Reverse undercompressive shock structures in driven thin film flow.

نویسندگان

  • Jeanman Sur
  • Andrea L Bertozzi
  • Robert P Behringer
چکیده

We show experimental and computational evidence of a new structure: an undercompressive and reverse undercompressive shock for draining films driven by a surface tension gradient against gravity. The reverse undercompressive shock is unstable to transverse perturbations while the leading undercompressive shock is stable. Depending on the pinch-off film thickness, as controlled by the meniscus, either a trailing rarefaction wave or a compressive shock separates from the reverse undercompressive shock.

برای دانلود رایگان 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

Kinetics and Nucleation for Driven Thin Film Flow

in which the flux f : R → R is non-convex. Here h = h(x, t) represents the height of the free surface of the film flowing over a solid substrate. The kinetic relation describes admissible nonclassical shock waves, known as undercompressive shocks, and the nucleation condition determines when a nonclassical solution is selected. The hyperbolic theory is able to capture features observed in thin ...

متن کامل

Undercompressive Shocks in Thin Film Flows

Equations of the type ht + (h2 − h)x = − (hhxxx)x arise in the context of thin liquid films driven by the competing effects of a thermally induced surface tension gradient and gravity. In this paper, we focus on the interaction between the fourth order regularization and the nonconvex flux. Jump initial data, from a moderately thick film to a thin precurser layer, is shown to give rise to a dou...

متن کامل

Pinch-off transition in Marangoni-driven thin films.

We present a mathematical model and analysis for the pinch-off transition as observed in dip-coating experiments at the base of thin liquid films driven up a vertical plate by a thermally induced surface tension gradient with a counteracting gravitational force. Our results show that this transition gives rise to a complex new wave structure involving a nonclassical, reverse undercompressive sh...

متن کامل

Meniscus solutions and shock dynamics for Marangoni-driven flows Submitted for Presentation in ECS2005 The European Coating Symposium 2005

We consider a situation where a thin liquid film is driven from a reservoir up a substrate by a thermally induced Marangoni shear stress and investigate the meniscus that connects the film with the reservoir, as well as the wave dynamics near the contact-line. We identify two types of meniscus solutions, and show, via a phase space investigation of the third order ODE that governs the profile, ...

متن کامل

Engineering flow states with localized forcing in a thin Marangoni-driven inclined film.

Numerical simulations of lubrication models provide clues for experimentalists about the development of wave structures in thin liquid films. We analyze numerical simulations of a lubrication model for an inclined thin liquid film modified by Marangoni forces due to a thermal gradient and additional localized forcing heating the substrate. Numerical results can be explained through connections ...

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

عنوان ژورنال:
  • Physical review letters

دوره 90 12  شماره 

صفحات  -

تاریخ انتشار 2003