Low Deborah Number Measurements

Some interfacial tension measurement techniques are essentially static, i.e. they operate at low Deborah number (De 1) capillary rise, shapes of sessile and pendant drops. Others (drop weight and detachment techniques) require extension of the interface. Then the procedure is static or dynamic depending on the rate of extension relative to the rate of adsorption equilibration, i.e. on De. 

At very low frequencies, G" is much larger than G, and hence liquid-Kke behaviour predominates. However as the testing frequency is increased, G takes over and solid-like behaviour prevails. The determinant of which kind of behaviour is most significant is the value of the test frequency co relative to the relaxation time x. This is a simple way to define a Deborah number, De—the ratio of the relaxation time to the test time—and a measure of De in this case is cox. Hence, low Deborah numbers always indicate liquid-like behaviour, whereas high Deborah numbers means solid-like response. At the midpoint, where G" goes through a maximum G = G", and this takes place at a critical crossover frequency of co = 1/x. 

The fluid s relaxation time A is the characteristic time of the fluid and, for oscillatory shearing, cu 1 can be taken as a measure of the characteristic time of the flow process, so De = A to. Thus, viscous behaviour occurs when the Deborah number is low, reflecting the fact that the fluid is able to relax. When the Deborah number is high, elastic behaviour is observed because the fluid is unable to relax sufficiently quickly. 

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