טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentMorozov Matvey
SubjectInterfacial Convection in Surfactant Solutions
DepartmentDepartment of Applied Mathematics
Supervisors Professor Alexander Oron
Professor Emeritus Alexander Nepomniashchy


Abstract

In this work we study theoretically long-wave interfacial (Marangoni) convection in binary liquids. Our main goal is to address Marangoni convection in surfactant solutions, thus, we focus our attention on the role that surfactant sorption kinetics plays in the onset of the Marangoni instability and in the formation of convective patterns.


We start off with the case of diffusion-controlled kinetics; specifically, we study nonlinear dynamics of the long-wave Marangoni convection in a layer of binary liquid by means of numerical analysis of evolution equations developed in an earlier work. Basing on the results of the numerical analysis, we develop a new model of the long-wave Marangoni convection taking surfactant sorption kinetics and interfacial transport of the adsorbed solute molecules into consideration. Then we carry out linear and weakly nonlinear stability analyses of the new model and validate our analytical predictions numerically.


Our investigation revealed numerous features of the physical system at hand, namely, the competition between the monotonic and oscillatory modes of instability, the onset of chaos, and the breakdown of the long-wave evolution equations. More importantly, we have gained a valuable insight into the physical mechanisms driving the deformational mode of Marangoni instability. In particular, we predict that adsorption as well as high surfactant concentration have a stabilizing effect on the long-wave instability.