Mechanisms and modeling of electrohydrodynamic phenomena

Abstract

The purpose of this paper is to review the mechanisms of electrohydrodynamic (EHD) phenomenon. From this review, researchers and students can learn principles and development history of EHD. Significant progress has been identified in research and development of EHD high-resolution deposition as a direct additive manufacturing method, and more effort will be driven to this direction soon. An introduction is given about current trend of additive manufacturing and advantages of EHD inkjet printing. Both theoretical models and experiment approaches about the formation of cone, development of cone-jet transition and stability of jet are presented. The formation of a stable cone-jet is the key factor for precision EHD printing which will be discussed. Different scaling laws can be used to predict the diameter of jet and emitted current in different parametrical ranges. The information available in this review builds a bridge between EHD phenomenon and three-dimensional high-resolution inkjet printing.

Keywords: Electrohydrodynamic; additive manufacturing; cone-jet; inkjet printing; jet stability.

Figure 1

(A) A schematic of electrohydrodynamic printing setup. Ethylene glycol liquid meniscus (B) at 0 volts; (C) at 2.5kV[34]. Adapted by permission from Lozano et al. (2004) under the Elsevier license.

Figure 2

(A) Phase diagram depicting flow transitions that occur as flow rate and/or electric field strength is varied[46]. Adapted by permission from Robert T. Collins et al. (2007) under the Cambridge University Press. (B) Time images of the pulsating Taylor cone with the four phases of the cycle. Delay time values measured from the most retracted meniscus (Δt) are shown under the individual images. Each frame is an average of 100 exposures with the same delay[14]. Adapted by permission from Marginean et al. (2004) under the ACS Publications.

Figure 3

(A-D) Different forms of the meniscus in cone-jet mode[57]. Adapted by permission from Michel Cloupeau et al. (1989) under the Elsevier.

Figure 4

Cone-jet mode: (A) Varicose instabilities; (B) kink instabilities[18]. Adapted by permission from Michel Cloupeau et al. (1994) under the Elsevier.

Figure 5

Operating diagram for (a) glycerol jet (K = 0.1 × 10⁻⁵S/m), ρ = 1.26 × 10³ Kg/m³, μ = 1.87 Pa·s). The shaded region is varicose perturbations, and no whipping instability is present. (b) PEO jet (K = 1.2 × 10⁻² S/m, ρ = 1.2 × 10³ Kg/m³, μ = 2 Pa·s). The lower shaded region is varicose perturbation, and the upper shaded region is whipping instability. The points represent experimental measurements are consistent with theoretical prediction[73]. Adapted by permission from Moses Hohman et al. (2001) under the AIP Publishing LLC.

Figure 6

(A) Growth rate σ versus the wavenumber k for a jet with b (distance between two radial electrodes) >>1, χ = 0.6, C (Ohnesorge number) = 1, and β (liquid relative permittivity) = 2 and several values of the relaxation parameter α; (B) Growth rate σ versus the wavenumber k for a jet with different values of the Ohnesorge number C (b >>1, α=1, β=1, χ=0.6). (C) Growth rate σ versus the wave number k for a jet with b>>1 and b=2. The other parameters are fixed at C=1, α=1, and β=2. Several values of the electrification number χ are plotted[81]. Adapted by permission from Jose Lopez-Herrera et al. (2005) under the AIP Publishing LLC.

Figure 7

The continuous curve is theoretical predictions of the transition between absolute and convective instability. Most of the points from experimental values are in the region of convective instability[85]. Adapted by permission from Jose Lopez-Herrera et al. (2010) under the AIP Publishing LLC.