Physical Chemistry of Foods

effect will transport wine upward (frame 2), hence a thicker rim of

ethanol-depleted wine is formed (frame 3). This rim is subject to

Rayleigh instability (comparable to the phenomenon discussed in

Question 2 at the end of Section 10.5), hence ‘‘tears’’ will be

formed at regular distance intervals. The tears will grow by further

upflow of wine caused by evaporation and become sufficiently

heavy to move downwards due to gravity. Other tears will grow,

and so on. This process goes on until the ethanol content has

become too low.

Spreading Rate. If a gradient in interfacial tension occurs in a
liquid interface, because the interface is suddenly expanded or some
surfactant is locally applied to the interface, theinterfacial tension will be
evened out, i.e., become the same everywhere at the interface. Therateat
which this occurs if of considerable importance for the extent of the
Marangoni effect. It proceeds as alongitudinal surface wave. The linear
velocity of the wave on an A–W interface is given by

v¼ 1 : 2 ðZrzÞ
^1 =^3 jDgj^2 =^3 ð 10 : 18 Þ

wherezis the distance over which the wave has to travel. The densityrand
viscosityZare those of the aqueous phase. For a wave on an O–W interface,
ZWrWmust be replaced byðZ^2 Wr^2 WþZ^2 Or^2 OÞ^0 :^5. This means that in many
cases,Z?rof the most viscous phase can be taken, the other one being
negligible.
If there is only one surfactant, the wave velocity can be interpreted as
‘‘the rate of spreading of surfactant’’ over the interface. Actually, the word
spreading is to some extent misleading, sinceit is the interface that moves,
taking the surfactant with it. Puttingv¼dx/dt, integration of Eq. (10.18)

FIGURE10.30 Formation of wine tears.