Electrowetting of Ionic Liquids in Solid–Liquid–Liquid Systems - Drops and Bubbles in Contact with Solid Surfaces - page 260

solid-ionic liquid-alkane systems perform very well in electrowetting and can be
integrated in suitable applications.
D.3. Dynamics of Electrowetting

There is a continuing interest in electrowetting as a possible mechanism for actu-
ation in microfluidics because it is electrically controlled, reversible and very fast.
Under the influence of an applied DC voltage, the ionic liquid droplet spreads so
that its base area, A (the area of the insulator-ionic liquid contact) expands expo-
nentially. There is no generally accepted description of the evolution of the base
area of a spreading droplet, but Lavi and Marmur [87], after reviewing extensively
experimental results, proposed the following empirical equation:

(t/τ) n A = A 0 { 1 − exp [− ]} . (12)

This equation has the advantage of not being related to a specific model of the
dynamic contact angle. In practice, the exponent n is often close to unity and an
exponential growth of the contact area has been recorded for a variety of systems:
the spreading of a silicone oil in air on a commercial polyurethane paint [88], the
spreading of liquid molybdenum on a glass surface in an argon-hydrogen atmo-
sphere [89], and the dewetting of a hydrophobic solid surface when contacted by
an air bubble [90, 91], to name a few. We did observe an exponential increase and
decrease of the base area for all ionic liquids studied (Fig. 12 and Fig. 13) and this
suggests that there is nothing exceptional in the spreading behaviour of ionic liquids
under electrowetting conditions.
The spreading of liquids is directly related to their bulk viscosity because the
liquid flows during spreading [85]. In electrowetting experiments, the droplet of
ionic liquid is subjected to a driving force which takes it from a spherical cap (the
influence of gravity is insignificant) with a small contact area (high contact angle)
to a spherical cap with a large contact area (small contact angle). Since the contact
angles at zero voltage and at saturation are rather similar for all the ionic liquids
studied (Fig. 6, Fig. 8, Fig. 9) the following estimate of the average viscous stress,
τ xy , can be made:

μ ∂u x μ u x μ x

μ

∂y = x = τx = τ =

τ xy = const. (13)

In this equation Newton's law is used to relate the bulk viscosity, μ , with a char-
acteristic spreading time, τ . If the stress τ xy is approximately constant, a linear
relation is predicted and, indeed, this was observed in our experiments—Fig. 15.
A similarly strong correlation between spreading time and viscosity was found for
the bmim.BF 4 -water mixtures but it was non-linear probably due to the more com-
plex hydrodynamic behaviour of less viscous droplets [49].
There is however, a distinct difference between the characteristic time during
spreading and retraction. Receding is definitely slower than advancing and we spec-
ulate that the arrangement of the bulky ions of the ionic liquids at the solid-liquid