Wetting Dynamics of Aqueous Surfactant Solutions on Polymer Surfaces - Drops and Bubbles in Contact with Solid Surfaces - page 82

In summary, the cosine of dynamic contact angle θ(t) is determined by the
spreading law (3), drop geometry (5) and evaporation rate law V ( t ). The problem
of the determination of cos θ(t) and r ( t ), assuming that drop volume remains con-
stant, was solved numerically [42], where the exponential factors b A und b R were
assumed to be identical. In this case, the spreading law of Eq. (3) reduces to
d r
d t =

A sinh (b( cos − cos θ)). (6)

3. Spreading of Aqueous Surfactant Solutions
If a surface-active substance and a real (i.e., rough, inhomogeneous) solid surface is
of interest, some attempts to describe the wetting behaviour theoretically are rather
of a speculative nature. Aqueous surfactant solutions differ from pure liquids by
the fact that their surface tension γ LV and solid-liquid interfacial tension γ SL are
functions of time, and the molecular orientation influences surfactant-solid surface
interactions. In the study of aqueous surfactant solutions, along with the solid sur-
face state (chemical and morphologic nature), additional factors such as the solution
concentration, the chemical nature of a surfactant (non-ionic, anionic, cationic, am-
photeric) have to be taken into account. In the last decade, various authors, using
dynamic contact angle measurements, found that the spreading velocity of aqueous
surfactant solutions is strongly affected by the solid surface energy.
An adequate interpretation of the results of contact angle measurements is ad-
ditionally complicated because a solid surface is able to adsorb water vapour from
humid air. So, the surface energy value γ SV depends on the thickness of the ad-
sorption film. Disjoining pressure isotherms in the presence of surfactants are well
investigated in the case of free liquid films [43], much less is known in the case
of liquid films on solid substrates [44]. At the present, an answer to the question
how surfactant molecules are transferred in the TPC line vicinity is not given. In
the case of aqueous surfactant solutions, the knowledge of the transition zone be-
haviour from meniscus to thin films in front is very limited as referred in [45].
Hitherto, either only the solid-vapour interfacial tension γ SV or only the sur-
face tension γ LV was assumed in the literature, though variations of the solid-liquid
interfacial tension γ SL was not excluded in this case. Depending on these assump-
tions, two fundamentally different spreading mechanisms of aqueous surfactant
solutions were proposed for hydrophobic surfaces [45]. Following von Bahr et al.
ideas [46] the surfactant molecules adsorb at the freshly formed solid-liquid in-
terface behind the advancing wetting front. The transfer of molecules from the
liquid-vapour interface occurs very quickly. The replenishment of this interface
happens by diffusion of surfactant molecules from the volume phase and depends
linearly on the root of time ( diffusion-controlled ). In contrast with it, Starov et
al. [40] assumed that the surfactant molecules adsorb onto the solid-liquid inter-
face before the wetting front. As this takes place, interfacial tension γ SV increases.
The transfer of molecules from the liquid-vapour interface occurs very slowly. The
reason for the spreading force is the difference ( S (t)

− e ) ,where S (t) is the