Electrowetting of Ionic Liquids in Solid–Liquid–Liquid Systems - Drops and Bubbles in Contact with Solid Surfaces - page 262

(a) (b)

Figure 16. Dynamic contact angle, θ , vs. contact line speed, u (DC voltage: P 150 V; Q − 150 V;
e 200 V; a − 200 V): (a) hydrodynamic approach, the line is the best fit of Voinov's equation (6);
(b) molecular-kinetic approach, the line is the best fit of the exponential approximation of Blake's
equation (8). Adapted with permission from Paneru et al. [50]. Copyright 2010 American Chemical
Society.

parameters derived from Fig. 16b (size of the average molecular jump λ = 1 . 1nm

and jump frequency at a static contact line k 0 = 70 MHz) are reasonable and in line

with previous reports [52, 58]. Thus the parameters obtained for both equations are
physically plausible.
The wetting dynamics, shown in Fig. 16, agrees with the concept given by
Brochard-Wyart and de Gennes [59], which considers both viscous, D HD ,and
molecular dissipation, D MK :
D HD +

exp λ 2 W A
k B T

.

D MK
μu 2

const
θ

ln L =

l +

(14)

The hydrodynamic term includes the dynamic contact angle, θ , and as the liquid
wedge becomes thinner during spreading, θ decreases, and the importance of the
viscous term increases [55]. At the same time, molecular dissipation (the second
term; we have used the hypothesis [92] G W A λ 2 ) is not affected by the contact

angle [58, 92] and thus, whenever θ is small, viscous dissipation dominates the total
dissipation. In Fig. 16, viscous dissipation is more significant at low speeds (later
stages of the spreading) when the contact angle is relatively small. We have used
Voinov's equation (6) which is a better approximation than the one used to obtain
the hydrodynamic term in equation (14). During the initial stages of spreading,
the dynamic contact angle is rather large and, although contact line speed is high,
molecular dissipation prevails.
Recent work by Fetzer and Ralston [91] on the receding contact line formed
when an emerging bubble encounters a hydrophobic solid surface provides another
example following the above scheme. In that case, hydrodynamic dissipation was
predominant at high speed, while molecular dissipation came into play when the
contact line moved relatively slowly. In qualitative agreement with equation (14),
viscous dissipation dominated at high speeds because dynamic contact angles (as

=