Spinning drop tensiometer method

The interfacial free energy between this cylindrical liquid (1) drop and the contacting immiscible liquid (2) along the surface area can be given from thermodynamics as [AG = AA/i2 = 2nr0lyn. Then the total energy of the cylinder on revolution can be expressed as 

Since dhT/dr0 = 0 at equilibrium, then differentiation of Equation (514) and equating it to zero gives 

Equation (515) is known as Vonnegut s equation and it is valid on the assumption that the drop is in equilibrium and its length is larger than four times its diameter (/ 4r ). The spinning drop tensiometer method is widely used for measuring liquid-liquid interfacial tension, and is especially successful for examination of ultra-low interfacial tensions down to l(T6mNnr1. In addition, it can also be used to measure interfacial tensions of high viscosity liquids when precise temperature control is maintained. 

The spinning drop tensiometer method is particularly suitable for measuring the interfacial tension of melted polymers and is generally used in polymer compatibility, blend and composites research. In this case, a spinning polymer drop (smaller density) is rotated inside another immiscible polymer (higher density). Measurement of drop diameter versus time allows the determination of relaxational and extensional properties of polymeric systems. 

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Figure 6.7 Liquid surface tension determination by the spinning drop tensiometer method. A liquid drop (7) is suspended in an immiscible denser liquid (2) in a horizontal transparent tube which can be spun about its longitudinal axis, and the drop (7) elongates from a spherical shape to a prolate ellipsoid with increasing speed of revolution. Later, the drop becomes approximately cylindrical, at very high rotational velocities. A camera with a frame grabber captures the images of the drop inside the transparent tube.

When the value of the interfacial tension is significantly less than 1 mN m 1, then we consider the measurement of ultra-low interfacial tension, which is common in liquid-liquid emulsification processes when effective surfactant solutions are used. The dynamic spinning drop tensiometer method is especially suitable for this purpose. Ultra-low interfacial tension measurement is important in the chemical industry because the cleaning of solid surfaces of dirt, grease, and oil the formulation of stable emulsions the recovery of petroleum, and other applications often rely on lowering the interfacial tension between immiscible liquids to ultra-low values by the use of surfactants. 

Interfacial tensions between the equilibrated oil and aqueous phases were measured by a spinning drop tensiometer using the method described by Schechter and co-workers (2,3,5). Each drop of oil was spun until a constant interfacial tension was reached. 

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