Numerical studies of the fingering phenomena for the thin film equation

Yibao Li, Hyun Geun Lee, Daeki Yoon, Woonjae Hwang, Suyeon Shin, Youngsoo Ha, Junseok Kim

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We present a new interpretation of the fingering phenomena of the thin liquid film layer through numerical investigations. The governing partial differential equation is ht + (h2-h3)x = -∇·(h3∇Δh), which arises in the context of thin liquid films driven by a thermal gradient with a counteracting gravitational force, where h = h(x, y, t) is the liquid film height. A robust and accurate finite difference method is developed for the thin liquid film equation. For the advection part (h2-h3)x, we use an implicit essentially non-oscillatory (ENO)-type scheme and get a good stability property. For the diffusion part -∇·(h3∇Δh), we use an implicit Euler's method. The resulting nonlinear discrete system is solved by an efficient nonlinear multigrid method. Numerical experiments indicate that higher the film thickness, the faster the film front evolves. The concave front has higher film thickness than the convex front. Therefore, the concave front has higher speed than the convex front and this leads to the fingering phenomena.

Original languageEnglish
Pages (from-to)1358-1372
Number of pages15
JournalInternational Journal for Numerical Methods in Fluids
Volume67
Issue number11
DOIs
Publication statusPublished - 2011 Dec 20

Fingerprint

Thin Film Equation
Liquid films
Numerical Study
Thin Liquid Films
Thin films
Film thickness
Advection
Finite difference method
Euler's method
Thermal gradients
Partial differential equations
Multigrid Method
Numerical Investigation
Discrete Systems
Difference Method
Finite Difference
High Speed
Partial differential equation
Nonlinear Systems
Numerical Experiment

Keywords

  • Fingering instability
  • Finite difference
  • Marangoni stress
  • Nonlinear diffusion equation
  • Nonlinear multigrid method
  • Thin film

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mechanics
  • Applied Mathematics
  • Mechanical Engineering
  • Mechanics of Materials

Cite this

Numerical studies of the fingering phenomena for the thin film equation. / Li, Yibao; Lee, Hyun Geun; Yoon, Daeki; Hwang, Woonjae; Shin, Suyeon; Ha, Youngsoo; Kim, Junseok.

In: International Journal for Numerical Methods in Fluids, Vol. 67, No. 11, 20.12.2011, p. 1358-1372.

Research output: Contribution to journalArticle

Li, Yibao ; Lee, Hyun Geun ; Yoon, Daeki ; Hwang, Woonjae ; Shin, Suyeon ; Ha, Youngsoo ; Kim, Junseok. / Numerical studies of the fingering phenomena for the thin film equation. In: International Journal for Numerical Methods in Fluids. 2011 ; Vol. 67, No. 11. pp. 1358-1372.
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