicone jet reveal that acceleration is not a constant, whereas the values fit the model for jerk. The findings should give a handle on the optimization of process parameters. To investigate the other factors that influence velocity (and hence the fiber diameter), the thinning and solidification are modeled. Results reveal that the jet thins drastically in the early stages, for both solution & melt electrospinning; however, thinning can continue till the end of the flight. In solution electrospinning, solvent evaporation during flight results in further thinning of the jet. The model reveals that solution electrospun fibers deposited on the collector could be retaining some residual solvent, limiting its applications. The kinematic model for melt electrospinning computes velocity, fiber diameter, viscosity & temperature. The field gradient expressed in V/m is shown to be equivalent to N/C. In the range where the voltage matches the flow rate (and viscosity), a steady state is attained, resulting in continuous fibers. In this range, the process parameters of flow rate, viscosity or the voltage could be varied to give fibers of uniform diameter. The spool speed has to match the terminal velocity, for producing continuous fibers, to ensure dimensional stability of the product. INTRODUCTION Spinning is the process used for drawing a fiber-forming polymer into filaments by passing through a spinneret. Solution spinning (wet or dry) and melt spinning are the major spinning techniques used in the production of fibers. In dry spinning the solvent evaporates in a spinning tower, resulting in solid fibers; in melt spinning the polymer melt solidifies to give the fiber. Conventional fiber-forming techniques are dependant on the spinneret diameter which may not be reduced indefinitely, due to limitations of the tools used for fabricating them. The major technique that can be used to make fibers thinner than 100 m is electrospinning; the process is capable of giving very long continuous fibers 1-4 . Electrospinning produces very thin fibers by electrostatically drawing a polymer jet through a virtual spatio-temporal orifice. The diameter of the virtual orifice at any time or space depends on the velocity at that point. The velocity is determined at any point by the continuity equation: Q = π r 2 v, where Q is the volumetric flow rate, r is the fiber radius and v is the velocity. END-OF-FLIGHT VELOCITY Dalton et al., have melt electrospun poly-(ethylene glycolblock-e-caprolactone) 5 ; with scanning electron microscopy, they have determined the diameter of the fibers. Using their data and the continuity equation, we have computed the terminal velocities (Table 1). Whether the velocity is built up by constant acceleration or by jerk is investigated in this paper; the findings should give a handle on the optimization of process parameters. Velocity, acceleration & jerk in electrospinning