Measuring Surface Tensions (Chapter 4, pp. 69-76 in Shaw)

1. Measuring Surface Tensions (Chapter 4, pp. 69-76 in Shaw) • Measurement techniques can be classified in three catagories: • Static Methods (most accurate) • Detachment Methods • Dynamic Methods (short term effects) ALL EXPERIMENTS MUST BE CONDUCTED UNDER EXTREMELY CLEAN CONDITIONS – YOU DO NOT WANT TO MEASURE THE EFFECT OF DIRT!!

2. 1. Maximum Bubble Pressure Method Radius of capillary Liquid surface h d = density Maximum Bubble Pressure P • = r/2 (P – hdg) (check your units!)

3. An Example: Glacial Acetic Acid r = 1.10 mm d = 1049 kg/m3 P = 420 Pa h = 3.56 cm • = r/2 (P – hdg) = 0.00055(420-0.0356x 1049 x 9.81) = 29 mN/m • = 29 mN/m Why is this so low for an acid?

4. 2. Capillary Rise Method Young-Laplace: DP = 2g/r And DP = Dr g h h Thus: Dr g h = 2g/r or a2 = 2g/Drg = rh Where a is defined as the capillary constant.

5. For a liquid which only wets the wall partially: Dr g h = 2g cos Q/r or g = Dr r g h/2cosQ where Q is the contact angle between the liquid and the glass. Q

6. If the liquid does not wet the glass (e.g. Hg), a depression of the liquid level occurs: For all practical purposes a zero contact angle is required (the liquid should wet the glass). And fairly large volumes are required. With glass capillaries there are limitations as to the alkalinity of the solutions. For accurate work a meniscus correction should be made: g = ½ r(h + r/3) Dr g

7. Contact Angle Hysteresis: To check for zero contact angle, a capillary is allowed to equilibrate in turn from below and above. If the contact angle is zero (i.e. the capillary is clean) then the equilibrium height should be independent of direction.

8. 3. Wilhelmy Plate Method Plate: length = x width = y Wdet – Wplate = 2 (x + y) g

9. 4. Du Nouy Ring Method Force Wtot = Wring + 4pR g Or: where b is a complicated correction factor. g = bF/4pR

10. 5. Drop Volume and Drop Weight Methods • = f mg/2pr = • f Vrg/2pr f is a correction factor: • 1) The drop does not completely leave the tip. • 2) The surface tension forces are not completely vertical. • 3) There is a pressure difference across the curved surface.

11. 6. Drop and Bubble Shape Methods The pendant drop method is similar to the falling drop weight method. It is useful for the observation of slow changes in surface tension and only a very small sample is required. The drop is deformed by gravitational forces. Pendant Drop Sessile Drop

12. 6. Rotating Drop Shape Methods w B ro A • is the angular speed of revolution • Dr is the density difference between phases A and B This equation is named after Vonnegut.

13. 7. Oscillating Jet Methods Dynamic methods measure interfacial tensions milliseconds after surfaces are formed: JET l n is fluid velocity; r is fluid density; r is the sum of the min and max half diameters; and b is the difference of the min and max half diameters

14. Some actual data from an oscillating jet: g, mN/m 0.05 g/100 mL Sodium di-(2-ethylhexyl) sulfosuccinate solution 70 50 30 10 20 30 40 50 time, msec

15. A Final Word: Surface tensions for pure liquids should and does come out the same irrespective of the methods used to determine it. Next lectures: Surfactants and Micelles