Numerical Simulation of Formation and Distortion of Taylor Cones

Abstract

Taylor cones are integral parts in many important applications like electrospinning and electrospray mass spectroscopy. A better understanding of this complex phenomenon of Taylor cone is critical for better control of these processes. As an example, if it is possible to identify and prioritize the roles of fluid characteristics and externally applied electric field, it might be easier to target and control the diameters of nanofibers in an electrospinning process. Under the influence of high electric fields, Taylor cones are formed by a number of liquids including many polymeric solutions. Because of small spatial (microns and below) and temporal (microseconds and below) scales, it is difficult to experimentally study the transient formation of Taylor cones. A number of theoretical analyses have been done under simplifying assumptions like uniform electric field, constant electrohydrodynamic behaviors of the fluid, stationary droplet, etc. Initial Taylor formulation included the introduction of “leaky dielectric” that accumulated charges only on the surface for certain dielectric fluids. Yarin et al. later developed analysis for stationary droplets assuming them to be “perfectly conducting”. To simulate the electrospinning process, the formulation needs the ability to analyze moving boundary conditions, complex fluid properties, three dimensional geometry, and nonlinear coupling between air and liquid, among others. To overcome some of the assumptions of theoretical analyses and as another complementary tool, a computer simulation method was proposed using a commercially available software. In this investigation, much studied aqueous polyethylene oxide (PEO) solution was used to study formation and distortion of Taylor cones. An initial velocity was given to the fluid from the tip of a nozzle and an appropriate electric field was applied to form the Taylor cones. Literature values were used for flow, fluid, and electrical characteristics of the solution. By appropriately manipulating fluid velocities and electric fields, simulations were successful to both replicate the classical cone and distort it to various degrees. These formation and distortion of Taylor cones were similar to reported experimental results. While the numerical and experimental Taylor cones were significantly different in sizes, nondimensional shapes, and sizes of both the results were strikingly similar. Velocities of the fluid in the jet jumped almost 50 times to meters/second as was experimentally observed. Unlike theoretical solutions, the simulation results showed the interaction of the electric fields between the air and advancing fluid tip.