Traveling Waves for a Thin Film with Gravity and Insoluble Surfactant

نویسندگان

  • Joachim Escher
  • Matthieu Hillairet
  • Philippe Laurençot
  • Christoph Walker
چکیده

Lubrication equations for a surfactant-driven flow of a thin layer of fluid are considered with a singular surfactant-dependent surface tension. It is shown that there exists a bounded traveling wave solution which connects a fully surfactant-coated film to an uncoated film. The regularity of the traveling wave depends on whether or not surface diffusion of the insoluble surfactant is included.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Growing Surfactant Waves in Thin Liquid Films Driven by Gravity

The dynamics of a gravity-driven thin film flow with insoluble surfactant are described in the lubrication approximation by a coupled system of nonlinear PDEs. When the total quantity of surfactant is fixed, a traveling wave solution exists. For the case of constant flux of surfactant from an upstream reservoir, global traveling waves no longer exist as the surfactant accumulates at the leading...

متن کامل

Gravity-driven Thin Liquid Films with Insoluble Surfactant: Smooth Traveling Waves

The flow of a thin layer of fluid down an inclined plane is modified by the presence of insoluble surfactant. For any finite surfactant mass, traveling waves are constructed for a system of lubrication equations describing the evolution of the free surface fluid height and the surfactant concentration. The one-parameter family of solutions is investigated using perturbation theory with three sm...

متن کامل

The Motion of a Thin Liquid Film Driven by Surfactant and Gravity

We investigate wave solutions of a lubrication model for surfactant-driven flow of a thin liquid film down an inclined plane. We model the flow in one space dimension with a system of nonlinear PDEs of mixed hyperbolic-parabolic type in which the effects of capillarity and surface diffusion are neglected. Numerical solutions reveal distinct patterns of waves that are described analytically by c...

متن کامل

Gravity-driven film flow down an inclined wall with three-dimensional corrugations

The gravity-driven flow of a liquid film down an inclined wall with three-dimensional doubly periodic corrugations is investigated in the limit of vanishing Reynolds number. The film surface may exhibit constant or variable surface tension due to an insoluble surfactant. A perturbation analysis for small-amplitude corrugations is performed, wherein the wall geometry is expressed as a Fourier se...

متن کامل

[hal-00627948, v1] Weak solutions to a thin film model with capillary effects and insoluble surfactant

Abstract. The paper focuses on a model describing the spreading of an insoluble surfactant on a thin viscous film with capillary effects taken into account. The governing equation for the film height is degenerate parabolic of fourth order and coupled to a second order parabolic equation for the surfactant concentration. It is shown that nonnegative weak solutions exist under natural assumption...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • SIAM J. Applied Dynamical Systems

دوره 14  شماره 

صفحات  -

تاریخ انتشار 2015