Thin Film Flows: Theory and Modeling

O’Brien, S.; Schwartz, Leonard W.

doi:10.1081/e-escs3-120000885

Cited by 8 publications

(7 citation statements)

References 44 publications

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“…In order for the thin film approximation to remain valid with a curved centre surface, the curvature of the centre surface, , must be everywhere much less than the reciprocal of the characteristic thickness scale, i.e. (O'Brien & Schwartz 2002).…”

Section: Methodsmentioning

confidence: 99%

“…These methods are computationally expensive and require sophisticated techniques to avoid spurious oscillations around each simulated interface (Denner et al 2017). Thin films can also be modelled using the thin film approximation (lubrication theory), which involves capitalising on the thickness of the film being much smaller than the lateral extent of the film to derive an evolution equation for the film thickness that incorporates essential physics (O'Brien & Schwartz 2002;Craster & Matar 2009). Thin film models, i.e.…”

Section: Introductionmentioning

confidence: 99%

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Thin film modelling of magnetic soap films

Lalli,

Giusti

2024

J. Fluid Mech.

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Magnetic soap films under the forcing of an inhomogeneous magnetic field are governed by a wide range of interconnected physics. The study of magnetic soap films requires the development of comprehensive models to support experimental observations. In this study, the thin film approximation is applied to the Navier–Stokes equations to derive a model for the film thickness of magnetic soap films that incorporates the effects of interfacial mobility, surfactant transport and magnetite nanoparticle (NP) transport. This derived model consists of a coupled system of equations for the film thickness, interfacial velocity, interfacial surfactant concentration and magnetite NP concentration. Simulations are performed for both soap films and magnetic soap films by solving the system of equations using the Galerkin finite element method, and results are compared with experiments. Simulation results highlight that interfacial flows can dominate the rate of film thinning and that accounting for the dependence of the magnetisation on the local magnetite NP concentration can influence the predicted speed of magnetically driven flows. Furthermore, simulation results demonstrate that the model is able to predict marginal regeneration in qualitative agreement with the experiments for soap films; the model also predicts the same flow pattern as seen in the experiments for magnetic soap films. Overall, this study advances the state of soap film and magnetic soap film modelling and will contribute to acquiring control over the drainage and stability of magnetic soap films in the long term.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thin film modelling of magnetic soap films

Lalli,

Giusti

2024

J. Fluid Mech.

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“…The no-slip and no-penetration conditions are assumed to hold at the solid disk At the free surface , the kinematic condition must hold, and, for a thin film, the shear stress vanishes, yielding (O'Brien & Schwartz 2002) Integrating the continuity equation (2.1 a ) across the film thickness, and using conditions (2.2 b ) and (2.3 a ), we arrive at By integrating (2.4) over the intervals and , and noting that the dimensionless flow rate is simply W ( t ), the conservation of mass equation at any location upstream and downstream of the jump takes the following dimensionless form: Equation (2.5) provides some insight as to the behaviour of the film thickness near impingement. In fact, since h is well behaved for small r , the first integral on the left-hand side must vanish in the limit r = 0.…”

Section: The General Problem and Physical Domainmentioning

confidence: 99%

The transient spread of a circular liquid jet and hydraulic jump formation

2022

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The transient flow of a circular liquid jet impinging on a horizontal disk, and the hydraulic jump formation, are examined theoretically and numerically. The interplay between inertia and gravity is particularly emphasised. The flow is governed by the thin-film equations, which are solved along with a force balance across the jump. The unsteadiness of the flow is caused by a linearly accelerating jet from an initial to a final steady state. To validate the predicted boundary-layer flow evolution, an analytical development is conducted for small distance from impingement, and for small time. In addition, the predictions of the film profile and jump location are compared against numerical simulation for the transient flow, and are further validated against experiment for steady flow. The evolutions of the film thickness and the wall shear stress in the developing boundary-layer region are found to be similar to those reported for a fluid lying on a stretching surface. The flow responds to the jet acceleration quasi-steadily near impingement but exhibits a long-term transient behaviour near the jump. Analysis of the jump evolution is considered in the range 5 < Fr < 40 for the Froude number (based on the jet radius and velocity). For Fr < 10, the jump reaches the final state instantly when the jet acceleration ceases. At higher Froude number, the jump settles at a later time, exhibiting an overshoot in the thickness due to the dominance of inertia.

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“…As shown in O'Brien and Schwartz (2006) and Schwartz and Weidner (1995), the mean curvature of the free-surface can be approximated using the following expression:…”

Section: Methodsmentioning

confidence: 99%

Mathematical modelling of surface tension effects in liquid wall films

Baleta

Vujanović

Duić

2017

IJISD

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Behaviour of liquid wall films finds its application in many industrial areas -internal combustion engines, air blast atomisers, heat exchanger ducts, etc. Given assumptions regarding thin liquid films, NavierStokes equations are converted to wall film governing equations. The main limitations of a continuous finite volume approach of the film model are at boundary edges of the liquid phase. To overcome those issues, mathematical model for description of surface tension effects was developed and implemented into the computational fluid dynamics (CFD) code. Further area where surface tension force effects are important is the behaviour of liquid film encountering a sharp edge. The analytical force balance approach from Friedrich was incorporated into the existing numerical framework. The improved model of liquid wall film behaviour developed within this paper is the important step in improvement of the accuracy of physical models used in CFD, necessary to comply with stringent requirements of the industry.Keywords: wall film; computational fluid dynamic; surface tension; droplet spreading; capillary force; Eulerian approach; analytical force balance; film rupturing.Reference to this paper should be made as follows: Baleta, J., Vujanović, M. and Duić, N. (2017) 'Mathematical modelling of surface tension effects in liquid wall films ', Int. J. Innovation and Sustainable Development, Vol. 11, No. 1, Biographical notes: Jakov Baleta is a Researcher at the Department of Energy, Power Engineering and Environment, Faculty of Mechanical Engineering and Naval Architecture. He has completed his graduate studies in Thermal Engineering with highest honour (summa cum laude) in 2013, and for outstanding achievement during the study, he was awarded with the medal of the Faculty. His areas of research interest are rational use of energy in buildings and industry, with a focus on heat pumps, energy analysis of HVAC systems and the development of mathematical models of computational fluid dynamics problems in the treatment of exhaust gases of internal combustion engines. This paper is a revised and expanded version of a paper entitled 'Modelling and implementation of surface tension effects into CFD wall film module' presented at Milan Vujanović is a Researcher and Team Leader of CFD Combustion

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Thin Film Flows: Theory and Modeling

Cited by 8 publications

References 44 publications

Thin film modelling of magnetic soap films

Thin film modelling of magnetic soap films

The transient spread of a circular liquid jet and hydraulic jump formation

Mathematical modelling of surface tension effects in liquid wall films

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