On the Law of Spontaneous Spreading of Liquid Droplets on Solid Substrates

Several theories deal with the spreading kinetics of liquids on solid substrate, notable amongst which is de Gennes’ law, which relates the contact radius, R, to the droplet volume, V, the surface tension, σ, and the viscosity, µ, by the equation R^3m+1 = (σ/µ) t V^m and ascertains that m = 3 is “indeed expected theoretically for all cases of dry spreading”. Validity of the proposed models is examined by measurements of the spreading of a number of liquids exhibiting a wide range of surface tension and viscosity on dry soda-lime glass. The measurements used a small droplet of constant volume to minimize gravitational effects. The droplet was released near the glass surface from automatic micro syring, supported on micromanipulator. The contact radius was acquired as a function of time by an image analysis system. Analyzed in terms of de Gennes law, it was noted that the m values for silicone oils fall within the suggested variance i.e., m = 3.0±0.5. However, significant disagreements were noted in the case of other liquids, where m ranged from 5.2 to 15.0 with no correlation with the parameters included. Mechanistic considerations suggest that whereas the surface tension acts to retain the spherical shape of the droplet, interfacial tension acts to maximize the contact area whereas the viscous forces determine the kinetics. The magnitude of the difference between the interfacial and surface energies likely determines whether spreading is complete or incomplete.