Wetting Dynamics of Aqueous Surfactant Solutions on Polymer Surfaces - Drops and Bubbles in Contact with Solid Surfaces - page 80

TPC line as a possible reason for the spreading force; it is suitable for describing
high spreading velocities far from equilibrium. Although this theory, in contrast
to the hydrodynamic theory, includes surface effects, its application to predict the
spreading velocity is rather problematic since the molecular parameters such as the
density of the adsorption centres and the distance between them on real surfaces
is unknown und generally inaccessible to experiments. By completely neglecting
the viscous drag, a theoretical dependence of the dynamic contact angle θ(t) on the
TPC line velocity is determined from the balance of the driving force and the fric-
tion force in the TPC zone. This approach is based on Eyring theory for transport
phenomena [25]. There are some attempts for simultaneous analysis of the bulk
flow and the TPC line friction [1, 21, 26, 27].

2. Spreading as a Rate Process

Spreading of evaporating droplets is determined by the spreading rate law d r/ d t
and evaporation rate law V ( t ), where r is the base radius of a spreading drop and V
is the drop volume. In many cases, the spreading rate law was found to be bi-
exponential [28], while the evaporation has a well documented proportionality to
the TPC line length [29-31]. If these two laws are in force, the spreading kinetics
of a liquid drop, i.e., the dependence of the base radius r and contact angle θ on
time, can be predicted. A more general step-mechanism of the TPC line motion was
recently proposed [32]. Here, surface energy fluctuations serve as energy barrier of
the spreading process, described as a nucleation process driven by capillary waves
at liquid surfaces. It was shown, that such a mechanism leads to a spreading rate
law similar to one obtained by molecular-kinetic treatment, without being based on
adsorption/desorption mechanism of spreading [23, 24, 28]. The well-documented
exponential law of spreading [28, 33-35] can also be interpreted by this mechanism.
Spreading rate law d r/ d t can be physically determined by bulk friction or by
friction in the vicinity of the TPC zone [1, 28] as schematically shown in Fig. 10.
In other words, spreading of droplets is a hydrodynamic problem with slip
boundary conditions at the TPC line [36] such as bulk properties, existing in the
hydrodynamic equations, or TPC zone properties, occurring in their boundary con-
dition, that are the decisive factors for spreading. In the following, the case, where
spreading rate is determined mainly by the TPC line region properties, is assumed.

(a) (b)

Figure 10. Schematic of a global spreading resistance (a); a parallel damper-slider model.