Stability analysis of a thinning electrified jet under nonisothermal conditions

The linear stability of a jet propagating under an electric field is analyzed under nonisothermal conditions. The electrified jet of a Newtonian fluid is modeled as a slender filament, and the leaky dielectric model is used to account for the Maxwell stresses within the fluid. The convective heat transfer from high-temperature jet to the surroundings results in formation of thicker fibers owing to increased viscosity upon cooling. The jet exhibiting substantial thinning under the action of tangential electric field is examined for stability toward axisymmetric nonperiodic disturbances. This is in contrast to most prior studies which analyzed the stability of a cylindrical jet of uniform radius without thinning under extensional flow by examining only periodic disturbances. Two case studies of reference fluids differing in viscosity and electrical properties are examined. The spectrum of discrete growth rates for axisymmetric disturbances reveal qualitatively distinct instabilities for the two fluids. For a fluid with high electrical conductivity, the conducting mode driven by the coupling of surface charges and an external electric field is found to be the dominant mode of instability. On the contrary, for low conductivity materials, the surface-tension-driven capillary mode is found to be the most critical mode. Heat transfer from the jet to the surroundings tends to stabilize both types of instability mode. Under sufficiently strong heat transfer, the axisymmetric instability, which is believed to be responsible for producing nanofibers with diametric oscillations in electrospinning process, is suppressed. The stabilization is attributed to the enhancement of viscous stress in the thinning jet upon cooling. It is observed that the stabilization effect is relatively more pronounced in a thinning jet compared to the cylindrical jet of uniform radius. The effects of various material and process parameters on the stability behavior is also examined.

Figure 1

Schematic of nonisothermal electrospinning process.

Figure 2

Magnitude of various dimensionless forces acting on the jet along $z$ direction. (a) Set I: Inertial and electric forces are dominant toward the end of the jet; (b) Set II: Viscous and electric forces are dominant.

Figure 3

Steady-state profile of dimensionless radius along the jet direction: (a) Set I; (b) Set II.

Figure 4

Steady-state profile of dimensionless surface charge density along the jet axis: (a) Set I; (b) Set II.

Figure 5

Dimensionless steady-state profile of thinning jet for various Biot numbers: (a) radius; (b) temperature. Parameters: Set II.

Figure 6

Steady-state profile of thinning jet for different values of activation energies. (a) Dimensionless radius; (b) dimensionless elongational viscosity. Parameters: Set II.

Figure 7

Eigenspectrum for isothermal and nonisothermal jets: Real part of growth rate, ${\omega }_r, vs$ imaginary part of growth rate, ${\omega }_i$, for a thinning jet with superimposed nonperiodic perturbations. (a) $\text{Bi}=0.0$; (b) $\text{Bi}=0.05$. Parameters: Set I.

Figure 8

Eigenspectrum for isothermal and nonisothermal cases: Real part of growth rate, ${\omega }_r, vs$ imaginary part of growth rate, ${\omega }_i$, for a thinning jet with superimposed with nonperiodic perturbations. (a) $\text{Bi}=0.0$; (b) $\text{Bi}=0.07$. Parameters: Set II.

Figure 9

Effect of heat transfer coefficient, Bi, on real part of the leading growth rate, ${\omega }_r$, for thinning jet: (a) Set I; (b) Set II.

Figure 10

Effect of activation energy on real part of the leading growth rate, ${\omega }_r$, for thinning jet: (a) Set I; (b) Set II.

Figure 11

Effect of air velocity, $V_{\mathrm{air}}$, on real part of the leading growth rate, ${\omega }_r$, for thinning jet. Parameters: Set II.

Figure 12

Effect of external electric field, $E_{\infty }$, on real part of the leading growth rate, ${\omega }_r$, for thinning jet: (a) Set I: Conducting mode; (b) Set II: Capillary mode.

Figure 13

Effect of conductivity given by electric Péclet number on real part of the leading growth rate, ${\omega }_r$, for thinning jet: (a) Set I: Conducting mode; (b) Set II: Capillary mode.

Figure 14

Effect of capillary number, Ca, on real part of the leading growth rate, ${\omega }_r$, for thinning jet: (a) Set I: Conducting mode; (b) Set II: Capillary mode.

Figure 15

Maximum growth rate of disturbance corresponding to thinning jet and uniform jet. Parameters for various heat transfer coefficients, Bi: (a) Set I; (b) Set II.