**2.1 Dripping, micro-dripping, spindle and intermittent cone-jet mode**

In dripping mode, when the liquid is pumped in to the nozzle or capillary without applying the electric field, the droplets disintegrate from the orifice, the size of the droplets are larger than the size of the nozzle orifice. As the electric field is increased, the frequency of the droplet generation is also increased and size of the droplet decreases. At relative low flow rate, the droplet disintegrate in much smaller size as compare to the inner diameter of nozzle, this mode is known as micro-dripping mode, the frequency of the droplet increases with increase in applied electric field and size decreases. Depending on the liquid properties, increasing further electric potential, the spindle mode observed. In spindle mode, the jet extended from the meniscus and breaks up into larger droplet and satellites droplets are also observed. Further increasing in applied voltage, with relative high flowrate intermittent cone-jet mode occurs, causing the pulsating cone-jet modes due to the high space charges reduce the electric field on the liquid jet and causing relaxation of the cone-jet into hemispherical meniscus. The pulsation in the intermittent cone-jet mode increases with increase in the applied voltage.

Fig. 2. Modes of electrohydrodynamic jetting captured through high speed camera (a) dripping, (b) micro-dripping, (c) spindle mode, (d) pulsating cone jet, (e) stable cone jet, and (f) multi-jet mode

### **2.2 Cone-jet mode**

548 Recent Advances in Nanofabrication Techniques and Applications

the nozzle instead of thermal or acoustic energy (Hartman, 1998). Based on the applied electric field energy, the electrohydrodynamic jetting can be used for continuous patterning, drop-on-demand printing and thin film deposition (electrospray). Electrohydrodynamic drop-on-demand, jetting or atomization has numerous applications in inkjet printing technology (Wang, 2009), thin film deposition (Jaworek, 2007), bio-application (Park 2008),

In electrohydrodynamic printing the liquid is pulled out the nozzle rather than the pushing out as in case of conventional inkjet systems. When the liquid is supplied to nozzle without applying the electric field, a hemispherical meniscus is formed the nozzle due to the surface tension at the interface between the liquid and air. When the electric field is applied between the liquid and the ground plate (located under the substrate), the ions with same polarity move and accumulate at surface of the meniscus. Due to ions accumulation, the Maxwell electrical stresses are induced by the Coulombic repulsion between ions. The surface of the liquid meniscus is mainly subjected to surface tension σs, hydrostatic pressure σh and electrostatic pressure σe. If the liquid is considered to be a pure conductor, then the electric field will be perpendicular to the liquid surface and no tangential stress component will be acting on the liquid surface. The liquid bulk will be neutral and the free charges will confined in a very thin layer. This situation can be summarized in the following equations.

0

Since the liquid is not a perfect conductor, the resultant electric stress on the liquid meniscus has two components, i.e. normal and tangential as shown in figure1. This repulsion force (electrostatic force) when exceeds the certain limit deforms the hemispherical meniscus to a cone. This phenomenon is known as the cone-jet transition, which refers to the shape of

(1)

 *hes* 

Fig. 1. Stresses due to different forces on the liquid meniscus (Kim et al. 2011)

For specific configuration and constant flow rate, there are different modes of electrohydrodynamic jetting as a function of applied voltage (Cloupeau & Foch, 1994). It should be noted that not for all liquids each mode can occur, because of the properties of the liquid. The different modes of the electrohydrodynamic jetting are discussed as follows:

mass spectrometry (Griss, 2002), etc.

**2. Electrohydrodynamic jetting** 

meniscus (Poon, 2002).

Further increase in voltage, the meniscus deforms into cone and thin stable jet emerges from the apex of the jet. This mode is known as cone-jet mode. In cone-jet mode, the intact jet used to fabricate the patterns on the surface of the substrates. The main advantage of conejet as compared to conventional method of ejection of the liquid is its large ratio between diameter of the nozzle and the jet. The typical jet diameters are about two orders of magnitude smaller than that of nozzle; this enables patterning at very fine resolution. However, the cone-jet also has shortcoming, it is very difficult to stabilize and control the

Electrohydrodynamic Inkjet – Micro Pattern Fabrication for Printed Electronics Applications 551

atomization, this behavior is used for the thin film deposition of functional material. The

Fig. 4. Effect of the applied voltage on shape of the cone-jet at constant flow rate (200µl/hr)

Nozzle diameter has significant influence on the operating envelope of the stable cone-jet region. Smaller nozzle diameters extend the lower and higher value of flow-rate limit. The voltage requirement for the cone-jet also decreases with decrease in nozzle diameter for any

The liquid conductivity affects both the shape of the liquid cone and stability of the jet, due to the amount of electric charge on the liquid surface and jet produces is also very unstable because of high radial electric field. Highly conductive liquid deforms into sharp cone-jet shape. Liquid with very low conductivity do not deform into cone-jet by applying electric field, only dripping mode is observed. Liquids with intermediate conductivity range

The role viscosity is in the stabilization of the jet and diameter of the jet produced. In high viscous liquid, the jet is stable for larger portion of the length but also produces the thicker diameter. This is due to charge mobility, which is reduced significantly in high viscosity

The formation of the jet occurs when the electrical forces overcomes the surface tension on the apex of the meniscus. The required applied voltage will be increased with increase in

In order to perform the patterning of any liquid containing nanoparticles, the operating parameters of flow rate corresponding to applied voltage for stable cone-jet has to be

**2.4.3 Nozzle diameter** 

given liquid.

**2.4.4 Conductivity** 

produce steady cone-jet.

**2.4.6 Surface tension** 

**2.5 Operating envelop** 

surface tension of the liquid.

liquid, and causes decrease in conductivity.

**2.4.5 Viscosity** 

typical shape of the come at different applied voltage is shown in figure 4.

trajectory of thin jet under an electric-field, and jet disintegrate into droplets and cause spray due to electrostatic repulsive forces between themselves.

### **2.3 Multi-jet mode**

If the applied voltage is further increased, the cone becomes smaller and smaller. With increasing the applied voltage, second jet emerges from the cone. With further increase in applied voltage, more and more jet emerges from the cone, this mode is called multi-jet mode.
