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Dear the wall of the container. The molecule, experiences both cohesive as well as adhesive, forces. In this case also, the net adhesive force, (AP) acting on the molecule A is horizontal, since the wall is vertical. Magnitude of, cohesive force is so large that the net force, (CAR ) is directed inside the liquid., , Sphere of influence T, , Air, , , , Fig, 2.19 (b): Obtuse angle of contact,, , For equilibrium or stability of a liquid, surface, the net force (AR) acting on all, molecules similar to molecule A must be, normal to the liquid surface at all points, The, liquid near the wall should, therefore, creep, inside against the solid boundary. This makes, the meniscus convex so that its tangent AT is, normal to AR. Obviously, such liquid does not, wet that solid surface., , iii) Zero angie of contact :, Sphere of influence, , , , Fig. 2.19 (c): Angle of contact equal to zero., Figure 2.19 (c) shows the angle of, contact between a liquid (e.g. highly pure, water) which completely wets a solid, (e.g. clean glass) surface. The angle, of contact in this case is almost zero (i.e., 6 0°). In this case, the liquid molecules near, the contact region, are so less in number that, the cohesive force is negligible, ic, 4C —0, and the net adhesive force itself is the resultant, force, ic, AP=AR. Therefore, the tangent, AT is along the wall within the liquid and the, angle of contact is zero., , ---- G>~~~~, , , , , , , tact : ol, gle oaown in the Fig. 2.19 (@. Inth, neg ee cohesive force AC is exactly ¢, case, the the surfaces and the result,, tly vertical (along the soli, , , , , , , , , —~=_ AC }, For this to occur, AP = i; where, AR, , the net force, From this y, , itude of, oe ditions for acute and o, , can write the com, angles of contact:, , —. AC, For acute angle of contact, ¥ 2 FE cand fo, obtuse angle of contact, AP< an, , , , , , , , , , , , , , , , , b) Shape of liquid drops on a solid, When a small amount of a liquid, dropped on a plane solid surface, the, will either spread on the surface or will, droplets on the surface. Which phenom, will occur depends on the surface tension ¢, the liquid and the angle of contact betwe, the liquid and the solid surface. The surf, tension between the liquid and air as wel, that between solid and air will also have ta, taken in to account., _ Let 6 be the angle of contact for the gi, solid-liquid pair,, T, = Force due to i, bcos bint tension at the, T, = Force due to a, ‘lid tana ave tension at the a

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T, = Force due to surfa i ,, inden., , As the force due t, , tangential to the sais iceans Ge 5, of T,, T, and T, are as shown in the Fig, 2.20., For equilibrium of the drop,, , T, =T,+T,cos0 .cos9 = B=, , ~~ eae We get the following cases:, , ae fe and (T,-7,) < T,, cos@ is positive, , ai © angle of contact @ is acute as, shown in Fig, 2.20 (a),, , , , Fig. 2.20 (a): Acute angle., , 2) If T,< T, and (T, — T,) < T,, cos@ is, negative, and the angle of contact @ is, obtuse = shown in Fig. 2.20(b)., , , , Fig. 2.20 (by: Obtuse angle., , 3) 1(%,-7)= T,,cos@ =1 and @ is nearly, equal to zero., , 4) If (7-1) >To Tp, + T0088? I, which is impossible. The liquid spreads, over the solid surface and drop will not be, formed., , c) Factors affecting the angle of contact:, , The value of the angle of contact depends on, , the following factors, F, , i) The nature of the liquid and the solid in, contact. Leon, , ii) Impurity : Impurities present in the liquid, change the angle of contact. ;, , iii) Temperature of the liquid : Any increase, in the temperature of a liquid decreases its, angle of contact. For a given solid-liquid, surface, the angle of contact is constant at, agiven temperature., , --- (2.18) :, , Table 2.2 — Angle of contact for pair of, liquid - solid in contact., , , , 2.4.4 Effect of impurity and temperature on, , surface tension:, , a) Effect of impurities:, , i) When soluble substance such as common, salt (i.¢., sodium chloride) is dissolved, in water, the surface tension of water, increases., , ii) When a sparingly soluble substance such, as phenol or a detergent is mixed with, water, surface tension of water decreases., For example, a detergent powder is mixed, with water to wash clothes. Due to this,, the surface tension of water decreases and, water makes good contact with the fabric, and is able to remove tough stains., , iii) When insoluble impurity is added, into water, surface tension of water, decreases. When impurity gets added, to any liquid, the cohesive force of that, liquid decreases which affects the angle, of contact and hence the shape of the, meniscus. If mercury gathers dust then, its surface tension is reduced. It does not, form spherical droplets unless the dust is, completely removed., , b) Effect of temperature: In most liquids,, as temperature increases surface tension, decreases. For example, it is suggested that, new cotton fabric should be washed in cold, water. In this case, water does not make good, contact with the fabric due to its higher surface, tension. The fabric does not lose its colour, because of this., , , , oo Ge ~~~~

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Hot water is used to remove tough stains, on fabric because of its lower surface tension., , In the case of molten copper ot molten, cadmium, the surface tension increases with, increase in its temperature., , The surface tension of a liquid becomes ,, , zero at critical temperature., 2.4.5 Excess pressure across the, , of a liquid: ;, , Every molecule on a liquid surface, experiences forces due to surface tension, which are tangential to the liquid surface at, rest. The direction of the resultant force of, surface tension acting on a molecule on the, , liquid surface depends upon the shape of that, , liquid surface. This force also contributes in, deciding the pressure at a point just below the, , surface of a liquid., Figures 2.21 (a), (b) and (c) show surfaces, , of three liquids with different shapes and their, , + F; be the downward force due to, the atmospheric pressure. All the three figures, show two molecules A and B. The molecule A, is just above, and the molecule B is just below, it (inside the liquid). Level difference between, A and B is almost zero, so that it does not, contribute anything to the pressure difference., In all the three figures, the pressure at the point, A is the atmospheric pressure p., , a) Plane liquid surface:, , Figure 2.21 (a) shows planar free surface, of the liquid. In this case, the resultant force, due to surface tension, /r on the molecule at B, is zero. The force /;, itself decides the pressure, and the pressure at A and B is the same., , free surface, , menisci. Le, , , , Fig. 2.21 (a): Plane surface., b) Convex liquid surface:, , Surface of the liquid in the Fig.2.21 (b), is upper convex. (Convex, when seen from, above). In this case, the resultant force due, to surface tension, /r on the molecule at B, is vertically downwards and adds up to the, , eee Mer, , , , , , , , , , , , , , , , 2.21 (b) Convex surface., fy. This develops greater, , d force “which is inside the liquig, , nwar, dow! oint :, ide of the meniscus., , tp, , ressure, , ncave S} ae, and on the °© the concave side i.e., inside the, , the pressure on vethan that on the convert sift, , vig., , de the liquid., , ie., outside :, ae oneave liquid cl, Si =_, Sr, A, Fig. 2.21 (c): Concave Surface., surface of the liquid in the Fig. 2.21 ©), , ve (concave, when seen from, above). In this case, the force due to surface, tension /r, on the molecule at B is vertically, upwards. The force f, due to atmospheri, pressure acts downwords. Forces J, and, thus, act in opposite direction. Theref, the net downward force responsible for, pressure at B is less than /4. This develo, lesser pressure at point B, which is inside, liquid and on the convex side of the meni:, Thus, the pressure on the concave side 1, outside the liquid, is greater than that on, convex side, i.e., inside the liquid., 2.4.6 Explanation of formation of drops, bubbles:, ee ae and small bubbles, ce ee ecause the forces of surfa, ate the gravitational force, , These force always try to minimize the surfa c, area of the liquid. A bubble or drop does n0, collapse because the resultant of the exter, Pressure and the force of surface tension, , smaller than the ae, ARs press, inside a liquid drop. ure inside a bubble, , is upper conca)