خواص مادة En p.p5 (1) - Surface Tension PDF

‫‪Chapter 5‬‬ ‫التوتر السطحى‬ ‫‪Surface Tension‬‬ ‫‪Introduction‬‬ ‫مقدمـة‪:‬‬ ‫ ‬ ‫النظرية الجزيئية للتوتر السطحى‬ ‫ ‬ ‫الطاقة السطحية‪Surface Energy :‬‬ ‫ ‬ ‫العالقة بين التوتر السطحى والشكل الكروى‬ ‫ ‬...

‫‪Chapter 5‬‬ ‫التوتر السطحى‬ ‫‪Surface Tension‬‬ ‫‪Introduction‬‬ ‫مقدمـة‪:‬‬ ‫ ‬ ‫النظرية الجزيئية للتوتر السطحى‬ ‫ ‬ ‫الطاقة السطحية‪Surface Energy :‬‬ ‫ ‬ ‫العالقة بين التوتر السطحى والشكل الكروى‬ ‫ ‬ ‫فقاعة الصابون‬ ‫ ‬ ‫‪Angle of Contact‬‬ ‫زاوية التالمس‪:‬‬ ‫ ‬ ‫‪Capillarity‬‬ ‫الخاصية الشعرية ‪:‬‬ ‫ ‬ ‫أمثلة محلولة‬ ‫ ‬ ‫‪1‬‬ 5-1 Introduction: From our daily observations, we see that liquids tend to ball in the form of droplets, for example, raindrops and water droplets on the end of the tap. We also note that mercury takes a spherical shape when a quantity of it is poured over a clean glass surface. These phenomena indicate that the liquid behaves as if it is surrounded by a tight elastic membrane, that is, the surface of the liquid is in a state of tension, which is why we call this property in liquids "surface tension". We have previously mentioned that we call the attraction forces between identical liquid molecules "cohesion forces" , in order to distinguish them from the attraction forces between the liquid molecules and the molecules of the container containing it, as we call this type of attraction forces between asymmetric molecules "adhesion forces". 2 There are tangible effects of the difference between these two types of "gravitational forces", including the following: a) Water spreads in the form of a thin membrane if we pour a small amount of it on a clean glass surface, while we find that mercury takes the form of spherical droplets, and this is because the "adhesion forces" between water molecules and glass molecules are greater than the "cohesion forces" between water molecules. If we put a capillary tube in a vessel with water and another in a vessel with mercury, we find that the water rises inside the tube above the level of the water in the vessel, and the surface of the water in the tube is concave in the direction of the air, but in the case of mercury, its column in the capillary tube is low on the surface of the mercury in the vessel and its surface in the tube is convex in the direction of the air (Figure 5-1). 3 This difference in behavior is due to the fact that the "adhesion forces" in the case of water are greater than the "cohesion forces", and in the case of mercury, the opposite is true. Figure (5-1): The behavior of water and mercury inside a capillary tube 4 5.2 Molecular theory of surface tension: The phenomenon of "surface tension" in liquids can be explained by studying the situation of "cohesive forces" between the molecules of the liquid. If we take the molecule A inside the liquid, we find that it is surrounded by an equal number of molecules from all sides (Figure5- 2), and therefore the result of the attraction forces acting on it is zero. Figure (5.2): Molecular theory of surface 5 tension Molecular theory of surface tension: Molecules A and B on the surface of the liquid are subject to the cohesion forces directed towards the liquid, and the result of these forces is perpendicular to the surface of the liquid, and these forces cause the "surface tension"  of a liquid , defined as: "The force acting in a perpendicular direction on the unit of lengths from the surface of the liquid," that is: F  L Where L the length of the surface of the liquid is taken into account, and the unit of "surface tension" is (N/m). 6 5-3 Surface Energy It is clear that in order for the surface area of the liquid to increase, it is necessary to bring molecules from within the liquid to its surface, which requires overcoming the cohesive force that pulls the molecules into the liquid, and this means that work must be done to overcome this force. On this basis, the energy of the particles is inside it, and this increase in energy is called "surface energy". 7 Surface Energy If we assume that a membrane of liquid is tightened on a frame of the wire ABCD as shown in Figure (5-3), the force acting on the wire BC according to the equation is: F  2L Coefficient 2 stands out in this relationship because the membrane has two surfaces. Figure(5-3): Calculation of 8 surface energy Surface Energy the work done to achieve this increase in the area of the membrane is : W  F.b  2L.b  .2Lb But quantity 2 Lb is the total increase in membrane area, so: Work done to increase surface area by a unit of area   W / 2Lb Another definition of surface tension is: " The work done to increase the surface area of the liquid by a unit of area in the case of heat stability," and the unit of "surface tension" here is (j/m2). 9 5-4 Relationship between surface tension and spherical shape: The condition of "stable equilibrium" requires that the surface area of the liquid contains the least possible number of particles, and this means that the surface area is as small as possible for a certain volume of liquid. Since the spherical shape is: "the geometric shape whose area is as small as possible for a certain size," we find that liquids in the case of the dominance of "surface tension" take a spherical shape. 10 Relationship between surface tension and spherical shape: The amount of curvature of the liquid drop depends on the amount of "surface tension" of the liquid. If we assume that a bubble with a radius r formed within a liquid as shown in Figure (5-4), the hemisphere is under the influence of the following forces: 1) The force πr2P1on it is the result of external pressure P1 , which is where the area of the circular face is πr2. 2) The force πr2P2 on it is the result of the pressure P2 inside the bubble. Figure (5-4): Bubble inside 3) The force caused by a liquid “surface tension,” which is 2r where the length of the 11 circle is 2πr.  Relationship between surface tension and spherical shape: Due to the equilibrium of the circle , the forces affecting it are balanced, and therefore: 2r  r 2 P1  r 2 P2 2  r ( P2  P1 ) 2 ( P2  P1 )  r 2 P  r Where P  ( P2  P1 ) is the difference between the pressure inside the bubble and the pressure outside it. 12  5-5-1 Soap Bubble: We find that the bubble has two surfaces in contact with the air, and this entails reconsidering the force caused by the "surface tension" in the previous case to become this force 2.2r , and thus the equation of the balance of the bubble becomes: 4r  r 2 P1  r 2 P2 4 4 (P2  P1 )  P  r r Equation (5-3) shows that the pressure inside a small bubble is greater than the pressure inside a large bubble, and this explains why it is difficult to inflate a balloon at first, and then the inflating process becomes easier when the balloon gets bigger. 13 5-6 Angle of Contact: The angle between the tangent of the surface of the liquid when it meets the surface of the glass, and the surface of the glass is known as the "contact angle", and this angle is always measured through the liquid as shown in Figure (5-5A). The water surface in the tube in the direction of air is concave. If the glass is not clean, the "angle of contact" is an acute angle We found that the situation is different in the case of mercury, as its surface decreases in the capillary tube and its convexity is upward. In this case, the "angle of contact" is an obtuse angle (Fig. 5-6a) 14 Angle of Contact: Figure (5-6a): Contact angle Figure (5-5a): Contact angle Water wetting the glass surface Figure 5.5 15 Angle of Contact: The "Angle of Contact" is based on the following: A. Nature of the liquid. B. The nature of the solid surface that comes into contact with the liquid. C. The nature of the medium above the liquid. We have defined "surface tension" as: "The force acting in a direction perpendicular to the unit of length," and therefore a drop of liquid on a solid surface spreads until it reaches the equilibrium position determined by the forces acting on this drop, namely: 16 Angle of Contact: : 1. Surface tension  L between the surface of the liquid and the surrounding medium of the liquid. 2) The surface tension  s between the surface of the liquid and the surface of the solid, and is given by the relationship  s  FL  Fs where FL it is the "cohesion force" directed towards the liquid, Fs is the "adhesion force" directed towards the solid surface as shown in Figure (5-7). Figure (5-7): The surface tension between the liquid surface and a solid surface 17 Angle of Contact: 3) Surface tension  m between the surface of the medium surrounding the liquid and the solid surface. Figure (5-8) shows the balance of forces at part A of a liquid spread over a solid surface, and the condition for the balance of forces affecting the unit of length of a row of particles perpendicular to the page at point A (Figure (5-8)) is:  L cos   s   m m s cos  L We see that this equation determines the magnitude of Figure (5-8): Forces affecting the unit of length the “angle of contact” in terms 18 of a row of particles of  s , L , m Angle of Contact: To take into account the situation in which the ambient air is liquid  m  0 , we write the equation (5-4) as follows: In this case, we get two modes: s cos   L 1) "Contact angle" is an acute angle (  90) : In this case, it is  s negative , and since  s  FL  Fs , this means that the "adhesion force" is greater than the "cohesion force", which leads to the spread of liquid particles on the solid surface, and the effect  L , in this case, is to determine the extent of this spread, the larger  L the acute angle . 2) The “contact angle” is an obtuse angle (  90) : In this case, it is cos of negative value, which means that it is  s positive, and therefore the "cohesion force" is greater than the "adhesion force", which leads to the cohesion of the liquid molecules to each other and combine them to reduce the area of the liquid. As for the impact, it  L is limited to determining the extent of this gathering, 19 the larger the obtuse angle, the  L larger it is  as. 5-6 Capillarity The height h within the capillary depends on the nature of the fluid and on the diameter of the capillary. The smaller the diameter of the capillary, the higher the height of a particular fluid. The relationship between the radius of the pipe r, and the height h (Figure: 5-9), we calculate the following: Elevated fluid volume in capillary tube = r 2 h Elevated fluid column weight in tube = r hg 2 Where  the density of the fluid, g the acceleration of gravity. The stability of the liquid surface at height h means that its weight has become equal to the force causing diffusion inside the tube, which is the "surface tension force" 2r acting upwards on the perimeter of the liquid surface in the 20 tube.   , r, h :)9-5( :Basing on this: If the "angle of contact" is greater than zero, the "surface tension" acting vertically on the surface of the liquid, and the relationship in this case becomes as follows: 2 cos h 21 rpg