Review on Kinetics of Spreading and Wetting by Aqueous Surfactant Solutions - Drops and Bubbles in Contact with Solid Surfaces - page 41

ular interactions between the solid and the liquid). In the evaporation/condensation
model, transfer of liquid at the triple line occurs due non-equilibrium Kelvin pres-
sures. The condensation effect is found to be of greater importance at higher contact
angles (e.g., in forced wetting), and the overall features are complementary to the
molecular kinetics approach.
The hydrodynamic model was derived from the Navier-Stokes equation by in-
troducing the so-called 'lubrication approximation', in which flow is assumed to
be uniquely parallel to the solid surface. It has been shown that the hydrodynamic
regime may be characterised asymptotically by the tendency of drop radius and
contact angle to follow the power laws: R(t)

t − 3 / 10 . Probably
the best-known result of the hydrodynamic approach is Voinov-Hoffman-Tanner
law [14]. In contrast to the hydrodynamic model, the molecular-kinetic model pro-
poses different dynamic behaviour: R

t 1 / 10

∼ and θ(t) ∼

t − 3 / 7 . It originates from
the molecular-kinetic theory of Eyring and the behaviour of the wetting line is
explained by individual adsorption/desorption molecular displacements. Similar
behaviour may be expected with the evaporation/condensation model. While the
hydrodynamic model successfully describes complete wetting for viscous systems,
the molecular-kinetic model seems to be more appropriate for partial wetting [21].
De Gennes and Brochard-Wyart concluded that hydrodynamics was essential for
low angles, while molecular features were important at high velocities and large
angles [22].
Ruijter et al . [23, 24] presented a combined model to describe the dynamics of a
spreading drop, allowing both dissipation by friction against the substrate and hy-
drodynamic effects. This approach allowed the identification of several stages in
the wetting process: a fast, early-time stage (with linear change of the drop radius
with time), followed by a kinetic stage, which can be successfully modelled by
molecular-kinetic and subsequently hydrodynamic model, and finally an exponen-
tial relaxation to the equilibrium state. All the models described above proved to be
a powerful tool for portrayal of wetting behaviour of pure liquids, especially when
they exhibited partial wetting. Nevertheless, none of them gave a satisfactory fit for
wetting by surfactant solutions.

t 1 / 7 ∼ and θ ∼

D. Spreading of Surfactant Solutions

Surfactants ( surf ace act ive a ge nts ) are amphiphilic molecules that consist of hy-
drophilic (polar) and hydrophobic (non-polar) parts. The hydrophilic part of the
molecule is commonly referred to as the head-group and the hydrophobic part as the
tail. 'Lipophilic tail' and 'lipophobic head-group' are also commonly used terms.
Depending on the nature of the head group, surfactant molecules can be charac-
terised as ionic (anionic, cationic, zwitterionic) or nonionic. The surfactant tail is
usually a sufficiently long hydrocarbon chain, although its chemistry may vary (flu-
orocarbon, siloxane). Due to their dual nature, surfactants tend to pack at interfaces