Review on Kinetics of Spreading and Wetting by Aqueous Surfactant Solutions - Drops and Bubbles in Contact with Solid Surfaces - page 56

until the CMC is reached. At concentrations above the CMC, advancing contact an-
gle remains constant and approximately equal to 35 ◦ . A non-zero value of the static
receding contact angle was found only in the case of pure water droplets. In all
other cases (even at the smallest SDS concentrations used 0.025%) the static reced-
ing contact angle was found equal to zero in the entire concentration range used:
from 0.025% (ten times smaller than CMC) to 1% (five times higher than CMC).
Comparison of Fig. 12 and Fig. 13 shows:

• The advancing contact angle dependence on SDS concentration on porous ni-

trocellulose substrates is significantly different from the static advancing con-
tact angle dependence on non-porous nitrocellulose substrates. The latter means
that in the case of porous substrates, the influence of both hydrodynamic flow
caused by imbibition into the porous substrate and the substrate roughness
changes significantly the advancing contact angle;

• The hydrodynamic receding contact angle, in the case of the porous substrates,

has nothing to do with contact angle hysteresis and is determined completely
by the hydrodynamic interactions in a way similar to the complete wetting case.

It is worth mentioning that observed dependencies during imbibition into porous
substrates in [86] are very similar to those noticed in droplet spreading and evap-
oration experiments [97]. When plotted in dimensionless time, changes in droplet
radius show surprising resemblance. In both cases, the radius of the drop, L , reaches
its maximum value in the very beginning, at time instant t m , after which it decreases.
Compared to the maximum duration of the process, t max , the time needed for com-
plete evaporation of the droplet, and t p , the time for imbibition into the porous
substrate, it was found that t m ∼ 0 . 08 t p , in the cases of evapora- 0 . 06 t max and t m ∼

tion and imbibition, respectively (Fig. 14).
Experimental data on a spreading/evaporation curve showed the same trend for
liquids with very different volatility: alkanes, water and silicone oils. Although the-
oretical models have been successfully developed, it is still necessary to explain
why mass loss in the case of sessile drops manifests itself in an identical manner.
Daniel and Berg [98] developed a model to predict the simultaneous spread-
ing and penetration of surfactant solutions, based on energy considerations of the
system. Comparison with [86] showed that the energy-based model is functionally
equivalent. The derived energy-based model was tested against experimental data
for spreading of commercial surfactants over a variety of papers relevant to thermal
ink-jet printing.
It is necessary to emphasise that, in spite of enormous industrial importance, the
kinetics of spreading/imbibition of surfactant solutions into porous media is far less
investigated than it deserves.