Numerical and experimental investigation on static electric charge model at stable cone-jet region

Abstract

In a typical electro-spinning process, the steady stretching process of the jet beyond the Taylor cone has a significant effect on the dimensions of resulting nanofibers. Also, it sets up the conditions for the onset of the bending instability. The focus of this work is the modeling and simulation of the initial stable jet phase seen during the electro-spinning process. The perturbation method was applied to solve hydrodynamic equations, and the electrostatic equation was solved by a boundary integral method. These equations were coupled with the stress boundary conditions derived appropriate at the fluid-fluid interface. Perturbation equations were discretized by the second-order finite difference method, and the Newton method was implemented to solve the discretized nonlinear system. Also, the boundary element method was utilized to solve the electrostatic equation. In the theoretical study, the fluid is described as a leaky dielectric with charges only on the jet surface in dielectric air. In this study, electric charges were modeled as static. Comparison of numerical and experimental results shows that at low flow rates and high electric field, good agreement was achieved because of the superior importance of the charge transport by conduction rather than convection and charge concentration. In addition, the effect of unevenness of the electric field around the nozzle tip was experimentally studied through plate-plate geometry as well as point-plate geometry.

Numerical simulation of jet mode in electrospraying of Newtonian and viscoelastic fluids

“…(13), and Eqs. (17) to (20) The eigenvectors of the conformation tensor create tensor , which can be computed by:…”

“…( 13), and Eqs. (17) to (20) are substituted into Eq. ( 13), the following relationships are obtained: The eigenvectors of the conformation tensor create tensor 𝑅, which can be computed by:…”

“…Moreover, in several previous studies, this model was used to simulate the deformation of a drop within a specified electric field strength [11][12][13][14] and the well-known oblate and prolate deformations and conditions under which these deformations were reached were thoroughly discussed. Due to its ability to exert tangential force on the fluid interface, the leaky dielectric model has been utilized for cone-jet simulation [15][16][17][18] and electrically controlled droplet generation 19 .…”

Jet diameter of the first coil in the electrospinning whipping region: the role of fluid viscosity

“…where c 1 is constant and the variable z is the height below the critical point B, as shown in Figure 1. Equation (11) indicates that the jet radius is determined by the fluid viscosity (l), electric current (I), and flow rate (Q m ). In contrast to the traditional model of equation (1), equation (11) considers the viscous force and states that the jet radius is proportional to 1/4 power of the fluid viscosity.…”

“…Equation (11) indicates that the jet radius is determined by the fluid viscosity (l), electric current (I), and flow rate (Q m ). In contrast to the traditional model of equation (1), equation (11) considers the viscous force and states that the jet radius is proportional to 1/4 power of the fluid viscosity. In addition, the relationship between the jet radius and axial distance follows a scaling law of r $ z À1=4 , which is in agreement with the previous research.…”