Vapour pressure of liquids
A liquid in a closed container is subjected to partial vapour pressure
due to the escaping molecules from the surface; it reaches a stage of
equilibrium when this pressure reaches saturated vapour pressure. Since
this depends upon molecular activity, which is a function of temperature,
the vapour pressure of a fluid also depends upon its temperature and
increases with it. If the pressure above a liquid reaches the vapour
pressure of the liquid, boiling occurs; for example if the pressure is
reduced sufficiently boiling may occur at room temperature. The
saturated vapour pressure for water at 20c is 2.45*10^3 N/m2.
SURFACE TENSION
Surface tension arises from the forces between the molecules of a
liquid and the forces (generally of a different magnitude) between the
liquid molecules and those of any adjacent substance. The symbol for
surface tension is γ and it has the dimensions [MT−2].
Water in contact with air has a surface tension of about 0.073 N·m−1
at usual ambient temperatures; most organic liquids have values between
0.020 and 0.030 N·m−1 and mercury about 0.48 N·m−1, the liquid in
each case being in contact with air. For all liquids the surface tension
decreases as the temperature rises. The surface tension of water may be
considerably reduced by the addition of small quantities of organic
solutes such as soapand detergents. Salts such as sodium chloride in
solution raise the surface tension of water. That tension which exists in
the surface separating two immiscible liquids is usually known as
interfacial tension. As a consequence of surface tension effects a drop of
liquid, free from all other forces, takes on a spherical form. The
molecules of a liquid are bound to one another by forces of molecular
attraction, and it is these forces that give rise to cohesion, that is, the
tendency of the liquid to remain as one assemblage of particles rather
than to behave as a gas and fill the entire space within which it is
confined. Forces between the molecules of a fluid and the molecules of a
solid boundary surface give rise to adhesion between the fluid and the
boundary.
If the forces of adhesion between the molecules of a particular liquid
and a particular solid are greater than the forces of cohesion among the
liquid molecules themselves, the liquid molecules tend to crowd towards
the solid surface, and the area of contact between liquid and solid tends to
increase. Given the opportunity, the liquid then spreads over the solid
surface and ‘wets’ it. Water will wet clean glass, but mercury will not.
Water, however, will not wet wax or a greasy surface The interplay of
these various forces explains the capillary rise or depression that occurs
when a free liquid surface meets a solid boundary. Unless the attraction
between molecules of the liquid exactly equals that between molecules of
the liquid and molecules of the solid, the surface near the boundary
becomes curved. Now if the surface of a liquid is curved the surface
tension forces have a resultant towards the concave side. For equilibrium
this resultant must be balanced by a greater pressure at the concave
side of the surface. It may readily be shown that if the surface has radii of
curvature R1 and R2 in two perpendicular planes the pressure at the
concave side of the surface is greater than that at the convex side by
γ(1/R1+ 1/R2)
(7)
Inside a spherical drop, for instance, the pressure exceeds that outside
by 2γ/R (since here R1 = R2 = R). However, the excess pressure inside a
soap bubble is 4γ/R; this is because the very thin soap film has two
surfaces, an inner and an outer, each in contact with air. Applying
expression 1.11 and the principles of statics to the rise of a liquid in a
vertical capillary tube yields
h = 4γ cos θ/gd
(8)
where h represents the capillary rise of the liquid surface (see Fig. 2), θ
represents the angle of contact between the wall of the tube and the
interface between the liquid and air, _ the density of the liquid, g the
gravitational acceleration, and d the diameter of the tube. (For two liquids
in contact γ represents the interfacial tension, and _ the difference of their
densities.) However, the assumption of a spherical interface between the
liquid and air (and other approximations) restricts the application of the
formula to tubes of small bore, say less than 3 mm. Moreover, although
for pure water in a completely clean glass tube θ = 0, the value may well
be different in engineering practice, where cleanliness of a high order is
seldom found, or with
Fig. 2
tubes of other materials. Equation 9 therefore overestimates the actual
capillary rise. Mercury, which has an angle of contact with clean glass of
about 130◦ in air, and therefore a negative value of cos θ, experiences a
capillary depression.
Surface tension becomes important when solid boundaries of a liquid
surface are close together or when the surface separating two immiscible
fluids has a very small radius of curvature. The forces due to surface
tension then become comparable with other forces and so may
appreciably affect the behaviour of the liquid. Such conditions may occur,
for example, in small-scale models of rivers or harbours. The surface
tension forces may be relatively much more significant in the model than
in the full-size structure; consequently a simple scaling-up of
measurements made on the model may not yield results accurately
corresponding to the full-size situation. In apparatus of small size the
forces due to surface tension can completely stop the motion of a liquid if
they exceed the other forces acting on it. It is well known, for example,
that a cup or tumbler may be carefully filled until the liquid surface is
perhaps 3 mm above the rim before overflowing begins.
Among other instances in which surface tension plays an important
role are the formation of bubbles, the break-up of liquid jets and the
formation of drops, the rise of water in soil above the level of the water
table, and the flow of thin sheets of liquid over a solid surface. In most
engineering problems, the distances between boundaries are
sufficient for surface tension forces to be negligible compared with the
other forces involved. The consequent customary neglect of the surface
tension forces should not, however, lead us to forget their importance in
small-scale work.
Capillary Rise or Depression
Refer Figure 10
Let D be the diameter of the tube and is the contact angle. The surface tension forces
acting around the circumference of the tube = × D ×.
The vertical component of this force = D × cos
This is balanced by the fluid column of height, h, the specific weight of liquid
being.
Equating,
h A = D cos, A =D 2/4 and so
h = (4 D cos)/(D 2) = (4 cos)/gD
……. (9)
This equation provides the means for calculating the capillary rise or
depression. The sign of cos depending on > 90 or otherwise determines the
capillary rise or depression.
(ii)
(i)




h
D

h


D

Figure 10 Surface tension, (i) capillary rise (ii) depression