The dynamics of the spreading of liquids on a solid surface. Part 2. Surfactants

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Abstract
A theoretical study is made of the effect of the presence of a surfactant on the dynamics involved in the movement of the contact line when one liquid displaces an immiscible second liquid where both are in contact with a smooth solid surface. The general procedure of solution is described for a general model for slip between solid and liquid near the contact line and also for a general macroscopic geometry. For small capillary number and for small values of the length over which slip occurs, it is shown, using singular perturbation analysis, that either 2 or 3 regions of expansion are necessary depending on the type of limiting process being considered. Solutions are obtained for both situations but for the more important three-region expansion case (where there can be large dynamic effects), a detailed discussion is given of the manner in which the observable macroscopic contact angle is shown to depend on the contact line velocity and on surfactant concentration. The conditions of validity for the theory are also discussed.

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