Biomedical Engineering Reference
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Figure 9. Photographs of spreading drop in 0.5 s from drop deposition. (a) Fingering on a thin water
layer; (b) fingering on a thick water layer [63].
fingers during spreading depends on time as t α ,where α
=
0 . 66 and 0.7 for the thin
and thick films, correspondingly.
Frank and Garoff [65] determined that the formation of fingering patterns de-
pend not only on the surfactant concentration gradients, but on a mechanism of
surfactant-surface interactions as well. The same surfactant can exhibit fingering or
'stick-jump' (autophobing) spreading behaviour on the same charged or opposite
charged substrates, correspondingly. The spreading behaviour of aqueous surfac-
tants SDS (anionic sodium dodecyl sulphate) and CTAB (cationic cetyltrimethy-
lammonium bromide) solutions on a clean and dry oxidized silicone wafer and
a polished sapphire disk has been examined. The SDS solution spreads with the
fingering formation on the silicone wafer, while on the sapphire substrate it ex-
hibits an autophobing effect. The spreading behaviour of CTAB solution on these
substrates is contrary to the SDS spreading. Authors have deduced that surfactant
cannot advance alone; fluid films must be present on the surface. For sufficiently
clean surfaces, thin precursor films of fluid move rapidly ahead of the dendrites
of the spreading solution. Moreover, on the substrates which are prewetted with a
surfactant solution monolayer, no the fingering spreading is observed.
The role of the underlying films on the substrates and viscosity of solvents in
the formation of the hydrodynamics instabilities at the contact-line of the spreading
drops has been intensively investigated by Cazabat and co-workers [57, 70, 71, 75,
76].
Cachile and Cazabat [70, 71] studied the influence of the ambient relative humid-
ity (RH) and the surfactant concentration on the fingering spreading of solutions of
non-ionic C 12 E 4 and C 12 E 10 surfactants in ethylene and diethylene glycol on hy-
drophilic silicon wafers. The results were summarized in a 'phase diagram', as a
function of the normalized surfactant concentration, C , defined as the ratio of the
bulk concentration to the CMC, and the relative humidity, RH (Fig. 10).
In the stable region, at RH
30%, there is a capillary spreading regime. The drop
spreads out as a uniform circle in the whole concentration range investigated and
the radius of the drop R scales as t 1 / 10 . With increasing RH (unstable region), the
spreading process is accelerated and the fingering instabilities are developed. It was
found that R 2 grew linearly in time when RH
60%, but at RH > 85%, spreading is
faster. At C > 1, the adsorption of surfactant at the solid-liquid interface creates a
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