We formulate a fluid-dynamical model describing the behaviour of solutions consisting of a fluid solvent and a dissolved solute, and whose surface tension depends on the concentration of the solute. By considering the surface excess of the dissolved solute, this model can describe the Marangoni-driven flow both of fluids in which there is a surfactant present (which decreases surface tension) and of fluids in which there is an anti-surfactant present (which increases surface tension). By investigating the linear stability of an initially quiescent fluid layer, we predict a novel instability that is possible for anti-surfactant solutions, but not for surfactant solutions, and analyse the conditions for the onset of this instability. We formulate the equations governing the flow of a thin film of surfactant or anti-surfactant solution, and demonstrate the wide range of dynamical behaviour that may be displayed by such solutions. In particular, we perform fully non-linear,unsteady numerical computations, and compare the results obtained with the linear approximation for an initially quiescent thin film subject to both small and large perturbations. We analyse the difference in behaviour between surfactants and anti-surfactants when the thin film is subject to large, local disturbances to either the surface concentration or the bulk concentration. We also obtain analytical solutions to reduced versions of the equations governing the flow of a thin film when the Marangoni effect is dominant. We focus on so-called âperfectly solubleâanti-surfactants for which the surface concentration is identically zero. For problems in which the initial condition is discontinuous, the method of characteristicsis employed to obtain simple-wave solutions. Finally, we derive a general,doubly-infinite family of similarity solutions of the reduced (i.e., Marangoni-only)equations, and investigate two of the most interesting cases in detail.
|Date of Award||18 May 2017|
- University Of Strathclyde
|Supervisor||Stephen Wilson (Supervisor) & Khellil Sefiane (Supervisor)|