A generalized linear stability analysis is applied to the case of a thin liquid film propelled to spread by a continuous supply of surfactant. The time-dependent base states for the film thickness and surfactant concentration give rise to a nonautonomous system describing disturbance propagation. As a first approximation, the nonautonomous operator is treated as time independent, thereby reduci...

The goal of this paper is to perform a general thermodynamic study of Marangoni-driven engines in which chemical energy is directly transformed into mechanical motion. Given that this topic has not been discussed before, we will explore here the most basic and fundamental aspects of the phenomena at work, which leads to a number of interesting observations typical of controversies in classical ...

this paper presents a model of a catchment area in northwest of iran. the researchers have studied ajichai basin which is located in the east part of orumiyeh lake, located at the longitude of 47 52’ e to 45 32’ e and the latitude of 37 26’ n to 38 30’ n. the researchers have chosen the data from tabriz upper air station which is the only one in the area. the research data are seven instability...

In this paper, we study a phase field model for a two-layer fluid where the temperature dependence of both the density (buoyancy forces) and the surface tension (Marangoni effects) is considered. The phase model consisting of a modified N-S equation, a Cahn-Hilliard phase field equation and an energy transport equation is derived through an energetic variational procedure. An appropriate variat...