Low-Dimensional Models for Vertically Falling Viscous Films

Panga, Mohan; Balakotaiah, Vemuri

doi:10.1103/physrevlett.90.154501

Cited by 24 publications

(21 citation statements)

References 7 publications

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“…However, it is more helpful to analyze this problem using the Weber and Kapitza number as shown in the work of Panga and Balakotaiah. 23 The Kapitza number is defined as Ka ¼ As explained by Panga and Balakotaiah, 23 for free falling vertical films, the magnitude of the Weber number determines the importance of inertial effects and the complexity of the film profile increases with increasing Ka and decreasing We values. Based on the magnitude of the Weber number, the film behavior can be divided into the viscocapillary (We !…”

Section: Governing Equations Boundary and Initial Conditionsmentioning

confidence: 99%

Flow structure underneath the large amplitude waves of a vertically falling film

Malamataris

Balakotaiah

2008

AIChE Journal

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in Wiley InterScience (www.interscience.wiley.com).Numerical solutions of the two-dimensional Navier-Stokes equations for vertically falling films show that when the wave amplitude exceeds a certain magnitude, two hyperbolic points on the wall and an elliptic point in the film are generated below the minimum of the wave and travel at the wave velocity. The shear stress along the wall between the hyperbolic points becomes negative and the instantaneous flow field in the film shows roll formation with flow reversal near the wall region. As the wave amplitude increases further, these rolls expand to the free surface dividing the film into regions of up and down flows. For high Kapitza number fluids such as water, multiple regions of up-flow and negative wall shear stress exist with their width oscillating in time. The flow field is interpreted in both stationary and moving frames of reference and in explaining transport enhancements at the wall and free surface.

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Section: Governing Equations Boundary and Initial Conditionsmentioning

confidence: 99%

Flow structure underneath the large amplitude waves of a vertically falling film

Malamataris

Balakotaiah

2008

AIChE Journal

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“…It is important to note that some studies on film flows use a Weber number defined as the inverse of We as defined in Eq. (10), for instance [3,19,[63][64][65].…”

Section: A Physical Mechanisms and Pertinent Dimensionless Groupsmentioning

confidence: 99%

Self-similarity of solitary waves on inertia-dominated falling liquid films

et al. 2016

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We propose the first consistent scaling of solitary waves on inertia-dominated falling liquid films, which accurately accounts for the driving physical mechanisms and leads to a self-similar characterization of solitary waves. Direct numerical simulations of the entire two-phase system are conducted using a state-of-the-art finite volume framework for interfacial flows in an open domain that was previously validated against experimental film-flow data with excellent agreement. We present a detailed analysis of the wave shape and the dispersion of solitary waves on 34 different water films with Reynolds numbers Re = 20 − 120 and surface tension coefficients σ = 0.0512 − 0.072 N m −1 on substrates with inclination angles β = 19 • − 90 • . Following a detailed analysis of these cases we formulate a consistent characterization of the shape and dispersion of solitary waves, based on a newly proposed scaling derived from the Nusselt flat film solution, that unveils a self-similarity as well as the driving mechanism of solitary waves on gravity-driven liquid films. Our results demonstrate that the shape of solitary waves, i.e. height and asymmetry of the wave, is predominantly influenced by the balance of inertia and surface tension. Furthermore, we find that the dispersion of solitary waves on the inertia-dominated falling liquid films considered in this study is governed by non-linear effects and only driven by inertia, with surface tension and gravity having a negligible influence.

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“…Free surface films are known to exhibit complex wave structures on the free-surface which were first demonstrated on vertical films by Kapitza [21]. The non-linearity of both the governing equations (Navier-Stokes) and the boundary conditions at the free surface make solution of the exact shape of the free-surface difficult and computationally untenable [22] with analytical solutions limited to long-wave (low amplitude) approximations (e.g., [22][23][24][25]). Solitary waves on the surface have been shown to travel up to three times faster than the mean velocity of the film (e.g., [26,27]).…”

Section: Theorymentioning

confidence: 99%