Surface Tension and Capillarity Lecture Notes PDF

SURFACE TENSION AND CAPILARITY Dr. Anastasia Hadjiconstanti Aknowledgements: Dr C.Zervides  LECTURE LOB’S 46. Understand the nature of surface tension. 47. Understand capillarity....

SURFACE TENSION AND CAPILARITY Dr. Anastasia Hadjiconstanti Aknowledgements: Dr C.Zervides  LECTURE LOB’S 46. Understand the nature of surface tension. 47. Understand capillarity. 3  INTRODUCTION The attractive forces between substances that are alike is known as cohesion. The attractive forces between unlike substances is called adhesion. Cohesive forces are responsible for surface tension. Adhesive forces between the surfaces of a liquid and solid can cause the edges of the liquid surface to be distorted, pulling the liquid up or down, an effect known as capillary action or capillarity. 4  SURFACE TENSION I Surface tension is a property of liquid surfaces resulting from intermolecular bonding which causes the liquid minimize its surface area and resist deformation of its surface. It causes liquids to act rather like they have a thin, elastic skin. This is not true, but is a useful analogy to visualize the behavior of liquids. https://www.shutterstock.com/search/surface+tension 5  SURFACE TENSION II Surface tension acts to reduce the surface area of a body of liquid. In general, the intermolecular forces on a molecule liquid from its neighbors in the liquid are stronger than those from any neighboring gas molecules. This means that the net force on surface molecules is directed into the liquid , and is stronger for more curved surfaces. 6  SURFACE TENSION III The size of the surface tension can be measured by determining the force required to hold in place a wire that is being used to stretch a film of a liquid as shown in figure. The surface tension is defined as the force per unit length along a line where the force is parallel to the surface and perpendicular to the line F 𝛾= 𝐿 The length over which the force is being applied in the diagram shown is twice the length of the wire, as the liquid film has two surfaces. The surface tension γ has the units 𝑁 𝑚−1. 7 EXAMPLE I A thin film of a mystery fluid is formed on a device like that shown in the figure. If the width of the apparatus is 3 cm and the force required to hold the movable wire steady is 4.8 mN, what is the surface tension of the fluid? Solution: F 𝛾= 𝐿 where 𝐹 = 4.8 𝑥 10−3 and 𝐿 = 0.06 𝑚 It is important to remember that L is twice the width of the apparatus as there are two surfaces to the fluid. 4.8 𝑥 10−3 𝛾= = 0.08 𝑁𝑚−1 0.06 𝑚 8  PRESSURE IN BUBBLES I Surface tension is important in the functioning of the lung. To see why, we will start by looking at the pressure in a spherical bubble. The pressure inside the bubble must be higher than the outside pressure to stop the surface tension from collapsing the bubble 4𝜋𝑟𝛾 = ΔPπ𝑟 2 4𝛾 ΔP = 𝑃𝑖𝑛𝑡 − 𝑃𝑒𝑥𝑡 = 𝑟 A consequence of this is that the (gauge) pressure inside grows larger as the bubble decreases in size. 9  PRESSURE IN BUBBLES II When two bubbles collide, air always flows from the smaller to the larger. This is because the pressure in the small bubble, is larger than that of in the bigger bubble. 10  SURFACTANTS A substance that, when added to a liquid, reduces the liquid’s surface tension is called a surfactant. This is a shortened form of “surface-active agent”. The surfactant molecules tend to concentrate near the surface. An example is of a surfactant is soap in water. A needle that can be supported by the surface tension of water will break through the surface and sink when soap or detergent is added to the water. Detergents and soap are surfactants because they have on hydrophilic (“water-loving”) and one hydrophobic (“water hating”) side, so the lowest-energy position for them is at the surface, with the hydrophobic end farther from the water molecules. Surfactants are of major importance to lung function. 11 EXAMPLE II A bubble of water (𝜸 = 𝟎. 𝟎𝟔𝟖 𝐍𝒎−𝟏 ) forms such that it has an internal gauge pressure of 13.6 Pa. (a) How large is the bubble? (b) A surfactant is added to the water reducing the surface tension to 𝟎. 𝟎𝟐𝟏 𝑵𝒎−𝟏. If the gauge pressure inside a new bubble is the same, what would the radius be in this case? 4γ Solution: (a) ΔP= 𝑟 4𝛾 4 𝑥 0.068 𝑁𝑚−1 𝑟= = = 0.020 𝑚 ΔP 13.6 𝑃𝑎 4𝛾 4 𝑥 0.021 𝑁𝑚−1 (b) 𝑟 = = = 0.0062 𝑚 ΔP 13.6 𝑃𝑎 After the surfactant has been added the bubble will decrease in size! 12  CAPILLARITY I Interfacial Tension In examining surface tension, the adhesive forces between the liquid and any molecules of gas near the surface could be largely ignored. In the case of liquid in contact with other immiscible (non-mixing) liquids, or solids, such the walls of the container that the liquid is held in, these forces are no longer negligible. The size of the adhesive forces between the materials will determine the interfacial tension (i.e. the tension at the interface). 13  CAPILLARITY II Example of Interfacial Tension I a) Water “wets” the surface of glass b) Mercury does not “wet” the glass. 14  CAPILLARITY III Example of Interfacial Tension II (A) Water beading on a waxy/oily surface. On such surface the cohesive intermolecular forces between water molecules are larger than the adhesive forces between water molecules and molecules on the surface. This results in a compact droplet with a large contact angle, θ. (A) Water wetting hydrophilic (“water-loving”) surface, like glass. If the adhesive forces between the water and the surface are stronger than the cohesive forces, between the water molecules, the droplet spreads out, and the contact angle is low. Adding a surfactant to the liquid has the same effect. 15  CAPILLARITY III Interfacial Tension A quantitative measure of the tendency to beat is the contact angle. This is the angle that the edge of the liquid – air surface makes with the liquid –solid surface. Contact angles more than 𝟗𝟎𝒐 are indicative of beading, and angles less than 𝟗𝟎𝒐 show wetting. 16  CAPILLARITY IV Interfacial Tension The angle of contact at the surface between the liquid and its container will depend on the relative strengths of cohesive and adhesive forces also. For a fluid in a vertical tube, if the cohesive forces are weak in comparison to the adhesive forces, the contact angle will be small and the liquid will be pulled slightly up at the edges of the tube, giving negative meniscus. If the cohesive forces are strong in comparison to the adhesive forces, the contact angle will be large and a positive meniscus is formed. 17  CAPILLARY ACTION I When a thin glass tube is placed in a liquid such as water, the liquid often rises up the tube. This is known as capillary action, or capillarity. The thinner the tube, the more the liquid rises. A smaller radius means more contact with the surface for a particular volume of liquid, and hence a greater mass of liquid that can be supported by the contact force. 18  CAPILLARY ACTION II In fact, the height depends on the inverse of the radius of the tube: 2𝛾𝑐𝑜𝑠𝜃 ℎ= 𝜌𝑔𝑟 h is the height the liquid travels up the tube above the level of the surrounding liquid γ is the surface tension θ is the angle the liquid surface makes with the tube surface ρ is the liquid density r is the tube radius g is the acceleration due to gravity 19  CAPILLARY ACTION III Forces The upwards component of the force will be 𝑭𝒚 = 𝑭𝒔𝒕 𝒄𝒐𝒔𝜽 𝑭𝒚 = 𝑭𝒔𝒕 𝒄𝒐𝒔𝜽 F 𝛾 𝑥 𝐿 𝑥 𝑐𝑜𝑠𝜃 = 𝛾2𝜋𝑟𝑐𝑜𝑠𝜃 (𝛾 = ) 𝐿 𝑭𝒙 = 𝑭𝒔𝒕 𝒔𝒊𝒏𝜽 This will pull the liquid upwards until the 𝑭𝒙 = 𝑭𝒔𝒕 𝒔𝒊𝒏𝜽 downwards force on the mass due to gravity is equal. The downward force is 𝐹𝑤𝑒𝑖𝑔ℎ𝑡 = 𝑚𝑔 = 𝜌𝑉𝑔 = 𝜌 𝜋𝑟 2 ℎ 𝑔 This rearranges to give the following equation: 2 𝛾2𝜋𝑟𝑐𝑜𝑠𝜃 𝜌𝜋𝑟 ℎ𝑔 = 𝛾2𝜋𝑟𝑐𝑜𝑠𝜃 → ℎ = 𝜌𝜋𝑟 2 𝑔 20  EXAMPLE III An engineer is designing an experimental dialysis machine. A vital component of this machine is a small hollow tube made from element unknownium with a 100 μm inner radius which will dip down into a chamber filled with blood. The surface tension of blood is 0.058 𝑁𝑚−1 and the density of blood is 1050𝑘𝑔 𝑚−3. (a) The engineer does not know what the adhesive forces, and hence contact angle, between blood and unkownium is. What is the maximum possible range of heights to which blood will be raised/lowered in the tube? (b) If the contact angle between unknownium and blood is measured at 78𝑜 , to what height is blood drawn up the tube of the unknownium? (c) c) Blood needs to be drawn up the small tube at least 3 cm. What is the simplest change that can be made to the tube of the unknownium to enable this to happen? 21  CLASS EXAMPLE III An engineer is designing an experimental dialysis machine. A vital component of this machine is a small hollow tube made from element unknownium with a 100 μm inner radius which will dip down into a chamber filled with blood. The surface tension of blood is 0.058 𝑁𝑚−1 and the density of blood is 1050𝑘𝑔 𝑚−3. (a) The engineer does not know what the adhesive forces, and hence contact angle, between blood and unkownium is. What is the maximum possible range of heights to which blood will be raised/lowered in the tube? Solution: The height to which a liquid will be drawn up a capillary tube is given by the equation 2𝛾𝑐𝑜𝑠𝜃 2𝛾 2 𝑥 0.058 𝑁𝑚−1 ℎ= =± =± −3 −2 −6 = ±0.113 𝑚 𝜌𝑔𝑟 𝜌𝑔𝑟 1050 𝑘𝑔 𝑚 𝑥 9.81 𝑚𝑠 𝑥 100 𝑥 10 𝑚 The cosine term could have any value from +1 for θ=0 (fully wetting the surface) to -1 for θ=180 (fully beaded upon the surface). 22  CLASS EXAMPLE III An engineer is designing an experimental dialysis machine. A vital component of this machine is a small hollow tube made from element unknownium with a 100 μm inner radius which will dip down into a chamber filled with blood. The surface tension of blood is 0.058 𝑁𝑚−1 and the density of blood is 1050𝑘𝑔 𝑚−3. b) If the contact angle between unknownium and blood is measured at 78𝑜 , to what height is blood drawn up the tube of the unknownium? Solution: With a specific contact angle, 𝜃 = 78𝜊 , we can calculate a specific height to which the blood will be drawn into the capillary. Given that the angle is less than90𝑜 we can say with certainty that the blood will be drawn up into the capillary (h>0). 2𝛾𝑐𝑜𝑠𝜃 2𝛾cos(78𝑜 ) 2 𝑥 0.058 𝑁𝑚−1 𝑥 0.208 ℎ78𝑜 = = = −3 −2 −6 = 0.0234 𝑚 𝜌𝑔𝑟 𝜌𝑔𝑟 1050 𝑘𝑔 𝑚 𝑥 9.81 𝑚𝑠 𝑥 100 𝑥 10 𝑚 23  CLASS EXAMPLE III An engineer is designing an experimental dialysis machine. A vital component of this machine is a small hollow tube made from element unknownium with a 100 μm inner radius which will dip down into a chamber filled with blood. The surface tension of blood is 0.058 𝑁𝑚−1 and the density of blood is 1050𝑘𝑔 𝑚−3. c) Blood needs to be drawn up the small tube at least 3 cm. What is the simplest change that can be made to the tube of the unknownium to enable this to happen? Solution: In order to increase the height to which the blood is drawn into the capillary we can: (a) increase the viscosity of the blood, (b) use a different material that has a higher contact angle (lower adhesive forces between the material and the blood) or (c) decrease the radius 2𝛾𝑐𝑜𝑠𝜃 of the tube. ℎ= 𝜌𝑔𝑟 2𝛾𝑐𝑜𝑠𝜃 2𝛾cos(78𝑜 ) 2 𝑥 0.058 𝑁𝑚−1 𝑥 0.208 𝑟= = = = 78.1𝑥 10−6 𝑚 𝜌𝑔ℎ 𝜌𝑔ℎ 1050 𝑘𝑔 𝑚−3 𝑥 9.81 𝑚𝑠 −2 𝑥 0.03 𝑚 24  SUMMARY I Cohesion: The intermolecular attraction between like molecules. Adhesion: The intermolecular attraction between unlike molecules. Surface Tension: The property of a liquid surface that causes it to behave like an elastic sheet, as the result of cohesive forces. Capillarity: The distortion of a liquid surface due to adhesive forces between the surface of the liquid and an adjacent solid surface. This can result in the liquid being pulled up or down a narrow tube. Surfactant: A substance that, when added to a liquid, reduces the liquid’s surface tension. 25  REFERENCES Authors Title Edition Publisher Year ISBN Kirsten Franklin, Paul Introduction to Biological John Wiley & Muir, Terry Physics for the Health and 1st Edition 2010 9780470665930 Sons Scott and Paul Life Sciences Yates I.P. Herman Physics of the Human Body 2nd Edition Springer 2016 978331923930 Martin Zinke Cengage Physics of the Life Sciences 3rd Edition 2016 9780176558697 Allmag Learning Lippincott Respiratory physiology: the John B. West 9th Edition Williams and 2015 9781609136406 essentials Wilkins Physics in Biology and Academic P. Davidovits 4th Edition 2012 9780763730406 Medicine Press