Surface and interfacial tension and its measurement

In this presentation:
Surface Tension
Interfacial Tension
Definition of inerfacial tension in different ways
Measurement of interfacial and surface tesion

1. Surface and Interfacial Phenomena Venkidesh Rajagopal

2. Surface is the boundary between a solid/liquid and air/ vaccum Interface is the boundary between two or more distinct phases exist together

3. Surface tension is defined as the force per unit length parallel to the surface to counter balance the net downward pull. Unit: dynes/cm ergs/m N/m

4. Interfacial tension is defined as the force per unit length parallel to the interface to counter balance the net inward pull. In the case of interface the molecules at the interface will be pulled by both faces into the bulk Since COHESIVE FORCE (between like molecules) are stronger than ADHESIVE FORCE (between unlike molecules) the net pull will be into the bulk of same phase.

5. INTERFACIAL TENSION always less than SURFACE TENSION Adhesive force between molecules at the surface and air molecules is negligible when compared to the adhesive force between two immiscible liquids. The inward pull will be opposed by the adhesive force to an extend in the case of an interface This is negligible in case of surfaces So net inward pull will be more in magnitude in the case of surface. So the counter balancing force also will be high in case of surface when compared to interface

6.     The soap film has two liquid-gas interfaces F = w × a a – acceleration due to gravity (g) F = γ × 2 l γ =   Interfacial Tension – Force per Unit Length

7. dW = F × dS dW = γ × 2l × dS dW = γ × dA 2 (l × dS ) = dA γ =   Thus, Surface tension may be defined as surface free energy per unit area increase. Thermodynamically a system is stable when the free energy is minimum. So systems will try to reduce the surface free energy by contracting the surface area and attain stability. Eg : When liquids suspended in air or immiscible liquids it assumes a minimum surface area to volume ( spherical shape) Interfacial Tension – Energy per Unit Area Increase

8. Interfacial Tension – Pressure difference across Curved Surface Total Surface Free Energy E 1 = ST × Total Area of Bubble 4 π r 2 γ When radius decreased by dr free energy E 2 = 4 π (r- dr ) 2 γ = 4 πγ (r 2 -2 r dr+dr 2 ) 4 πγ r 2 - 8 πγ r dr + 4 πγ dr 2 d r is very small when compared to r So 4 πγ dr 2 can be omitted from the equation So E 2 = 4 πγ r 2 - 8 πγ r dr

9. Surface free energy change E 1 – E 2 = 4 π r 2 γ – (4 πγ r 2 - 8 πγ r dr ) = 8 πγ r dr Due to decrease in radius by dr free surface energy will decrease by 8 πγ r dr This change will be opposed by pressure difference across the wall of the bubble Pressure is Force acting on Unit Area ( δ P = F/A) Ie , Force is the pressure multiplied by total area F = δ P × A F = δ P × 4 π r 2

10. Energy change = Work done = Force × Displacement Free Energy change due to decrease in radius by dr W = F × dr W = δ P × 4 π r 2 × dr W = E 1 – E 2 δ P 4 π r 2 dr = 8 πγ r dr γ = As the radius of the bubble decreases pressure inside the bubble increases. Smaller the bubble greater will be the internal pressure. Or as surface tension decreases internal pressure in the bubble increases  

11. EFFECT OF TEMPERATURE ON SURFACE TENSION Surface tension will be reduced when the temperature of the liquid increased. This is due to the thermal expansion of liquids This continues till the temperature of the liquid reaches the CRITCAL TEMPERATURE of the liquid At this point Surface tension becomes zero

12. γ = γ [ 1 - ]   – Critical Temperature γ - Surface tension at thermodynamic zero (0 K)  

13. MEASUREMENT OF SURFACE AND INTERFACIAL TENSION Capillary Rise Method Maximum Bubble Pressure Method Drop Method Wilhelmy Plate Method Ring Detachment Method (Du - Nuoy Tensiometer)

14. Capillary Rise Method

15. Capillary rise occurs because of upward force due to surface tension Upward movement stops when this force is counterbalanced by the downward force due to weight of the capillary column Surface tension at any point of circumference of capillary tube = γ cos θ Total upward force = 2 π r γ cos θ Counter balancing force due to weight of the column = m g = π r 2 h ( ρ – ρ ) g + w ρ – Density of Liquid ρ – Density of vapour w – Weight of liquid above meniscus

16. ρ >> ρ W is very negligible when compared to weight of column Therefore Downward force due to weight of the column = π r 2 h ρ g At equilibrium Upward force = Downward force 2 π r γ cos θ = π r 2 h ρ g γ = In case of water θ is taken as 0. ie , cos θ = 1 Thus γ =  

17. Precautions to be taken Outer vessel should have larger diameter Capillary tube should have uniform diameter through out its length Height of the column should measure accurately Temperature must be maintained uniform Better to allow meniscus to fall down than allow to rise

18. Maximum Bubble Pressure Method Mercury is allowed flow through each capillaries Difference in pressure when bubbles form in sider and narrow capillaries noted. When radius of narrow capillary is less than 0.01cm ( r 1 ) and wider is greater than 0.2cm (r 2 ) surface tension is given by   A – Instrument constant D – Density of the liquid P – Difference in pressure

19. Drop Method When a liquid is allowed to flow through a capillary tube it forms a drop at the tip of the tube It increases in size and detaches from the tip when weight of the drop just equals the surface tension at the circumference of the tube w = 2 π r γ γ =  

20. STALAGMOMETER

21. Drop Weight Method Suck the liquid up to the mark A Allow the liquid to drop from tip of the stalagmometer Collect 20 – 30 drops and find out the weight Find average weight of drops γ = Generally relative surface tension with respect to water is found out =  

22. Drop Count Method Suck the liquid up to the mark A Allow the liquid to drop from tip of the stalagmometer Count the number of drops formed till the liquid reach mark B γ = W(weight of total number of drops)= mg = vdg d- density of the liquid Generally relative surface tension with respect to water is found out =  

23. Precautions to be taken Tip of pipette should have no imperfections in the outer circumference Drops should be formed slowly About 20 – 30 drops should be collected to find the average weight Temperature should be maintained constant

24. Wilhelmy Plate method Consist of a plate made up of platinum suspended vertically from a beam attached to a torsion balance Liquid is taken in a dish and raised until it just touches bottom of the plate When plate touches the surface, the surface force will drag the plate downward Rotate the torsion wire and measure the force required to bring back the plate to former position The force measured in torsion balance will be equal to the surface tension around the perimeter of the plate W = 2 (L+T) γ γ =  

25. Ring Detachment Method Torsion Balance or Du Nuoy balance consist of a platinum ring of around 4 cm in circumference suspended on a torsion wire attached to a scale Liquid is taken in a pan and position of pan is adjusted so that the ring just touches the liquid Torsion wire is rotated till the ring just detached from the surface of the liquid Force require to detach the ring from the surface is obtained from the scale The force is proportional to surface tension

26. P = 2π (r 1 +r 2 ) γ γ = P / 2π (r 1 +r 2 ) r 1 and r 2 are inner and outer radius of the ring For thin rings r 1 = r 2 = r γ = P / 4 π r

27. Precautions to be taken The ring should lie in flat plane The plane of the ring must be horizontal Vessel containing liquid should have wider diameter Temperature must be kept constant