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# Measurement of surface tension

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Surface Tension is defined as the tension of the surface film of a liquid caused by the attraction of the particles in the surface layer by the bulk of the liquid, which tends to minimize surface area.
It is due to the phenomena of surface tension that the drops of water tend to assume a spherical shape to attain minimum surface area. the presentation gives a brief description of the methods to measue this important property of the interface of two fluid.

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### Measurement of surface tension

1. 1. SURFACE TENSION SEMINAR PRESENTATION ON GROUP GUIDE: Mr. PANKAJ DUMKA COMPILED BY: GROUP NO. 21 GAURAV UPADHYAY (121739) MAYANK TRIVEDI (121751) MOHIT SINGH (121752) PANKAJ SHARMA (121755) PIYUSH SINGH (121756)
2. 2. TABLE OF CONTENTS 1. INTRODUCTION TO SURFACE TENSION 2. FACTORS AFFECTING SURFACE TENSION 3. PHENOMENA OBSERVED DUE TO SURFACE TENSION 4. METHODS OF MEASUREMENT OF SURFACE TENSION i. CAPILLARY RISE METHOD ii. DROP ANALYSIS METHODS a) STALAGMOMETER METHOD b) SPINNING DROP METHOD iii. MAXIMUM BUBBLE PRESSURE METHOD iv. OSCILLATING JET METHOD v. DU NOUY METHODS a) RING TENSIOMETER b) ROD PULL METHOD
3. 3. WHAT IS SURFACE TENSION? • Surface Tension is defined as the tension of the surface film of a liquid caused by the attraction of the particles in the surface layer by the bulk of the liquid, which tends to minimize surface area. • It is due to the phenomena of surface tension that the drops of water tend to assume a spherical shape to attain minimum surface area.
4. 4. The effect of surface tension on the interface area between two liquids may be equivalently defined either through force or through energy. 1. In terms of force: surface tension γ of a liquid is one-half the force per unit length required to keep still a movable side of a frame over which the liquid is stretched (say, into a thin film). γ=F/2L 2. In terms of energy: surface tension γ of a liquid is the ratio of 1) the change in the energy of the liquid, and 2) the change in the surface area of the liquid (that led to the change in energy). γ= F/2L= F Δ x/2LΔ x= W/ΔA
5. 5. 1. Temperature 2. Solute concentration 3. Intermolecular forces 4. Hydrogen bonding FACTORS EFFECTING SURFACE TENSION
6. 6. PHENOMENA OBSERVED DUE TO SURFACE TENSION 1. Excess pressure in a soap bubble. 2. Formation of spherical droplets. 3. Capillarity. 4. Wetting and non-wetting properties of certain liquids
7. 7. METHODS OF MEASUREMENT (SURFACE TENSION)
8. 8. CAPILLARY RISE METHOD
9. 9. PRINCIPLE • A consequence of the surface tension appearance at the liquid/gas interface is moving up of the liquid into a thin tube, that is capillary, which is usually made of glass • If the interaction forces of the liquid with the capillary walls (adhesion) are stronger than those between the liquid molecules (cohesion), the liquid wets the walls and rises in the capillary to a defined level and the meniscus is hemispherically concave
10. 10. • In the opposite situation the forces cause decrease of the liquid level in the capillary below that in the chamber and the meniscus is hemispherically convex. • If the cross-section area of the capillary is circular and its radius is sufficiently small, then the meniscus is hemispherical. Along the perimeter of the meniscus there acts a force due to the surface tension presence Ref: http://zzm.umcs.lublin.pl/Wyklad/FGF-Ang/2A.F.G.F.%20Surface%20tension.pdf
11. 11. f1=2πr𝛾cosθ Where: r – the capillary radius, 𝛾– the liquid surface tension, θ– the wetting contact angle. The force f1 in Eq.(1) is equilibrated by the mass of the liquid raised in the capillary to the height h, that is the gravity force f2. In the case of non- wetting liquid – it is lowered to a distance –h. MATHEMATICAL ANALYSIS
12. 12. f2 =πr2 hdg where: d : the liquid density (g/cm3) (actually the difference between the liquid and the gas densities), g : the acceleration of gravity In equilibrium (the liquid does not moves in the capillary) f1= f2
13. 13. DROP ANALYSIS METHODS
14. 14. 1. DROP VOLUME METHOD (STALAGMOMETER METHOD) This method was first time described by Tate in 1864 who formed an equation, which is now called the Tate’s law. 𝑾 = 𝟐𝝅𝑹𝜸 W is the drop weight, r is the capillary radius, and 𝛾 is the surface tension of the liquid. Ref: zzm.umcs.lublin.pl/Wyklad/FGF.../2A.F.G.F.%20Surface%20tension.pdf
15. 15. In the case of a liquid which wets the stalagmometer's tip the r value is that of the outer radius of the capillary and if the liquid does not wet – the r value is that of the inner radius of the capillary. The drops wetting area corresponding to the outer and inner radii of the stalagmometer's tip. Ref: zzm.umcs.lublin.pl/Wyklad/FGF.../2A.F.G.F.%20Surface%20tension.pdf
16. 16. CORRECTION FACTOR Up to 40% of the drop volume may be left on the stalagmometer tip. Therefore a correction f has to be introduced to the original Tate's equation. 𝑾′ = 𝟐𝝅𝒓𝜸𝒇 the weight of the falling drop W' is lower than W. This is a result of drop formation, as shown Ref: zzm.umcs.lublin.pl/Wyklad/FGF.../2A.F.G.F.%20Surface%20tension.pdf
17. 17. f expresses the ratio of W’/ W. Harkins and Brown found that the factor f is a function of the stalagmometer tip radius, volume of the drop v, and a constant, which is characteristic of a given stalagmometer, f = f (r, a, v) 𝒇 = 𝝋 𝒓 𝒂 = 𝝋 𝒓 𝒗 𝟏/𝟑 The f values for different tip radii were determined experimentally using water and benzene, whose surface tensions were determined by the capillary rise method. EXPERIMENTAL ANALYSIS OF THE CORRECTION FACTOR Ref: C. E. Stauffer, “Measurement of surface tension by pendant drop technique”, The journal of physical chemistry (1965) 1933.
18. 18. Values of the factor f Ref: C. E. Stauffer, “Measurement of surface tension by pendant drop technique”, The journal of physical chemistry (1965) 1933.
19. 19. PROCEDURE FOR MATHEMATICAL CALCULATIONS  The factor f changes the least if: 0.6 < 𝑟 𝑣1/3 < 1.2  After having determined the mean weight m of the liquid drop calculated from several drops weighed, one can calculate its volume at the measurement temperature if the liquid density is known, and then the value of 𝒓 𝒗 𝟏/𝟑.  Next the f value can be found in the table.  Finally, the surface tension can be calculated from 𝜸 = 𝒎𝒈 𝟐𝝅𝒓𝒇 Ref: zzm.umcs.lublin.pl/Wyklad/FGF.../2A.F.G.F.%20Surface%20tension.pdf
20. 20. RELATIVE SURFACE TENSION MEASUREMENT USING STALAGMOMETER  The f value depends also on the kind of liquid tested.  Therefore the relative measurements (in comparison to another liquid of known surface tension) can not be applied here.  However, such measurement can be done with 0.1 % accuracy if the shape of the stalagmometer tip is like that shown in figure. Shape of the stalagmometer tip for relative surface tension measurements. Ref: Method and apparatus for detecting relative dynamic liquid surface activity, Miller Brewing , citing patent, US4646562
21. 21. MATHEMATICAL ANALYSIS The relative surface tension is given by: 𝛾1 𝛾2 = 𝑚1 𝑚2 2/3 = 𝑑1 𝑑2 2/3 Having known the drop volume the surface tension can be calculated from : 𝛾 = 𝑚𝑔 2𝜋𝑟𝑓 = 𝑚𝑔 𝑘 = 𝑉𝑑𝑔 𝑘 𝜸 = 𝑽𝒅𝒈 𝒌 Ref: Method and apparatus for detecting relative dynamic liquid surface activity, Miller Brewing , citing patent, US4646562
22. 22. 2. SPINNING DROP METHOD  The spinning drop method (rotating drop method) is one of the methods used to measure interfacial tension.  Measurements are carried out in a rotating horizontal tube which contains a dense fluid. A drop of a less dense liquid or a gas bubble is placed inside the fluid. Ref: en.wikipedia.org/wiki/Spinning_drop_method
23. 23. MATHEMATICAL ANALYSIS  A fluid drop of mass density ρ1 is suspended in a liquid with the density ρ2 > ρ1 .  The drop and the liquid are contained in a horizontal tube cell.  At low rotational velocities ω, the drop will take on an ellipsoidal shape, but when ω is sufficiently large, it will become cylindrical. 𝛾 = 1 4 𝜌2 − 𝜌1 𝜔2 𝑟3 Ref:On two direct methods for measurement of interfacial tension at microdroplet surfaces, J. Tothova, M. Richterova and V. Lisy Institute of Physics, P.J. Safarik University, Jesenna 5, 041 54 Kosice, Slovakia The Vonnegut’s equation
24. 24. MAXIMUM BUBBLE PRESSURE METHOD
25. 25. PRINCIPLE • One of the useful methods to determine the dynamic surface tension is measuring the "maximum bubble pressure method • Bubble pressure tensiometer produces gas bubbles (ex. air) at constant rate and blows them through a capillary which is submerged in the sample liquid and its radius is already known
26. 26. • The pressure (P) inside of the gas bubble continues to increase and the maximum value is obtained when the bubble has the completely hemispherical shape whose radius is exactly corresponding to the radius of the capillary. • Applying Young–Laplace equation in the reduced form 𝛾 = 𝑝 𝑚𝑎𝑥 ∗ 𝑟𝑐𝑎𝑝 2
27. 27. • A, B: As the size increases, the radius of curvature of the bubble decreases • At the point of the maximum bubble pressure, the bubble has a complete hemispherical shape whose radius is identical to the radius of the capillary denoted by Rcap Fig.1 http://en.wikipedia.org/wiki/Maximum_bubble_pressure_method
28. 28. Fig.2 • The measured value corresponds to the surface tension at a certain surface age, the time from the start of the bubble formation to the occurrence of the pressure maximum • The dependence of surface tension on surface age can be measured by varying the speed at which bubbles are produced. http://www.kruss.de/services/education-theory/glossary/bubble-pressure- tensiometer/
29. 29. APPARATUS The capillary of radius r is immersed in the liquid of density ρ and surface tension γ, such that the bottom of capillary is at the depth of h bellow the water level (Figure 2. The additional pressure ph 𝑝ℎ = ℎ ⋅ 𝜌 ⋅ 𝑔 ……..2 The pressure equal or greater than p = 𝑝ℎ+ 𝑝 𝑘 ……………3
30. 30. would push the air all the way through the capillary and will create a bubble at its end. The combination of equations  and  with the equation  yields p= 2σ/t+hρg …………… 5 Pressure at knob c1 p=ℎ 𝑣*ρ 𝑣 ∗ 𝑔………. 6 The combination of the equation  and  determines the surface tension 𝛾 = 𝑟 2 ℎ 𝑣 ∗ 𝜌 𝑣 − ℎ ∗ 𝜌
31. 31. OSCILLATING JET METHOD
32. 32.  Measures “Dynamic Surface Tension”  Dynamic surface tension is the tension per unit length developed at a specified point in a surface and observed as a function of time.  The oscillating jet method consists of forcing a stream of liquid under constant pressure through an orifice. Ref: link.springer.com/content/pdf/10.1007/978-1-4615-7972-4_4.pdf
33. 33. The jet flows out from an elliptic orifice and therefore it oscillates as shown in Figure (Figure -1): http://www.thermopedia.com/content/4740/SURFACE_AND_INTERFACIAL_TENSION_FIG15.gif (Figure -1)
34. 34.  The oscillating crests and troughs are the result of surface tension forces in the liquid .  Bohr (1909) presented the theory and relationship between surface tension and measurable physical properties such as the flow rate of the liquid, wavelength and major and minor axes radii.  Wavelengths are frequently measured by passing parallel light waves perpendicular to the jet stream. Ref: http://www.seas.ucla.edu/stenstro/r/r18.pdf
35. 35. Ref: http://www.seas.ucla.edu/stenstro/r/r18.pdf
36. 36. Ref: http://www.seas.ucla.edu/stenstro/r/r18.pdf
37. 37. 213         dr kt 2 2 2          v r dk Mathematical analysis : or
38. 38. Where t = the oscillation period time λ = the wave length v = the jet flow rate r = the radius of the jet at its spherical place = surface tension Ref: zzm.umcs.lublin.pl/Wyklad/FGF.../2A.F.G.F.%20Surface%20tension.pdf
39. 39. DU NOUY METHODS
40. 40. Du Nouy ring method • The du nuoy method is one technique by which the surface tension of a liquid can be measured • The method involves slowly lifting a ring, often made of platinum, from the surface of a liquid. • The force, F, required to raise the ring from the liquid's surface is measured and related to the liquid's surface tension. Ref :http://en.wikipedia.org/wiki/Du_No%C3%BCy_ring_method
41. 41. Ref :http://en.wikipedia.org/wiki/Tensiometer (surface tension) DU NOUY RING TENSIOMETER
42. 42. 𝐹 = 2𝜋 𝑟𝑖 + 𝑟𝑎 𝛾 Where: ri = the radius of the inner ring of the liquid film pulled ra= the radius of the outer ring of the liquid film. GOVERNING EQUATION FOR RING TENSIOMETER
43. 43. Ref :http://en.wikipedia.org/wiki/Du_No%C3%BCy_ring_method • This type of Tensiometer uses a platinum ring which is submersed in a liquid. As the ring is pulled out of the liquid, the tension required is precisely measured in order to determine the surface tension of the liquid. • This method requires that the platinum ring be nearly perfect; even small blemish or scratch can greatly alter the accuracy of the results. • This method requires that the platinum ring be nearly perfect; even small blemish or scratch can greatly alter the accuracy of the results.
44. 44. Du Nouy–Padday method • This method uses a rod which is lowered into a test liquid. The rod is then pulled out of the liquid and the force required to pull the rod is precisely measured • This is a rather novel method which is accurate and repeatable. The Du Nouy-Padday Rod Pull Tensiometer will take measurements quickly and unlike the ring and plate methods, will work with liquids with a wide range of viscosities
45. 45. • The Du Noüy Padday rod consists of a rod usually on the order of a few millimeters square making a small ring. The rod is often made from a composite metal material that may be roughened to ensure complete wetting at the interface. • The rod is cleaned with water, alcohol and a flame or with strong acid to ensure complete removal of surfactants. The rod is attached to a scale or balance via a thin metal hook. • The Padday method uses the maximum pull force method, i.e. the maximum force due to the surface tension is recorded as the probe is first immersed ca. one mm into the solution and then slowly withdrawn from the interface.
46. 46. • The main forces acting on a probe are the buoyancy (due to the volume of liquid displaced by the probe) and the mass of the meniscus adhering to the probe. This is an old, reliable, and well-documented technique • An important advantage of the maximum pull force technique is that the receding contact angle on the probe is effectively zero. The maximum pull force is obtained when the buoyancy force reaches its minimum.