1994 IChemE RESEARCH EVENT

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1994 IChemE RESEARCH EVENT UNIVERSITY COLLEGE
LONDON CAPILLARY WAVE DAMPING BY CARBOXYLIC
ACID MONOLAYERS RD MACIVER NH THOMAS FAST
Team Chemical Engineering University
Birmingham funded by Admiralty Research
Establishment Holton Heath for all
correspondence (Neale_at_Thomas.net)
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SUMMARY An optical refraction experimental
technique has been used to determine the
attenuation coefficient of capillary waves in the
presence of surfactant films. A new treatment of
linearised wave theory (Thomas 1988) expresses
the attenuation coefficient explicitly in terms
of the coupled dilational viscoselastic
properties. A study of the viscoelastic
properties of surface films of carboxylic (fatty)
acids has been undertaken. Such compounds are
representative of materials found in naturally
occurring sea slicks (Garrett. 1967). A
representation of the non-zero tangential stress
condition at a free surface that is introduced by
a surfactant film has been incorporated into a
finite difference numerical code in order to
model free surface motions in the presence of a
surfactant film.
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INTRODUCTION Surfactant films are common features
on liquid surfaces and are formed through natural
processes as well as, perhaps more influentially.
at the hand of man. They can have wide-ranging
effects on processes that occur at liquid
interfaces.Primarily. this study has investigated
the enhanced attenuation of surface waves that
occurs in the presence of a surfactant film,
especially in capillary wave regime. The
phenomenon of wave attenuation is of great
importance in many physical processes, especially
in remote sensing of the ocean surface for
inferences on heat and mass transfer across the
interface.This important role of surfactant films
introduces a need for an understanding of the
relation between the film properties, both
chemical and structural, and its attenuation
performance.
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THEORY The linearised dispersion relation S.L
?2(k-m)2 0 with S ?k2/? g/? - ?/k i?(km)
L ?k2/? i?(km) accommodates simple
partitioning according to S -i?m(1-k/m)e and L
-i?m(1-k/m)l with e and le-1 complex coupling
parameters (Thomas 1988). Simple manipulation
gives the attenuation coefficient as ? 1/?2
?2?3/2?1/2(?2 2??3)B B 1 ? (?-1)/?2
(?-1)2 ? 1/?2 (? ??)?2?-1/2?-3/2 and ? 1/?2
(? - ??)?2?-1/2?-3/2 conveying fundamentally
coupled dependence on surface tension and
viscoelasticity. The prediction of maximum
attenuation at relatively low dilation modulus
(figure 1) is consistent with earlier theoretical
predictions (Dorrestein 1951) and experimental
observations (Davies Vose 1965).
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EXPERIMENTAL METHODS An interfacially refracted
image of a submerged object (figure 2a) appears
to oscillate in phase with propagating
interfacial wave trains (figure 2b). The
magnitude d of the oscillation is related through
Snells law (figure 3a) to both the instantaneous
wave slope tan? and the elevation L of the
observation plane above the undisturbed interface
by d 1/3Ltan?. Thus the maximum deflection of
the image decays with distance from the wave
origin following the attenuation rate of the
capillary wave. For linear waves the deflection
angle is very small lt0.02? and hence so is the
deflection distance. Mounting a traveling
microscope in front of the video camera used to
record the oscillation (figure 3b) magnifies the
observed deflections thus improving the
measurement accuracy.
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NUMERICAL SIMULATIONS Previous work either
excluded interfacial properties or incorporated
only uniform surface tension as a normal stress
constraint. To model film effects we extended a
standard finite difference scheme using the
volume of fluid (VOF) code of Nichols et al
(1980) to incorporate a nonzero tangential stress
condition at the free surface. The surface film
is represented by a series of massless marker
particles constrained to lie in the free surface.
Being massless they have no direct effect on the
fluid motion but the particle separation is used
as measure of local dilation of the surface film
to estimate concentration dependent surface
tension and surface tension gradients. The normal
and tangential stress conditions are incorporated
by iterating on fluid velocities in the
interface. Figure 4 demonstrates the effect in
suppressing a breaking bore.
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CONCLUSIONS FUTURE WORK A reliable and accurate
experimental technique for establishing
viscoelastic properties of surfactant films has
been validated. The surfactants studied have been
simple molecules representative of components in
naturally occurring films. Studies of more
complex molecules are reported here by Fox
Thomas (1994). The numerical simulation is a
first attempt to incorporate non-zero tangential
stress conditions at the free surface. Although
tracking of the marker particles has proved
problematical, the method provides a useful basis
for further development. Main points of a simple
analysis by Thomas (1988) show how coupling of
surface properties suffices to capture film
damping effects without any appeal to mode
resonance.
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NOMENCLATURE G gravitational acceleration ? surf
ace tension ? kinematic viscosity ? wave
number ? attenuation coefficient ? dilational
elasticity ? dilational viscosity ? wave
frequency k?i? complex wave number mk2i?/? pen
etration depth of rotational motion
??i?? dilational modulus Davies JT Vose RW
(1965) Proc Roy Soc 286 218-234 Dorrestein R
(1951) K Ned Ak Wetcn B54 260-272 Fox JS Thomas
NH (1994) Abs IChemE Research Event Garrett WD
(1967) Deep Sea Res 14 211-127 Nichols BT Hirt CW
Hotchkiss RS (198O) Rep LA-8355 Thomas NH (1988)
Priv Rep FRED8807 (ARE HH)
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Figure 1 Dependence of Reynolds scaled
attenuation coefficient on dilational elasticity.
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Figure 2 Object viewed through a) undisturbed
surface b) surface supporting propagating waves.
Nominal line width 180?m diameter of bright
points about 5?m.
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Figure 3 a) Refraction at sloping interace b)
Experimental arrangement
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Figure 4 Breaking bores with surface tension a)
absent b) uniform c) variable