# MLC

## Seminar

### Liquid dielectrophoresis and wrinkling on the surface of a fluid layer

Seminar Room 1, Newton Institute

#### Abstract

There is a growing technology-driven interest in using external forces to move or shape small quantities of liquids. One existing technique, electrowetting, involves the application of an electric field to a conducting liquid. A disadvantage of this technique is that the liquid must remain in contact with the electrodes. However, this is not the case in liquid dielectrophoresis, where a dielectric (i.e. non-conducting) liquid is used. A common aspect to both these techniques is that electrical surface stresses at liquid-air or liquid-liquid interfaces play an important role.
In this work we consider a layer of dielectric liquid of non-dimensional depth $h(x,t)$ wetting a horizontal electrode with a hydrodynamically passive dielectric fluid (e.g. air) above. A second electrode is located at a distance $d>h$ above the lower substrate. When the applied voltage is increased past a critical value, an instability occurs on the free surface of the liquid. We investigate how the material and cell geometry parameters affect the critical applied voltage and the form of the instability. Using linear stability analysis, we find that there exists a critical spacing $d_{c}$ above which the fastest growing unstable mode has a non-zero wave number, so that undulations (``wrinkles'') form on the free surface. Below this critical spacing, the fastest growing unstable mode has a zero wave number, so that wrinkles do not form. In general, we also find that higher values of the inverse Bond number $\tau$ (proportional to the surface tension) lead to a stab ilisation of the zero wave number mode, i.e. higher values of $d$ are required for wrinkling to occur. Furthermore, if the inverse Bond number is sufficiently low, a second critical spacing $\tilde{d}_c

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