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. (i) (ii) h D h D Figure 10 Surface tension, (i) capillary rise (ii) depression