Steady bilayer channel and free-surface isothermal film flow over topography

Abdalla, Ayad A.; Veremieiev, Sergii; Gaskell, Philip

doi:10.1016/j.ces.2018.01.031

Cited by 4 publications

(3 citation statements)

References 64 publications

(143 reference statements)

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“…A complex variable formulation of the governing evolution equations, as in the case of Newtonian liquids and Hookean materials, is also available for any generalised material [18] with an elegant embodiment of the respective rheological model equations in the first integral approach. By applying the complex transformations (4) and (5) to the general momentum balance in place of the Navier-Stokes equations and following the procedure described in [14], one obtains the following complex equations:…”

Section: Field Equations For Viscoelastic Layer Typesmentioning

confidence: 99%

“…Different aspects of film flows involving two or more immiscible liquid layers have been investigated in [5][6][7] with a focus on both confined shear-driven flows, the topic of interest here, and free-surface flows due to their relevance in the production and deposition of functional coatings [8]. Current studies addressing the material modelling of articular cartilage, see for example [9], reveal an appreciable complexity of material behaviour, which among other things includes chemo-elastic effects and anisotropy; here standard simplified viscoelastic models are considered as a first step.…”

Section: Introduction and Model Assumptionsmentioning

confidence: 99%

See 1 more Smart Citation

Multilayer Modelling of Lubricated Contacts: A New Approach Based on a Potential Field Description

Scholle

Mellmann

Gaskell

et al. 2020

Springer Tracts in Mechanical Engineering

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A first integral approach, derived in an analogous fashion to Maxwell’s use of potential fields, is employed to investigate the flow characteristics, with a view to minimising friction, of shear-driven fluid motion between rigid surfaces in parallel alignment as a model for a lubricated joint, whether naturally occurring or engineered replacement. For a viscous bilayer arrangement comprised of immiscible liquids, it is shown how the flow and the shear stress along the separating interface is influenced by the mean thickness of the layers and the ratio of their respective viscosities. Considered in addition, is how the method can be extended for application to the more challenging problem of when one, or both, of the layers is a viscoelastic material.

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Section: Field Equations For Viscoelastic Layer Typesmentioning

confidence: 99%

Section: Introduction and Model Assumptionsmentioning

confidence: 99%

Multilayer Modelling of Lubricated Contacts: A New Approach Based on a Potential Field Description

Scholle

Mellmann

Gaskell

et al. 2020

Springer Tracts in Mechanical Engineering

View full text Add to dashboard Cite

show abstract

“…As a first step, a two–layer system for articular cartilage and synovia can serve as a simple model. Similarly, shear and film flows of two or more layers of immiscible liquids have recently become the subject of numerical studies, [6], with a focus on free surface film flows due to their relevance in coating technologies. Corresponding investigations for two‐layer Couette flows include also stability analyses [7].…”

Section: Introductionmentioning

confidence: 99%

Bilayer Couette flow over a profiled plate

Scholle,

Gaskell,

Ismail–Sutton

et al. 2023

Proc Appl Math and Mech

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The shear–driven, bilayer flow of two immiscible liquids sandwiched between a moving planar and a stationary corrugated plate, in parallel alignment and under Stokes flow conditions, is explored. The motivation, partly inspired by biomimetic considerations, is the use of surface texturing/topography to reduce friction and wear while increasing load carrying capacity in lubrication problems. The starting point of the associated mathematical formulation is a variational principle which, in addition to the classical fluid mechanical field quantities, includes potential fields enabling an elegant reformulation of the dynamic condition at the interface separating the two layers. Two methods of solution are utilised: (i) an analytic one of the field equations, boundary and interface conditions by invoking the long–wave approximation; (ii) an exact semi–analytic one, obtained after transformation to complex variables and application of a spectral method. For validation and comparison purposes a FE formulation of the classical continuity and Navier–Stokes equations is solved for. Resulting streamline patterns, interface shapes and wall shear stresses are discussed.

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Computational study of a thin film flow over a topographical feature using phase-field lattice Boltzmann method

Singh,

Tiwari

2024

Physics of Fluids

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The study employs the phase-field lattice Boltzmann method (PFLBM) to explore the dynamics of a thin film flowing over a topographical feature such as a mound or a trench. The mesoscopic nature of PFLBM makes it a suitable technique for problems involving tracking the evolution of a liquid–air interface. PFLBM simulation results are validated with experimental and analytical results confirming the viability of the numerical approach for such problems. The effect of changing the topographical height, aspect ratio, viscosity ratio, and presence of multiple mounds on the film profiles are systematically analyzed. It is observed that a steady-state solution could not be obtained for large height topographical features. The transition from a steady-state interfacial pattern to an unsteady-steady state is found to depend on the width of the topography. Geometry-based condition is employed to deal with the contact points present in the film dynamics beyond rupture. For large contact angles, the unsteady cases result in film rupture and form a continuous array of droplets of equivalent dimensions at a periodic interval. Increasing the aspect ratio reduces the width of the capillary ridge formed above the topographical feature, while the viscosity ratio reduces the maximum height of the ridge. The shapes of the capillary ridges formed over multiple mounds in the flow direction are independent if the separation between the successive mounds is beyond a critical value. This critical value strongly depends on the capillary number and is independent of the dimensions of the mound.

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Steady bilayer channel and free-surface isothermal film flow over topography

Cited by 4 publications

References 64 publications

Multilayer Modelling of Lubricated Contacts: A New Approach Based on a Potential Field Description

Multilayer Modelling of Lubricated Contacts: A New Approach Based on a Potential Field Description

Bilayer Couette flow over a profiled plate

Computational study of a thin film flow over a topographical feature using phase-field lattice Boltzmann method

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