CHAPTER 3: SURFACE AND INTERFACIAL TENSION Objective To measure surface tension using both, the DuNouy ring and the capillary tube methods. Introduction In a fluid system, the presence of two or more phases may be observed because of interfaces between the components. This happens only if the fluids are immiscible (oil/water, water/air, oil/gas). Figure 3-1 is a sketch of forces occurring in an air/liquid system. The figure shows molecules of a fluid, which are bonded together by electro-chemical forces. Molecules far from the interface are equally affected in every direction by the same type of molecules resulting in zero net force acting upon those molecules. However, molecules close to the surface are surrounded by different types of molecules resulting in an unbalanced net force normal to the surface. Figure 3-1. Surface Tension (Force Unbalance at Surface) For liquid/liquid systems the term used to describe these interfacial forces is interfacial tension. For liquid/vapor or liquid/air systems the term commonly used is surface tension. Interfacial tension is the force per unit length required to create a new surface. Interfacial 3-1
tensions ( ) are commonly expressed in dynes per centimeter. Surface Gibbs energy per unit area has units of ergs per square centimeter. These are identical units (erg=dyne*cm) for. To understand the concept of interfacial tension, imagine a wire holding a liquid film as shown in Figure 3-2. If a force (F) is applied to the wire for a distance (d), the liquid will expand creating two new surfaces (2A) (Beltran-1990). Figure 3-2. Interfacial Tension - Creating a New Surface The work per unit area done to the system is W / A 2Fd / A (the coefficient two comes into the equation since two surfaces are created, one in front and one in the back) and the interfacial tension is the force applied to the system per distance Fd / A, therefore W / 2A. The interfacial tension can be viewed as the energy per unit of area (cohesion work) required to creating a new surface of liquid. In this laboratory, the student is asked to measure and compare results for surface tension using two different methods: (i) capillary tube method and the DuNouy ring method. Capillary Tube Method When a capillary tube is wetted by a liquid, the liquid rises in the tube. When the liquid reaches equilibrium, the downward force of gravity is equal and opposite to the upward capillary force. Surface tension is calculated using the following equation: 3-2
hrg...(8-1) 2cos where is interfacial tension (dyne/cm), h is the height of the liquid inside the tube (cm), is the density of the fluid (g/cm), g is acceleration due to gravity (cm/s 2 ), and is the contact angle, which is the angle between the tube wall and the tangent crossing the liquid curvature at the point of contact with the tube. It is measured through the liquid (see Figure 3-3). This angle is known for different simple fluids systems and can often be found in the literature or directly measure in the laboratory. For air/water and oil/water on glass surface, is approximately 0 o. Figure 3-3. Fluid Rise in Capillary Tubes (Engler-2003) DuNouy Ring Method This method uses an iridium wire through which a force is applied to the fluid/fluid interface. It is equivalent to the experiment shown in Figure 3-2. The force is applied to the interface creating a new fluid surface till it snaps. The tension given by the apparatus is the interfacial tension of the system. Figures 3-4 (a) and (b) show the equipment and the working principle of the device. 3-3
Figure 3-4 (a). Photograph of a DuNuoy Apparatus (Apparatus Manual, Ref. 2) Figure 3-4 (b). Top View, Cross-Section View, and Operation Mechanism of DuNuoy Apparatus (Modified from PETR 345L Fall-1999 Manual, Ref. 1) 3-4
Laboratory Experiments Part1: Capillary Tube Method Fill a glass cylinder approximately 1/3 full with the liquid to be tested. Attach a height scale to the capillary tube and insert it (in a rubber stopper) in the cylinder so that the bottom of the capillary and the scale are submerged. Use a squeeze bulb to displace the capillary meniscus up, and then allow it to come to equilibrium. Use the scale to record the height of the fluid in the tube (between the meniscus and the fluid level in the cylinder). Measure the fluid density (Pycnometer). The acceleration of gravity must be corrected by latitude and altitude. The latitude gravity corrected in Socorro (34 o N) is 979.652cm/s 2 and the altitude correction is 0.0003066 cm/s 2. Part 2: DuNuoy Ring Method Clean the platinum-iridium ring by rinsing it with acetone and passing it through a Bunser burner flame. Attach the clean ring to the hook at the end of the lever arm. Place the vessel containing the fluid sample beneath the ring on the adjustable platform of the instrument. With the apparatus adjusted so that the ring system is in its zero position when the ring is dry and the scale reading is zero, raise the platform until the liquid makes contact with the ring. Slowly lower the platform, by means of the platform adjusting screw, and increase the torsion of the wire simultaneously, proportioning these two adjustments so that the torsion arm remains exactly in its zero position. As the film adhering to the ring approaches to the breaking point proceed more slowly with the adjustments to make certain that the moving system is in its zero position when the rupture occurs. 3-5
The scale reading at which the ring detaches from the fluid is the surface tension of the fluid. References 1. Petroleum and Chemical Engineering Department, PETR 345 Lab Manual. Fall 1999. 2. CSC Scientific Company INC., DuNuoy Tensiometers, Bulletin 102, Surface Tensiometer NO. 70530. 3. Engler, T.W., Fluid Flow in Porous Media Notes of Class Petroleum Engineering 524 Fall 2003. 4. Beltran, R., Introduccion a la Mecanica de Fluidos, McGraw-Hill, Bogotá, Colombia (1990). 3-6