1.Microfluidics and electro-hydrodynamics

We investigate micro scale flows in the presence of electric field using both experiments and modeling. Electro-hydrodynamic instabilities in microchannels are employed for efficient mixing of miscible liquids or microdroplet formation for immiscible liquids. The mathematical methods used include linear stability analysis, long wave analysis and solving eigenvalue problems.

1.1. Model and Physical System

The physical system consists of two immiscible liquids with different physical properties flowing in a microchannel. The liquids are Newtonian or non-Newtonian. The interface is allowed to deflect.

Figure 1. Physical system

In a microchannel Reynolds number is small as the channel is small. Therefore, the liquids flow side by side sharing a common flat interface. To obtain the droplet of one phase into another, the interface needs to be deflected. External electric field is applied either parallel (Fig. 1a) or normal (Fig. 1b) to the flat interface. The voltage at which the interface loses its flatness is recorded as the critical voltage, which is determined via linear stability analysis. For that purpose momentum equation for velocity and Laplace equation for voltage are solved for both phases. Surface coupled model is assumed as there is a jump in the physical properties of the liquids at the interface. The liquids may be assumed perfect dielectric, leaky dielectric or conducting.

Figure 2. Effect of the electric field

For fast electric charge relaxation times, i.e. when the charge relaxation time is much smaller compared to the fluid time scale, without solving the pertubaton equations, conditions for which the electric field has a stabilizing or destabilizing effect derived analytically and presented on a conductivity ratio versus permittivity ratio graph. As seen in Fig. 2, there are six regions. Parallel electric field has a destabilizing effect in regions 1 and 4, whereas normal field has a destabilizing effect in regions 1, 2, 4, and 5. However, the magnitude of the electric field to destabilize the interface is not known. In regions 3 and 6 the electric field has a stabilizng effect, i.e. the interface cannot be deflected by applying an electric field.

1.2.Experiments

Two different types of micro channels are machined out of Plexiglas to apply an electric field either parallel (Fig. 3a) or normal (Fig. 3b) to the flat interface.

Figure 3. Micro channels to apply an electric field parallel (a) or normal (b) electric field.

Various liquid pairs are used and the critical voltage, i.e. the voltage at which interface becomes unstable is recorded using a setup as in the figure.

Figure 4. Experimental setup

A typical data includes set of pictures (Fig. 5) and the aim is to determine the critical voltage.

Figure 5. Set of pictures from an experiment showing the evolution of the interfacial instability between ethylene glycol and 50 cSt silicone oil flowing at 10 μL/min in a micro channel of 1.0mm width. The critical voltage of 880V is reached in (b). The rupture occurred in (h). The electric field is turned off in (o) and the flat interface is recovered in (t).