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Effetto Marangoni (da Wikipedia)

Dal momento che un liquido con una tensione superficiale pi elevata esercita una maggiore forza sul liquido
circostante di un liquido con una bassa tensione superficiale, la presenza di un gradiente di tensione superficiale fa s
che il liquido scorra via da regioni a bassa tensione superficiale. Il gradiente di tensione superficiale, a sua volta, pu
essere causato da un gradiente di concentrazione (di alcool etilico, nel caso degli archetti del vino) o da un gradiente di
temperatura (la tensione superficiale funzione della temperatura).

Esempio 1 - Archetti del vino

Gli archetti del vino (o lacrime) sono un fenomeno che si osserva facendo roteare il vino dentro ad un bicchiere ben
pulito: si forma un anello di liquido dal quale discendono delle gocce che scorrono lungo il vetro tornando nel vino.
Questo fenomeno, che si osserva pi facilmente in vini ricchi di alcool etilico, una delle manifestazioni dell'effetto

L'effetto dovuto al fatto che l'alcool ha una tensione superficiale minore dell'acqua. Se l'alcool fosse mischiato in
modo non omogeneo con acqua, una regione con una minore concentrazione d'alcool farebbe pressione sul liquido
circostante in modo pi forte che una regione con una concentrazione alcolica pi alta. Il risultato che il liquido tende
a fluire via dalle regioni con concentrazioni d'alcool maggiori. Questo pu essere facilmente dimostrato stendendo un
sottile strato d'acqua su una superficie liscia: facendovi cadere al centro una goccia d'alcool, il liquido si allontaner dal
punto in cui caduta la goccia.

Il vino una miscela di alcool (da 10% al 15% in volume) e acqua (le altre sostanze sono presenti in quantit
trascurabili). Facendo roteare il bicchiere il vino incontra la superficie interna del bicchiere, e per capillarit la risale; sia
l'acqua che l'alcool evaporeranno quindi dalla superficie, ma l'alcool evaporer pi in fretta a causa della pi alta
pressione di vapore e del pi basso punto di ebollizione. Questo cambiamento nella composizione del vino (minor
concentrazione alcolica) provoca un aumento della tensione superficiale, facendo risalire ancora di pi il liquido nella
superficie interna del bicchiere. Le gocce di vino, infine, tenderanno a ricadere per effetto del loro stesso peso, formando
gli archetti.

L'effetto pi evidente nei vini molto alcolici a causa della maggior differenza di tensione superficiale tra il vino allo
stato "iniziale" e quello che gi andato incontro al processo di evaporazione.

Esempio 2 - Bolle di sapone

Una bolla pu esistere perch lo strato superficiale di un liquido (molto spesso acqua) ha una certa tensione superficiale,
ci lo fa comportare similmente ad un foglio elastico. In ogni caso, una bolla fatta da un liquido puro da solo non
stabile ed necessario sciogliervi un surfattante come il sapone per stabilizzarla. Un concetto comune ma errato che il
sapone aumenti la tensione superficiale dell'acqua. vero il contrario, cio il sapone decrementa la tensione superficiale
dell'acqua in superficie approssimativamente a 1/3. Il sapone non rinforza le bolle ma le stabilizza grazie ad un
fenomeno conosciuto come effetto Marangoni. Quando il film superficiale della bolla si va allungando e assottigliando
(ad esempio quando una bolla si gonfia), la concentrazione di sapone nel film diminuisce e ci causa un aumento della

tensione superficiale. Cos il sapone va a rinforzare le parti pi deboli della bolla e tende a non farla ingrandire
ulteriormente. Il sapone inoltre riduce l'evaporazione permettendo alla bolla di durare pi a lungo, sebbene questo
effetto sia relativamente scarso.

La forma sferica anch'essa dovuta alla tensione superficiale. La tensione superficiale porta alla formazione di una sfera
perch questa possiede la minima superficie per un dato volume.

Esperimento - Soap propelled boat (propulsione a effetto marangoni)

From: Advanced Fluid Dynamics (Lecture Notes) - T.R. Akylas (MIT)

LECTURE 4: Marangoni flows

Marangoni flows are those driven by surface tension gradients. In general, surface tension de-
pends on both the temperature and chemical composition at the interface; consequently, Marangoni
flows may be generated by gradients in either temperature or chemical concentration at an interface.
In lecture 2, we derived the tangential stress balance at a free surface:

nTt = tr , (1)

where n is the unit outward normal to the surface, and t is any unit tangent vector. The tangential
component of the hydrodynamic stress at the surface must balance the tangential stress associated
with gradients in . Such Marangoni stresses may result from gradients in temperature or chemical
composition at the interface. For a static system, since n T t = 0, the tangential stress balance
equation indicates that: 0 = r . This leads us to the following important conclusion:
There cannot be a static system in the presence of surface tension gradients. While pressure jumps
can sustain normal stress jumps across a fluid interface, they do not contribute to the tangential
stress jump. Consequently, tangential surface stresses can only be balanced by viscous stresses
associated with fluid motion.

4.1 Tears of wine

The first Marangoni flow considered was the tears of wine phenomenon (Thomson 1885), which
actually predates Marangonis first published work on the subject by a decade. The tears of wine
phenomenon is readily observed in a glass of any but the weakest wines following the establishment
of a thin layer of wine on the walls of the wine glass.
The tears or legs of wine are taken by sommeliers to be an indicator of the quality of wine.
An illustration of the tears of wine phenomenon is presented in Figure 1 (see also http://www- bush/tears.html ). Evaporation of alcohol occurs everywhere along the free surface.
The alcohol concentration in the thin layer is thus reduced relative to that in the bulk owing to the
enhanced surface area to volume ratio. As surface tension decreases with alcohol concentration,
the surface tension is higher in the thin film than the bulk; the associated Marangoni stress drives
upflow throughout the thin film. The wine climbs until reaching the top of the film, where it
accumulates in a band of fluid that thickens until eventually becoming gravitationally unstable and
releasing the tears of wine. The tears or legs roll back to replenish the bulk reservoir, but with
fluid that is depleted in alcohol.
The flow relies on the transfer of chemical potential energy to kinetic and ultimately gravitational
potential energy. The process continues until the alcohol is completely evaporated.

4.2 Surfactants

Surfactants are molecules that have an affinity for interfaces; common examples include soap
and oil. Owing to their molecular structure (often a hydrophylic head and hydrophobic tail), they
find it energetically favourable to reside at the free surface. Their presence reduces the surface
tension; consequently, gradients in surfactant concentration result in surface tension gradients.
Surfactants thus generate a special class of Marangoni flows. There are many dierent types of
surfactants, some of which are insoluble (and so remain on the surface), others of which are soluble

Figure 1: The tears of wine. Fluid is drawn from the bulk up the thin film adjoining the walls of
the glass by Marangoni stresses induced by evaporation of alcohol from the free surface.

in the suspending fluid and so diuse into the bulk. For a wide range of common surfactants, surface
tension is a monotonically decreasing function of until a critical concentration is achieved, beyond
which remains constant.
The concentration of surfactant on a free surface evolves according to
+ rs ( us ) + (rs n)(u n) = J( , Cs ) + Ds r2s , (2)
where us is the surface velocity, rs is the surface gradient operator and Ds is the surface diusivity
of the surfactant. J is a surfactant source term associated with adsorption onto or desorption from
the surface, and depends on both the surface surfactant concentration and the concentration
in the bulk Cs . Tracing the evolution of a contaminated free surface requires the use of Navier-
Stokes equations, relevant boundary conditions and the surfactant evolution equation (2). The
dependence of surface tension on surfactant concentration, ( ), requires the coupling of the flow
field and surfactant field. In certain special cases, the system may be made more tractable. For
example, for insoluble surfactants, J = 0, and many surfactants have sufficiently small Ds that
surface diusivity may be safely neglected.
The principal dynamical influence of surfactants is to impart an eective elasticity to the in-
terface. Specifically, the presence of surfactants will serve not only to alter the normal stress
balance (through the reduction of ), but also the tangential stress balance (through the gener-
ation of Marangoni stresses). The presence of surfactants will act to suppress any fluid motion
characterized by non-zero surface divergence. For example, consider a fluid motion characterized
by a radially divergent surface motion. The presence of surfactants results in the redistribution
of surfactants: is reduced near the point of divergence. The resulting Marangoni stresses act to
suppress the surface motion, resisting it through an eective surface elasticity. Similarly, if the flow
is characterized by a radial convergence, the resulting accumulation of surfactant in the region of

Figure 2: The footprint of a whale, caused by the whales sweeping biomaterial to the sea surface.
The biomaterial acts as a surfactant in locally suppressing the capillary waves evident elsewhere
on the sea surface. Observed in the wake of a whale on a whale watch from Boston Harbour.

convergence will result in Marangoni stresses that serve to resist it. It is this eective elasticity
that gives soap films their longevity: the divergent motions that would cause a pure liquid film to
rupture are suppressed by the surfactant layer on the soap film surface.
The ability of surfactant to suppress flows with non-zero surface divergence is evident throughout
the natural world. It was first remarked upon by Pliny the Elder, who rationalized that the absence
of capillary waves in the wake of ships is due to the ships stirring up surfactant. This phenomenon
was also widely known to spear-fishermen, who poured oil on the water to increase their ability to
see their prey, and by sailors, who would do similarly in an attempt to calm troubled seas. Finally,
the suppression of capillary waves by surfactant is responsible for the footprints of whales (see
Figure 2). In the wake of whales, even in turbulent roiling seas, one seas patches on the sea surface
(of characteristic width 5-10m) that are perfectly flat. These are generally acknowledged to result
from the whales sweeping biomaterial to the surface with their tails; this biomaterial serves as a
surfactant that suppresses capillary waves.

4.3 The soap boat

Consider a floating body with perimeter C in contact with the free surface, which we assume for
the sake of simplicity to be flat. Recalling that may be thought of as a force per length in a
direction tangent to the surface, we see that the total surface tension force acting on the body is:
Fc = s d` , (3)

where s is the unit vector tangent to the free surface and normal to C, and d` is an incremental
arc length along C. If is everywhere constant, then this line integral vanishes identically by the
Divergence Theorem. However, if = (x), then it may result in a net propulsive force.

Figure 3: The soap boat. A floating body (length 2.5cm) contains a small volume of soap, which
serves as its fuel in propelling it across the free surface.The soap exits the rear of the boat, decreasing
the local surface tension. The resulting fore-to-aft surface tension gradient propels the boat forward.
The water surface is covered with Thymol blue, which parts owing to the presence of soap, which
is visible as a white streak.

The soap boat may be simply generated by coating one end of a toothpick with soap, which
acts to reduce surface tension (see Figure 3). The concomitant gradient in surface tension results
in a net propulsive force that drives the boat away from the soap. We note that an analogous
Marangoni propulsion technique arises in the natural world: certain water-walking insects eject
surfactant and use the resulting surface tension gradients as an emergency mechanism for avoiding
predation. Moreover, when a pine needle falls into a lake or pond, it is propelled across the surface
in an analogous fashion owing to the influence of the resin at its base decreasing the local surface

4.4 Bubble motion

Theoretical predictions for the rise speed of small drops or bubbles do not adequately describe
observations. Specifically, air bubbles rise at low Reynolds number at rates appropriate for rigid
spheres with equivalent buoyancy in all but the most carefully cleaned fluids. This discrepancy may
be rationalized through consideration of the influence of surfactants on the surface dynamics. The
flow generated by a clean spherical bubble of radius a rising at low Re = U a/ is intuitively obvious.
The interior flow is toroidal, while the surface motion is characterized by divergence and convergence
at, respectively, the leading and trailing surfaces. The presence of surface contamination changes
the flow qualitatively.
The eective surface elasticity imparted by the surfactants acts to suppress the surface motion.
Surfactant is generaly swept to the trailing edge of the bubble, where it accumulates, giving rise
to a local decrease in surface tension. The resulting fore-to-aft surface tension gradient results in a

Marangoni stress that resists surface motion, and so rigidifies the bubble surface. The air bubble
thus moves as if its surface were stagnant, and it is thus that its rise speed is commensurate with
that predicted for a rigid sphere: the no-slip boundary condition is more appropriate than the
free-slip. Finally, we note that the characteristic Marangoni stress /a is most pronounced for
small bubbles. It is thus that the influence of surfactants is greatest on small bubbles.